National Aeronautics and Space Administration National Aeronautics and Space Administration

Office of the Chief Engineer

NASA/SP-20230002470

Rev 1
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

ii

February 2023

NASA/SP-20230002470 Rev 1

This is the first revision by the Office of the Chief Engineer of the 2020 Handbook updated to 

reflect the release of NPR 8079.1, NASA Spacecraft Conjunction Analysis and Collision 

Avoidance for Space Environment Protection.

The cover photo is an image from the Hubble Space Telescope showing 

galaxies NGC 4038 and NGC 4039, also known as the Antennae Galaxies, 

locked in a deadly embrace. Once normal spiral galaxies, the pair have 

spent the past few hundred million years sparring with one another. 

Image can be found at:

https://images.nasa.gov/details-GSFC_20171208_Archive_e001327
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Table of Contents

Preface................................................................................................................ 1

1.0 Introduction................................................................................................... 3

2.0 Roles and Responsibilities............................................................................ 5

3.0 Conjunction Assessment: Past, Present, and Future.................................... 6

Origins..................... ....................................................................... 6

USSPACECOM Conjunction Assessment Process ............................ 7

NASA Partnership with USSPACECOM........................................... 10

Conjunction Assessment in Cislunar Space ..................................... 12

4.0 Spacecraft and Constellation Design.......................................................... 15

Ascent to/Disposal from the Constellation’s Operational Orbit.......... 15

General Orbit Selection: Debris Object Density ................................ 16

Vehicle- and Constellation-Specific Orbit Selection: Spacecraft 

Colocation......................................................................................... 17

Launch-Related Conjunction Assessment ........................................ 18

Spacecraft Trackability ..................................................................... 19

Spacecraft Reliability ........................................................................ 20

Development of Capabilities for Ephemeris Generation and 

Conjunction Risk Assessment and Mitigation ................................... 20

5.0 Pre-Launch Preparation and Early Launch Activities.................................. 23

CONOPS Discussions and Arrangements with USSPACECOM 

Pertaining to Launch Phase.............................................................. 23

CONOPS Discussions and Arrangements with USSPACECOM and 

NASA Pertaining to On-Orbit Mission Phase.................................... 25

CONOPS Discussions and Arrangements with USSPACECOM and 

NASA Pertaining to Conjunction Assessment................................... 26

In situ Launch Products and Processes............................................ 28

6.0 On-Orbit Collision Avoidance...................................................................... 30

Spacecraft Information and Orbital Data Needed for Conjunction 

Assessments .................................................................................... 30
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Conjunction Assessment Screenings ............................................... 33

Conjunction Risk Assessment .......................................................... 35

Conjunction Risk Mitigation............................................................... 38

Automated Trajectory Guidance and Maneuvering........................... 41

Other Considerations........................................................................ 43

7.0 Contact Information .................................................................................... 47

Appendix A. Acronyms ...................................................................................... 49

Appendix B. Glossary........................................................................................ 52

Appendix C. Best Practices List ........................................................................ 55

Appendix D. Best Practices for NASA Missions ................................................ 65

Appendix E. Use of Analytic Theory Orbital Data in Conjunction Assessment.. 81

Appendix F. Expected Conjunction Event Rates ............................................... 85

Appendix G. Orbital Debris Density................................................................... 88

Appendix H. Long-Term Collision Risk and Satellite Colocation Analysis ......... 93

Appendix I. Satellite Covariance Realism Assessment Procedures ................ 103

Appendix J. CARA Conjunction Risk Assessment Tools Validation ................ 114

Appendix K. R-15 Message............................................................................. 115

Appendix L. Commercial Data in NASA Conjunction Assessment .................. 118

Appendix M. Use of the Probability of Collision (Pc) as the Risk Assessment 

Metric for Conjunction Assessment .......................................................... 123

Appendix N. Pc Calculation Approaches......................................................... 130

Appendix O. Collision Consequence ............................................................... 163

Appendix P. Event Actionability....................................................................... 176

Appendix Q. Notional Display Flow for Conjunction Event Processing............ 190

Appendix R. List of Works Cited...................................................................... 204
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List of Figures

Figure 3-1 Locations and Types of SSN Sensors and Nodes ............................. 8

Figure E-1 Miss-Distance Distributions for Critical (Pc > 1E-04) and Non-critical 

(Pc < 1E-04) Events .......................................................................................... 82

Figure E-2 eGP and Regular SGP4 Errors: LEO > 500 km (log scale) ............. 83

Figure E-3 Expansion of Figure E-1 to Include CDFs for Pc Thresholds of 1E-03 

and 1E-02.......................................................................................................... 84

Figure F-1 Conjunction Event Frequencies as a Function of Orbit Regime and 

Event Severity ................................................................................................... 87

Figure G-1 Debris Flux as a Function of Orbit Inclination, Orbit Altitude, and 

Object Size........................................................................................................ 90

Figure H-1 Kessler Collision Rates between NewSat and HST ........................ 96

Figure H-2 Total NewSat Collision Rates Among All Cataloged Satellites ........ 97

Figure H-3 NewSat Collision Rates Excluding the Starlink Constellation.......... 97

Figure H-4 Predicted Rates for NewSat and HST Satellite Conjunctions........ 100

Figure H-5 Predicted Rates for NewSat and FGST Satellite Conjunctions ..... 101

Figure H-6 Predicted Rates for NewSat and Swift Satellite Conjunctions ....... 102

Figure N-1 Relative Positions and Uncertainties of Two Objects .................... 131

Figure N-2 Combining the Sizes of the Primary and Secondary Objects ........ 132

Figure N-3 Geometry at TCA .......................................................................... 132

Figure N-4 Two Equivalent Representations of the Conjunction Plane........... 133

Figure N-5 Pc Rate and Cumulative Pc for a Non-Rectilinear Conjunction..... 138

Figure N-6 Pc Rate and Cumulative Pc for a Low Velocity Conjunction.......... 139

Figure N-7 Comparison of Monte Carlo Collision Probabilities with the TwoDimensional Pc Method (left), the Three-Dimensional Nc Method (center), and 

the Two-Dimensional Nc Method (right) for a Large Set of CARA Conjunctions

........................................................................................................................ 141

Figure N-8 Cumulative Three-Dimensional Nc Risk Over Four Repeating 

Conjunctions ................................................................................................... 143

Figure N-9 Behavior of Relative Density Error by Perigee Height and Solar 

Activity............................................................................................................. 145

Figure N-10 Two-phase Application of Consider Parameters ......................... 146
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Figure N-11 Profiles of 250 Conjunctions with Primary and Secondary Satellites 

of Non-negligible Drag..................................................................................... 150

Figure N-12 Three-Dimensional Nc Temporal Risk Plot with Monte Carlo from 

Epoch Result Overlay (in Pink) ....................................................................... 154

Figure N-13 Mismatch between Elongated In-track Covariances and Forced 

Cartesian Ellipsoidal Representation............................................................... 155

Figure N-14 Comparative Results of 373 High-Pc Conjunctions..................... 157

Figure N-15 Comparative Results of 63,603 Conjunction Events ................... 158

Figure O-1 Range of Debris Production Possibilities ...................................... 165

Figure O-2 CDF of the Ratio of Calibrated HBR Values to Known HBR Values 

for 586 Satellites ............................................................................................. 168

Figure O-3 CDF of the Ratio of Calibrated RCS+BC Mass Estimates to Known 

Masses for 554 Satellites ................................................................................ 171

Figure O-4 CDF of the Ratio of Calibrated RCS+SRPC Mass Estimates to 

Known Masses for 303 Satellites .................................................................... 173

Figure O-5 Collision and Fragmentation Probabilities for Known-on-Unknown 

Conjunctions ................................................................................................... 175

Figure P-1 SWTS Plot for Invariant Situation .................................................. 185

Figure P-2 SWTS Plot for “Ridge” Situation .................................................... 186

Figure P-3 SWTS Plot for Variation Situation.................................................. 187

Figure P-4 LUPI Upper Bound for Certain EDR Values .................................. 189

Figure Q-1 Ground Trace Plot......................................................................... 193

Figure Q-2 Conjunction Plane Plot.................................................................. 194

Figure Q-3 Probability of Collision Time-History Plot....................................... 195

Figure Q-4 Total Miss Distance Plot................................................................ 196

Figure Q-5 Componentized Miss Distance Plot............................................... 197

Figure Q-6 State Comparison Consistency Plot.............................................. 199

Figure Q-7 Solar Storm Prediction .................................................................. 200

Figure Q-8 Space Weather Trade-Space Plot................................................. 201

Figure Q-9 Maneuver Trade-Space Plot ......................................................... 202
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List of Tables

Table 7-1 NASA Contact and Reference Information........................................ 47

Table 7-2 Contact and Reference Information for Non-NASA Personnel.......... 47

Table C-1 Best Practices Summary .................................................................. 55

Table D-1 Best Practices for NASA Projects..................................................... 65

Table P-1 Geopotential, Atmospheric Drag, and Solar Radiation Pressure .... 188

Table P-2 Ballistic Coefficient and Solar Radiation Pressure Coefficient 

Reasonability................................................................................................... 188

Table P-3 LUPI Minimum and Maximum Values............................................. 189

Table Q-1 Primary Satellite Vital Statistics ...................................................... 191

Table Q-2 Secondary Satellite Vital Statistics ................................................. 192
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Preface 1

Preface

Since Explorer 1 was launched on January 31, 1958, the United States (U.S.) has reaped the 

benefits of space exploration. New markets and new technologies have spurred the economy and 

changed lives in many ways across the national security, civil, and commercial sectors. Space 

technologies and space-based capabilities now provide global communications, navigation and 

timing, weather forecasting, and more. 

Space exploration also presents challenges that impact not only the U.S. but also its allies and 

other partners. A significant increase in the volume and diversity of activity in space means that 

it is becoming increasingly congested. Emerging commercial ventures such as satellite servicing, 

in-space manufacturing, and tourism as well as new technologies enabling small satellites and 

large constellations of satellites present serious challenges for safely and responsibly using space 

in a stable, sustainable manner.

To meet these challenges, the U.S. seeks to improve global awareness of activity in space by 

publicly sharing flight safety-related information and by coordinating its own on-orbit activity in 

a safer, more responsible manner. It seeks to bolster stability and reduce current and future 

operational on-orbit risks so that space is sustained for future generations. To this end, new and 

better Space Situational Awareness (SSA) capabilities are needed to keep pace with the 

increased congestion, and the U.S. seeks to create a dynamic environment that encourages and 

rewards commercial providers who improve these capabilities.

The overall purpose of the National Aeronautics and Space Administration (NASA) Spacecraft 

Conjunction Assessment and Collision Avoidance Best Practices Handbook is to equip 

owners/operators (O/Os) with the best practices they need to conduct their operations safely. The 

Handbook 

• Reflects the goal of Space Policy Directive-3, the National Space Traffic Management 

Policy (SPD-3), to develop safety standards and best practices that consider 

“maneuverability, tracking, reliability, and disposal.”

• Reflects how NASA currently operates in space, which evolves over time. 

• Is organized around a spacecraft’s life cycle. Consideration is given to important topics 

such as spacecraft and constellation design; spacecraft “trackability;” pre-launch 

preparation and early launch activities; on-orbit collision avoidance; and automated 

trajectory guidance and maneuvering.

• Encourages the use of commercially available SSA data and information, and for large 

constellations, it encourages mitigating light pollution to ground-based astronomy. 

• Focuses on current NASA best practices. It will be updated as new approaches for 

conjunction assessment and on-orbit operations are developed. 

• Provides guidance for the requirements in NASA Procedural Requirements (NPR)

8079.1, NASA Spacecraft Conjunction Analysis and Collision Avoidance for Space 

Environment Protection.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Preface 2

A parallel document may be developed to highlight additional practices as the U.S. Department 

of Commerce develops the Open Architecture Data Repository (OADR) mandated by 

SPD-3. Other commercial services may be offered to supplement or replace the government 

services currently offered.

The approaches outlined in this document are offered to spacecraft Owners/Operators (O/Os) as 

an example of responsible practices to consider for lowering collision risks and operating safely 

in space in a stable and sustainable manner. Entities offering, or intending to offer, SSA or 

conjunction assessment services should consider the information in this handbook from the 

perspective of augmenting or improving upon existing capabilities as the entire space industry 

benefits from advancing these capabilities. In the near term, raw observation data can be used to 

improve close approach predictions. Longer-term improvements might be found in enhancing 

notifications and data sharing, developing new models, and enabling increased automation.

NASA continuously examines and actively updates its best practices for conjunction assessment 

as the industry undergoes rapid evolution. Large constellations of satellites, for example, 

comprise a new and evolving paradigm for which NASA is developing in-house expertise. 

NASA seeks input from the community to improve the content presented in this document. 

Comments or suggestions may be submitted to ca-handbook-feedback@nasa.onmicrosoft.com.

For space operations regulated by other U.S. agencies such as the Department of Commerce, the 

U.S. Federal Aviation Administration (FAA), and the U.S. Federal Communications 

Commission (FCC), NASA defers to those agencies. As part of interagency consultations and to 

contribute to safe and sustainable space operations, NASA partners such as the FAA and FCC 

request NASA review of license, payload, and/or policy applications made by commercial space 

operators to U.S. Government regulatory agencies. In addition to the information required by 

those regulatory agencies, NASA has prepared examples of information for various types of 

missions that is valuable in expediting NASA’s review. Current examples can be found at 

https://www.nasa.gov/recommendations-commercial-space-operators. Commercial space 

operators are welcome to contact NASA with questions about these examples.

This document was developed in close collaboration with the U.S. Space Command 

(USSPACECOM), one of NASA’s closest interagency partners in ensuring safe operations in 

space, as part of the NASA/U.S. Department of Defense (DOD) Interagency Working Group for 

Large Constellation Conjunction Assessment Best Practices. Special thanks are due to working 

group members Mr. Jeff Braxton of USSPACECOM’s Strategy, Plans, and Policy Directorate, 

and Ms. Diana McKissock and Ms. Cynthia Wilson of the U.S. Space Force’s 18th Space 

Defense Squadron (18 SDS).
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1.0 Introduction 3

1.0 Introduction

This document is intended to provide NASA spacecraft program and project managers, 

generically referred to in this handbook as O/Os, with more details on implementing

requirements in NPR 8079.1 and to provide non-NASA O/Os with a reference document 

describing existing NASA conjunction assessment and collision avoidance practices. 

Within NASA, space flight missions are typically implemented through a program/project office 

structure. For example, a human exploration program might involve multiple missions (i.e., 

discrete launches) to a common goal. In this document, the term “mission” means the end-to-end 

activity that results in the creation, launch, operation, and eventual disposal of a spacecraft.

This document provides detailed information on spacecraft conjunction assessment and collision 

avoidance topics. Best practices for each topic are described and justified throughout this 

document by mission phase. A summary list of these best practices without the supporting 

explanatory text is provided in appendices C and D. Appendix C is a complete listing of all the 

best practices so that non-NASA mission managers can review them to determine which are 

useful for their mission. The mission manager would then need to identify the person or group 

responsible for performing the best practice and arrange for that effort. For NASA missions, 

Appendix D lists the best practices and the party responsible for performing them.

Different organizations use the term “conjunction assessment” in different ways, but NASA 

defines a 3-step process:

1. Conjunction assessment (otherwise referred to as “screening”) – The process of 

comparing trajectory data from the “primary object” (the “protected asset” in NPR 

8079.1) against the trajectories of the objects in the applicable database1 and predicts

when a close approach will occur within a chosen protective volume placed about the 

asset.

2. Conjunction risk assessment – The process of determining the likelihood of two space 

objects colliding and the expected consequence if they collide in terms of lost spacecraft 

and expected debris production.

3. Conjunction mitigation – An action taken to remediate conjunction risk including a 

propulsive maneuver, an attitude adjustment (e.g., for differential drag or to minimize 

frontal area), or provision of ephemeris data to the secondary O/O to enable that 

spacecraft to plan and execute an avoidance maneuver.

1 For Earth-orbiting objects, screening is performed against the space object catalog maintained by the United States 

Space Command (USSPACECOM) to predict when a close approach will occur within a volume of space called a 

“safety volume” placed about the asset. This catalog includes information about international and commercial 

operational spacecraft as well as all trackable debris. For non-Earth-orbiting objects, the ephemeris of the primary 

(protected) asset is only screened against other provided ephemerides.
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1.0 Introduction 4

This document compiles best practices based on the U.S. Government process that exists today

where conjunction assessment screening is performed by USSPACECOM/18 SDS and 19 SDS. 

The risk assessment process is necessary because the orbit solutions of the catalog objects have 

varying accuracies depending on factors described in this document. Currently, O/Os need to 

perform this function for themselves (or hire a third party) because 18 SDS and 19 SDS are not 

tasked to perform this necessary risk assessment function. In the future, the Department of 

Commerce may offer risk assessment services as it takes on a space traffic management role, and 

broader commercial services will be available.

Some entities use Two-Line Elements (TLEs) to perform conjunction assessment. This practice 

is not recommended because the TLE accuracy is not sufficient to perform the necessary 

conjunction assessment calculations. (See Appendix E for more information on TLEs.)

The terms “satellite” and “spacecraft” are interchangeable in this document. The word “object” 

means any discretely identifiable debris or other cataloged item in addition to satellites and 

spacecraft.

The term “large constellation” is defined loosely in this document. The U.S. Government Orbital 

Debris Mitigation Standard Practices (ODMSP) defines “large constellation” as containing 100 

or more spacecraft. However, because constellations having as few as 10-20 spacecraft can 

experience greater conjunction risk, the O/O of any constellation of spacecraft is asked to 

consider the intent of the best practices in this document and implement all of them to the degree 

possible.
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2.0 Roles and Responsibilities 5

2.0 Roles and Responsibilities

This section provides a brief introduction to the organizations referenced in this document.

The U.S. Space Command (USSPACECOM), one of the combatant commands within DOD, is 

responsible for U.S. military space operations. For the purposes of this document, it is the entity 

responsible for establishing SSA sharing agreements with domestic and international entities, 

both governmental and private. It establishes guidance and direction governing execution of the 

congressionally mandated SSA sharing program on behalf of the U.S. Secretary of Defense. It

also oversees execution of the SSA sharing program as well as day-to-day operations of the 

USSPACECOM SSA and space flight safety support.

The U.S. Space Force's 18th and 19th Space Defense Squadron (18 SDS and 19 SDS)

maintain the U.S. catalog of space objects and provide 24/7 space flight safety support on behalf 

of USSPACECOM. 18 SDS conducts advanced analysis, sensor optimization, human space 

flight support, reentry/break-up assessment, and launch analysis; 19 SDS conducts conjunction 

assessment and launch conjunction assessment.

The NASA Human Space Flight Operations Directorate (FOD) of the Johnson Space Center

(JSC), through the console positions Trajectory Operations Officer (TOPO) and Flight Dynamics 

Officer (FDO), provides conjunction risk analysis support to the space flight missions that fall 

under NASA human space flight. The International Space Station (ISS) and vehicles visiting the

ISS receive conjunction risk assessment support from the TOPO,

2 while Artemis space flight 

missions receive conjunction risk assessment support from their assigned FDO. The TOPO 

group is the sole liaison to USSPACECOM and the U.S. Space Force for matters related to 

trajectory maintenance and the orbital safety of human space flight assets.

The NASA Conjunction Assessment Risk Analysis (CARA) Program located at the Goddard 

Space Flight Center (GSFC) provides conjunction analysis and risk assessment services for all 

NASA spacecraft not affiliated with human space flight. CARA is responsible for protecting the 

orbital environment from collision between NASA non-human space flight missions and other 

tracked and cataloged on-orbit objects. CARA is responsible for routinely collecting predicted 

orbital information from NASA spacecraft operators, passing it to NASA Orbital Safety Analysts 

(OSAs) for screening against the space object catalog, analyzing the screening results to 

determine the risk posed by predicted close approaches, and working with NASA spacecraft 

operators to determine an appropriate mitigation strategy for the risks posed by close approaches. 

CARA is the sole entity with authority to submit Orbital Data Requests (ODRs) to DOD on 

behalf of NASA non-human space flight entities in accordance with NPR( 8715.6, NASA 

Procedural Requirements for Limiting Orbital Debris and Evaluating the Meteoroid and Orbital 

Debris Environments. CARA is the designated point of contact between NASA and

USSPACECOM and the U.S. Space Force for matters related to trajectory maintenance and 

orbital safety of non-human space flight assets.

2 However, for missions deployed from ISS or visiting vehicles, JSC FOD certifies that the mission has a 

conjunction assessment process as outlined in jettison policies but does not provide direct conjunction risk 

assessment support. 
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3.0 Conjunction Assessment: Past, Present, and Future 6

3.0 Conjunction Assessment: Past, Present, and Future

This section provides a brief history of the conjunction assessment function, including an 

overview of who the actors are and why the activities are arranged as they are. It explains why 

the conjunction assessment and related safety-of-flight services currently available exist in their 

present forms and how they are evolving to accommodate new requirements.

Origins

The present conjunction assessment process, which predicts close approaches between space 

objects, began in support of the NASA Space Shuttle Program return-to-flight effort after the 

Challenger accident in 1986. Drawing on the DOD’s ability to track space objects for missile 

defense and SSA, the two U.S. Government entities partnered to expand the capability to offer a 

methodology that would protect humans in space. 

What most people consider the “space catalog” is a database of TLE sets that permits a mediumfidelity propagation and orbit prediction of all tracked objects larger than approximately 10 cm in 

Low Earth Orbit (LEO) using Simplified General Perturbation Theory #4 (SGP4).

3 The satellite 

catalog was originally designed not for conjunction assessment but for generalized space safety,

predicting the location of objects with sufficient accuracy for sensors in the network to reacquire 

those objects, thereby maintaining custody for purposes such as ensuring that intercontinental 

ballistic missile threats could be differentiated from satellites in orbit. The catalog was then, and 

is today, maintained using the radars, telescopes, and other sensors comprising the Space 

Surveillance Network (SSN). In recent years, however, USSPACECOM has been working to 

augment the existing network by incorporating observations from international and commercial 

entities. 

For ISS conjunction assessment to better protect humans in space, NASA collaborated with the 

U.S. Air Force to develop an improvement to the TLE catalog that would be accurate enough to 

compute a Probability of Collision (Pc) between two objects. To compute Pc, orbit determination 

covariance data were needed. Since the general perturbations theory used to maintain the TLE 

catalog (SGP4) did not produce a usable covariance, the current Special Perturbations (SP) Space

Object Catalog was developed. 18 SDS, the U.S. Space Force unit that currently maintains the 

catalog at Vandenberg Space Force Base (VSFB) on behalf of USSPACECOM, 18 SDS at 

VSFB, California and 19 SDS at Dahlgren Naval Base, Virginia have greatly expanded the 

process of screening protected assets since that time (especially since the Iridium 33/COSMOS 

2251 collision in 2009) to include all operational assets currently on orbit. 

However, since the process was developed 50 years ago and was grown piecemeal to meet 

existing needs, it contains certain oddities of evolution that may not be anticipated by O/Os who 

are accustomed to using current technology and methods. Understanding how the 18 and 19 SDS

process works is key to using it properly to protect on-orbit assets and the space environment.

3 Hoots and Roehrich 1980.
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3.0 Conjunction Assessment: Past, Present, and Future 7

USSPACECOM Conjunction Assessment Process

The full conjunction assessment screening process used by USSPACECOM with all 

accompanying details is documented in the Spaceflight Safety Handbook for Satellite Operators 

(the Spaceflight Safety Handbook), which can be obtained along with other helpful information 

from the USSPACECOM website space-track.org. This website is the principal way

USSPACECOM communicates and exchanges conjunction assessment-related information with 

O/Os. 

• All non-NASA spacecraft O/Os should familiarize themselves with the Spaceflight 

Safety Handbook as well as other website contents and offerings. 

• NASA spacecraft O/Os do not need to be familiar with the Spaceflight Safety Handbook

since CARA or JSC FOD will perform all actions on their behalf. 

(See Section 7 in this document for USSPACECOM contact information including Uniform 

Resource Locators (URLs) to obtain products. See Sections 5.1 through 5.3 for details of some 

topics from the Spaceflight Safety Handbook to provide end-to-end understanding of the

conjunction assessment process.)

Commercial conjunction assessment providers, often using space catalogs assembled from 

private sector space tracking assets, are now an available resource for O/Os who wish to obtain 

conjunction assessment services. NASA encourages the use of validated commercial conjunction 

assessment services when they can augment the existing USSPACECOM capabilities. NASA 

recommends that all O/Os avail themselves of the USSPACECOM conjunction assessment

service at a minimum as an adjunct to a commercially procured service. (See Section 6.1 for 

additional information about orbital data for conjunction assessment; Appendix J, which outlines 

conjunction risk assessment tools validation procedures; and Appendix L, which addresses the 

question of the use of commercial SSA data in conjunction risk assessment.)

To address this topic, the following specific practices are recommended:

A. Obtain a space-track.org account.

B. Become familiar with the Spaceflight Safety Handbook contents.

C. Use USSPACECOM conjunction assessment service as a minimum for screenings, 

even if additional commercial data or services are used.

SSN Tracking Functionality Description

The Space Surveillance Network (SSN), a global sensor network made up of optical telescopes 

and radars, is used to collect the tracking observations that are processed to maintain the High 

Accuracy Catalog (HAC) of on-orbit space objects. Figure 3-1 shows the current locations of the 

member sensors.
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3.0 Conjunction Assessment: Past, Present, and Future 8

SDA = Space Domain Awareness

Figure 3-1 Locations and Types of SSN Sensors and Nodes4

Because most sensors have other purposes in addition to collecting data for SSA, tracking data 

cannot be simply requested and obtained on demand. Objects are placed in tasking categories, 

and a list of objects to attempt to track by category is sent to each sensor, which then sorts the list 

to determine which requests are feasible given the sensor’s calculation of the probability of 

detection of the requested satellite and competing activities.

Priority is given to military operational needs and special needs within conjunction assessment

such as human space flight. If a USSPACECOM conjunction assessment operator determines 

that there is insufficient tracking data available to create a good orbit determination solution for 

an object, the operator may attempt to obtain additional data by increasing the priority of the 

object or by tasking additional sensors to track it. Sensors may not be able to track an object due 

to geometric and power constraints, weather, equipment outages, and other exigencies. 

4 Figure courtesy of USSPACECOM.

Our Sensor Network

Optical elescopes echanical Radars

SDA Command and Control hased Arra Radars

UNCLASSIFIED
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3.0 Conjunction Assessment: Past, Present, and Future 9

The USSPACECOM process is different from a commercial process in which a vendor is 

compensated directly for the tracking of an object with the flexibility of being able to obtain 

additional data if more funds are available to support the request. Because of the time required to 

collect additional data on an object of concern using the USSPACECOM process, it is 

recommended that O/Os provide a significant length of ephemeris prediction (including planned 

maneuvers) to USSPACECOM for screening. This screening duration allows time for 

USSPACECOM conjunction assessment operators to increase tasking for identified secondary 

objects with insufficient orbit determination solutions, and thus to enable the best Pc to be 

computed for use in conjunction risk assessment decisions. (See Section 6.1 for a more detailed 

discussion of these issues.)

To address this topic, the following specific practice is recommended:

A. Provide seven (7) days of predicted ephemeris (including maneuvers) to 

USSPACECOM for screening for LEO spacecraft, and provide 14 days for other 

Earth orbits; e.g., High Earth Orbit (HEO)/Geosynchronous Orbit (GEO).

USSPACECOM Conjunction Assessment Screening Timeline and Process

Personnel at the USSPACECOM facility at Dahlgren Naval Base currently perform screenings 

of protected assets against the entire HAC once per day at a minimum and up to three times per 

day every day. Screenings are performed using both the ephemeris data that O/Os share (which 

include planned maneuvers for the asset) as well as the SSN-derived orbit determination solution 

for the asset (which does not consider predicted maneuvers).

Results from the screenings, in the form of Conjunction Data Messages (CDMs), are posted to 

space-track.org for customers with accounts. Entities without accounts who have provided an 

email address to USSPACECOM may receive basic prediction information by email if an 

emergency is detected.

Special/off-cycle screenings can be requested per the guidance in the Spaceflight Safety 

Handbook. It is important for safety of flight for all spacecraft operators to ensure that there are 

no large latencies or gaps in the process as uncertainties in the propagated orbit continue to grow 

over time. For instance, submitting an ephemeris for screening today at noon that has an epoch of 

today at 0 hours means that the data is already 12 hours old. If it then takes 8 hours to screen that 

data and another 2 hours to analyze the results, the data will be very old indeed. Ensure that the 

data screened is for a future time and is analyzed and acted upon before it becomes stale. (See 

Section 6.2 for more information.)
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3.0 Conjunction Assessment: Past, Present, and Future 10

To address this topic, the following specific practices are recommended:

A. Provide at least one ephemeris per day to be screened and three ephemerides per 

day in the lower-drag LEO regime (perigee height less than 500 km).

B. Determine whether the O/O’s process for obtaining screening results and 

performing conjunction risk assessment aligns with the timeline of the 

USSPACECOM process. If the timelines do not align in such a way as to enable 

timely and efficient screening support, pursue a rearrangement of the O/O’s 

process to minimize data latency and optimize screening efficiency.

Data Sharing with Other O/Os

To facilitate communication between operators to mitigate a close approach, USSPACECOM 

maintains a list of contacts for each asset. Maintaining this list of contacts is critical so that 

someone can always be reached. Data sharing is further facilitated though the use of standard 

formats and coordinate frames. (See Section 6.4 for a more thorough treatment.)

To address this topic, the following specific practices are recommended:

A. Populate and maintain the point of contact section on space-track.org with your 

operations contact data. Be sure that the operations contact can be reached 24/7 

due to time zone differences between operators and the immediate nature of 

certain conjunction assessment emergencies.

B. Use standard ephemeris, CDM, and maneuver notification formats defined by the 

Consultative Committee for Space Data Systems (CCSDS).

SSA Sharing Agreements

USSPACECOM/J535, SSA Data Sharing Branch, negotiates SSA sharing agreements, which 

establish the parameters within which data will be exchanged by the signing parties to facilitate 

ongoing cooperation and advance space flight safety. These agreements are useful because they 

substantially expand the types of data products that can be received over the default products 

provided to entities without agreements. 

Any member of the space community, including satellite operators, launching agencies, 

commercial service providers, and research/academic institutions, that wishes more and more 

frequent SSA products than are provided through a generic space-track.org account should 

contact USSPACECOM. (See Section 7 of this document for contact information.)

U.S. Government organizations and their contractors have implied agreements and do not need 

to pursue a separate formal arrangement with USSPACECOM.

NASA Partnership with USSPACECOM

Since the development of the HAC and its use in routine conjunction assessment screenings, 

NASA has partnered with USSPACECOM and its predecessor organizations. That partnership 

currently includes special, dedicated conjunction assessment screening support. The human 
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space flight program uses U.S. Air Force civilians for conjunction assessment screening support, 

while NASA’s non-human space flight missions are supported by NASA contractors called 

Orbital Safety Analysts (OSAs) who work on the operations floor in the VSFB operations center. 

While both groups do essentially the same work with the same input data, NASA OSAs focus 

specifically on NASA needs and can write scripts that are used to tailor the output data for use by 

CARA.

Conjunction assessment is a 3-step process:

1. The first step is conjunction assessment “screening,” which involves computing the 

predicted close approaches between the protected asset and the catalog of space objects. 

This is the step performed at the USSPACECOM facility for mission customers, and 

screening results are provided that describe predicted close approaches. Both the 

USSPACECOM conjunction assessment cell and NASA OSAs perform this function. 

2. The second step is conjunction “risk assessment,” in which the screening results are 

analyzed to determine the level of risk posed by each predicted close approach and to 

determine whether the predicted close approaches warrant additional investigation and, 

ultimately, mitigation. This step is critical because not all predicted close approaches 

require mitigation, and often close approaches require analysis to determine what action 

is warranted. This step is not performed by USSPACECOM as it is a responsibility 

allocated to O/Os or organizations that perform this activity on the O/O’s behalf. NASA 

JSC FOD performs this function for human space flight program assets, and NASA 

CARA performs this function for all other NASA spacecraft. 

3. The third step, if required, is conjunction “mitigation,” in which the O/O plans, and 

perhaps executes, a collision avoidance maneuver or other mitigation solution to reduce 

the collision risk to an acceptable level. This activity is allocated to the individual O/Os 

although NASA CARA does provide some basic support tools to aid in the initial choice 

of mitigation actions for its mission customers.

Because risk assessment requires different products and yields different analyses than screening, 

it is important to consider the tools and processes required to assess risk properly and adequately. 

For large constellations, the cadence of conjunctions and the consequence of a collision for the 

proper operation of the constellation are both heightened. (See Section 6 for more detail on risk 

assessment processes.)
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To address this topic, the following specific practices are recommended:

A. Develop a robust safety-of-flight process that includes both conjunction 

assessment screening and risk assessment to inform close approach mitigation 

decisions.

B. Large constellation operators should work with USSPACECOM pre-launch to 

determine if variations from the standard approach are necessary and, if so, to 

define a tailored screening process.

C. Large constellation operators should consider working with NASA to define a 

risk assessment process. NASA is an experienced representative operator.

Including NASA in discussions regarding establishing a conjunction assessment

process will ensure that the process will work with most operators for risk 

assessment purposes.

Conjunction Assessment in Cislunar Space

Significant investments by the U.S., China, other nations, and commercial companies in missions 

to cislunar space between Earth and the Moon have highlighted the need for proper measures to 

ensure the safety of the space environment in that regime. While cislunar space will remain “big” 

for some time yet, popular locations and transit trajectories are likely to experience rapid growth, 

requiring effective conjunction risk analysis to maintain safety. Implementing appropriate 

measures for spacecraft will ensure readiness to perform effective conjunction risk assessment as 

cislunar space traffic increases.

In November 2022, the White House National Science & Technology Policy Council released 

the National Cislunar Science & Technology Strategy, an interagency strategy to guide 

developments across a spectrum of emerging areas in the cislunar “ecosystem” (National 

Cislunar Science & Technology Strategy, 2022). Several objectives espoused in this document 

pertain to Space Situational Awareness (SSA) and space safety, including the following:

• Develop technical foundations of best practices for safe cislunar space flight operations.

• Develop an integrated cislunar object catalog.

• Develop procedures for publicly sharing cislunar SSA data as well as navigation and 

space flight safety support in cislunar space.

• Ensure that capabilities for U.S. Government cislunar operations are scalable and 

interoperable with systems operated by private and international actors.

(For additional details and context, refer to the Strategy document.)

Key Goals

For the purpose of outlining best practices for conjunction risk assessment, key goals center on 

sharing data and ensuring interoperability. These goals can be achieved through the delivery of 
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standardized file formats and content, along with the use of consistent trajectory models and 

coordinate frame definitions. 

The use of consistent trajectory models and coordinate frame definitions is best realized by 

conforming to the recommendations in the recently released NASA Technical Publication 

“Astrodynamics Convention and Modeling Reference for Lunar, Cislunar, and Libration Point 

Orbits” (Folta et al. 2022). This document details coordinate and time systems, numerical 

integration techniques, and trajectory modeling of three-body systems at different levels of 

fidelity appropriate for mission design and navigation of spacecraft well beyond geosynchronous 

orbit (GEO). A cislunar conjunction risk assessment best practice is to conform to the 

astrodynamics conventions and modeling recommendations of this NASA technical publication 

to enforce consistency across ephemerides from different sources, thereby enabling more 

accurate conjunction assessments. 

The goal of standardizing file formats and content has been addressed by DOD, NASA, and 

academia through a Cis-Lunar SSA Technical Steering Group led by the National GeospatialIntelligence Agency (NGA). The Steering Group has produced a draft document outlining an 

enhanced message set that enables communication of space object catalog and observational data 

for the cislunar regime (Butt 2021).5 The recommended set covers object state and covariance 

information in the catalog content message and sensor observations in the tracking data message. 

These formats overcome shortcomings of the current SSA message set that prohibits accurate 

expression of cislunar data and also update features of the current set that have not evolved with 

advances in SSA since their inception in the 1960s. 

A cislunar conjunction risk assessment best practice is to conform to these recommendations 

when developing SSA architectures to support cislunar missions.

Conjunction Screening Process

Sharing of standardized ephemeris and covariance data is the intent of the current practice of 

Earth orbiter owner/operators (O/Os) delivering files to conjunction screening providers such as 

the U.S. Space Force 18

th Space Defense Squadron (18 SDS), 19th Space Defense Squadron (19 

SDS), or CARA for use in computing a probability of collision (Pc) during encounters. However, 

cislunar conjunction assessment currently has no catalog of cislunar objects with independent 

trajectory and covariance solutions and so requires a different screening process. 

NASA currently performs conjunction assessment around Mars, the Moon, and Sun/Earth 

libration points through the Multimission Automated Deepspace Conjunction Assessment 

Process (MADCAP) based at the Jet Propulsion Laboratory (JPL). More information about 

MADCAP and related processes is available on the organization’s website: 

https://www.nasa.gov/cara/madcap and in the document Tarzi et al. 2022. Spacecraft operators, 

including for non-NASA and even non-partner international spacecraft, deliver ephemerides to 

the NASA Deep Space Network (DSN) Service Preparation Subsystem (SPS) portal, through 

5 https://www.nasa.gov/sites/default/files/atoms/files/cislunar_ssa_proposed_message_setnov2021_rev2_without_emailspdf.pdf
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which MADCAP can access them. MADCAP assesses conjunction risk based on Pc if a 

covariance is provided, or (if necessary) via typical radial and timing prediction uncertainties 

provided by the respective mission navigation teams. These uncertainties are fit to polynomials 

in time and mapped to the relative node of the two orbits to assess the risk of collision at the 

crossing. However, as described in Tarzi et al. 2022, MADCAP has implemented the capability 

to compute two-dimensional Pc (2D-Pc) when given ephemerides with covariance. When 

potentially risky conjunctions are discovered, notifications and conjunction event data are 

forwarded to both satellites’ operations teams, who then are expected to work with each other to 

determine if a mitigation action is necessary and, if so, execute it. JPL’s MADCAP Team will 

facilitate the decision process if the operations teams cannot agree on a course of action. 

Regarding the lack of a centralized catalog of cislunar objects, that is currently in work by 

19 SDS. In fact, many cislunar conjunction assessment capabilities are evolving with the 

potential for significant advances in deep space tracking, trajectory modeling, and ephemeris 

sharing interfaces. Because many of these advances are still in development, the baseline for 

conjunction risk assessment must rely on ephemeris and covariance produced by the O/O rather 

than catalog screening. 

As such, the O/O should deliver a CCSDS Orbit Ephemeris Message (OEM) formatted 

ephemeris with covariance to both space-track.org and to the DSN SPS portal. This will allow 

access to the trajectory and its uncertainty for screening by both 19 SDS (through SpaceTrack) 

and MADCAP (through SPS). 

The CCSDS format is the current industry standard, aligning with the standardization goal 

outlined above. Because a non-cooperative orbit solution for cislunar spacecraft is not currently 

available, inclusion of the covariance in the O/O ephemeris file is essential to allow computation 

of the probability of collision. Establishing the best practice of O/Os providing accurate 

trajectory and covariance for their spacecraft in cislunar space to current ephemeris interfaces 

sets the stage for effective conjunction screenings as operational advances continue to be made in 

the cislunar regime.

To address this topic, the following specific practices are recommended:

A. Owner/operators should conform to recommendations in the NASA Technical 

Publication “Astrodynamics Convention and Modeling Reference for Lunar, Cislunar, 

and Libration Point Orbits.”

B. Cislunar mission support entities (sensors, catalog maintainers, etc.) should conform to 

the enhanced SSA message set (Butt 2021) when creating cislunar SSA architectures. 

C. Owner/operators should maintain accurate orbit determination solutions and predicted 

covariance for objects in cislunar space.

D. Owner/operators should deliver predicted ephemeris with covariance in the CCSDS 

format to space-track.org and to the DSN SPS portal.
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4.0 Spacecraft and Constellation Design

Safety of flight is an integral aspect of satellite space operations and should be considered as part 

of design decisions to enable cost- and mission-effective solutions so that potential impacts to 

other operators in the space environment can be avoided. Specific design areas for which the 

consideration of on-orbit safety issues is appropriate include:

• orbit selection, 

• spacecraft ascent and disposal activities, 

• sensor trackability of the spacecraft, 

• spacecraft reliability,

• capabilities for ephemeris generation, and

• capabilities for risk assessment and mitigation. 

Each of these items is treated in more detail in this section.

Ascent to/Disposal from the Constellation’s Operational Orbit

Safety-of-flight issues may be considerable when related to the ascent from the launch injection 

point to the satellite’s on-station position or to the descent to an orbit from which disposal/reentry can be accomplished directly. Typical ascent and descent trajectory design using now

common electric propulsion or low-thrust chemical propulsion can take months to accomplish, 

potentially passing through highly populated regions of space along the way. For large 

constellations, the amount of nearly continuous transiting satellite traffic could be especially

large as old satellites pass out of service and replacement satellites are added. 

All missions should plan for orbit disposal to reduce long-term orbital debris. Reducing the 

number of inactive space objects minimizes the probability of generating debris through orbital 

collisions, and the fastest disposal option should be pursued; for example, existing large 

constellations are promptly deorbiting end-of life spacecraft. The U.S. Government has 

established Orbital Debris Mitigation Standard Practices (ODMSP) including for post-mission 

disposal.

6 NASA missions are required by NPR 8715.6 to comply with NASA Standard 8719-

14B, Process for Limiting Orbital Debris, which defines how NASA implements the ODMSP. 

During ascent and descent, a spacecraft will pass by other assets that are already on orbit. Some

but not all of those may be maneuverable. The ascending/descending spacecraft that is equipped 

to maneuver needs to yield the right-of-way to existing on-orbit assets by performing risk 

mitigation maneuvers or ascent/descent trajectory alterations.

Special caution is needed to protect humans on orbit. If the ascent or descent trajectory will pass 

through the ISS altitude, operators should coordinate with the NASA JSC FOD to avoid perigeelowering approaches that pose persistent and problematic orbital crossings with ISS and other 

human space flight assets. 

6 U.S. Government Orbital Debris Mitigation Standard Practices. 2019 version 

https://orbitaldebris.jsc.nasa.gov/library/usg_orbital_debris_mitigation_standard_practices_november_2019.pdf.
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To address this topic, the following specific practices are recommended:

A. Perform a study to compute the number of expected close approaches anticipated 

during ascent and descent as well as the imputed additional satellite reliability that 

will be required to meet satellite disposal requirements at the chosen operational 

orbit. 

B. If the results of the study show a large burden, consider choosing a different 

mission orbit with a lower burden. 

C. All missions should review and follow the ODMSP guidance standards.

D. When practicable, pursue active disposal using the fastest disposal option 

available.

E. Recognize that transiting spacecraft should yield way to on-station spacecraft and 

thus take responsibility for any conjunction risk mitigation maneuvers or transient 

trajectory alterations that may be required.

F. When planning descent using thrusters, if not planning an approach of circularorbit altitude reduction, coordinate with the NASA JSC TOPO to ensure that 

perigee-lowering approaches do not present persistent and problematic orbital 

crossings with the ISS and other human space flight assets.

General Orbit Selection: Debris Object Density

Space debris is not uniformly distributed about the Earth. Because most of the present space 

debris is generated from a relatively small number of satellite collisions or explosions, the orbital 

parameters of these collided or exploded satellites determine where the large debris fields reside.

For example, the debris object density is much greater in the 750-900 km altitude band than in 

other parts of LEO. If possible, this region is one to avoid as a destination orbit since a larger 

number of serious satellite conjunctions with debris objects can be expected. An orbit that results 

in a high number of close approaches can lead to the need to perform many maneuvers that may 

not fully mitigate the risk of close approach. Spacecraft that cannot maneuver will operate at 

higher risk of debris creation, effectively presenting additional risk to other operators.

Orbit selection should be informed by a study to determine expected conjunction rates; that is, 

the expected number of lifetime conjunction risk mitigation maneuvers and the amount of 

satellite fuel needed to permit the number of desired years on orbit. Published results by NASA 

CARA are available and can be consulted to obtain first-order high-interest event density 

information. (See Appendix F for more information and examples.) Use this information to 

assess the mission impact for conjunction risk mitigation maneuvers, given the expected lifetime 

of each satellite (e.g., additional propellant required, impacts on data collection).
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To address this topic, the following specific practices are recommended:

A. Include considerations of orbital debris density when selecting candidate mission 

orbits. Debris density diagrams, indexed by object size, are published by the 

NASA Orbital Debris Program Office (ODPO). (See Appendix G for more 

information and examples.)

B. When choosing from the final set of candidate orbits, perform a conjunction 

frequency analysis to determine the number of conjunction high-interest events 

per spacecraft per year that can be expected in each of the proposed orbital areas. 

Vehicle- and Constellation-Specific Orbit Selection: Spacecraft 

Colocation

While there is a process used by the International Telecommunication Union (ITU) to ensure that 

spacecraft locations are deconflicted from a radio frequency perspective, there is no similar 

centralized process for ensuring that spacecraft locations are deconflicted from a location 

perspective. This gap has resulted in spacecraft injecting into their planned mission orbit only to 

find another spacecraft already in or very near that location (colocated), which causes close 

approaches that then have to be mitigated, potentially very frequently, over the whole mission 

lifetime. 

Another similar problem is that of systematic or repeating conjunctions in which a spacecraft has 

multiple repeated close approaches on successive orbits with another object over a long period of 

time; for example, when using electric propulsion to move slowly through a congested area. Two 

actively maintained spacecraft with very similar orbits can present a permanent recurring 

collision hazard because both spacecraft can be planning future maneuvers that result in a 

collision if not coordinated. Therefore, active coordination for every maneuver is required to 

prevent the execution of simultaneous maneuvers that could create a collision. 

Due to the lack of centralized coordination, it is incumbent upon individual operators to protect 

themselves and the space environment by performing their own colocation analysis. The goal 

would be to prevent choosing a location already occupied by another spacecraft, or, if that is not 

possible, to work with the other operator before launch to devise a strategy to share the space.

Colocation situations can often be ameliorated through relatively small changes to the planned 

orbits during the design phase. For NASA missions, CARA can perform this analysis using the 

current USSPACECOM catalog data. (See Appendix H for more information and examples.) For 

non-NASA missions, CARA will make their software tool available via public release.

In performing the analysis, it is not necessary to consider proximity to objects that are not 

maneuverable (debris, rocket body, dead spacecraft) since the non-maneuverable object will pass 

through the area under the control of non-conservative forces such as atmospheric drag and not 

present a future issue for the (largely) static orbital parameters of the asset that is maintaining its 

orbit using maneuvers.
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To address this topic, the following specific practices are recommended:

A. During orbit selection, perform an orbit colocation analysis to determine whether 

any of the proposed orbits is likely to create systematic conjunctions with existing 

actively maintained satellites. 

B. If the orbit colocation analysis identifies systematic conjunctions, consider 

modifying the proposed orbit(s) slightly to eliminate this possibility. Optimizing 

orbit placement may be appropriate.

C. If the selected orbit is likely to present systematic conjunctions with a pre-existing 

spacecraft, then coordinate with the other operator(s) to arrange a process to 

coordinate maneuver plans routinely during the life of the mission.

Launch-Related Conjunction Assessment

Launch Collision Avoidance (Launch COLA or LCOLA) is the evaluation of a particular launch 

trajectory to determine whether the launch assembly, following this trajectory, will produce any 

close approaches with other space objects. LCOLA is sometimes expanded to include more 

indirect analyses to ensure that launch offscourings (rocket bodies, fairings, etc.) do not produce 

close approaches with other objects during the first three days after launch, after which they can 

be presumed to be cataloged and thus handled by the usual on-orbit conjunction assessment

methods.

LCOLA requirements are governed by the individual launch range or launch licensing agency. 

Requirements are in the form of stand-off distances Pc depending on whether the on-orbit 

conjuncting asset is a piece of debris, operational payload, or human space flight mission. 

Examples of the current requirements are 200 km stand-off distance or 1E-6 Pc between the 

object to be launched and human space flight assets and 25 km or 1E-5 Pc between the object to 

be launched and non-human space flight operational payloads. In practice, LCOLA covers 

launched objects from the time they reach 150 km through three hours. Launch times found in 

violation of these requirements are enforced as launch hold periods by the respective wing 

commanders. 

A large study conducted by NASA (Hejduk et al. 2014) questioned the added value of LCOLA, 

given the uncertainties typical of most predicted launch trajectories. However, recent 

improvements in the fidelity of these predicted trajectories have made the LCOLA enterprise 

potentially more meaningful, suggesting that the situation may need to be reevaluated. 

The period between when traditional LCOLA ends and when an on-orbit asset can mitigate a risk 

using standard on-orbit conjunction assessment methods is called the COLA gap. The O/O 

should ensure that newly launched objects and their detritus will not come into conjunction with 

protected assets during the COLA gap (i.e., until the 18 and 19 SDS can catalog the new 

object(s) so it is available for conjunction assessment screening). Such analyses should consider 

not just the predicted nominal launch injection but the expected (up to three-sigma) launch 

dispersions. 
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Specific criteria defining COLA gap launch cutouts do not exist since they are dependent on both 

what is being launched and the capabilities of the protected on-orbit asset. For example, ISS 

needs 36 hours for the COLA gap, which allows 24 hours for 18 and 19 SDS to track the launch 

objects and then 12 hours for ISS to assess the risk and mitigate if required. Other assets might 

require more time to close this risk gap. The methodology for this risk assessment can be a standoff distance phasing analysis, nodal separation and in-track screening, or a probability density 

model. Note that this analysis is typically performed by Aerospace7for DOD missions and the 

NASA Launch Services Program for NASA missions. These organizations can be consulted for 

details on the analysis techniques and criteria, which are also listed in Appendix Q (Hametz and 

Beaver 2013; Jenkin et al. 2020). NASA JSC FOD can also be consulted for analysis methods 

and to obtain details on the assets that could be at risk for each specific launch.

To address this topic, the following specific practices are recommended:

A. Protect human space flight assets from close approaches during the COLA gap 

using stand-off distance or statistical measures. 

B. Conform to additional LCOLA requirements that the launch range may impose.

Spacecraft Trackability

Effective conjunction assessment requires an accurate orbital state. Accurate orbital state data 

requires tracking data to maintain a comprehensive space catalog available to all space operators. 

The USSPACECOM catalog serves this purpose and uses the data collected by the SSN. 

Because even active spacecraft become debris after their end-of-life and therefore need tracking 

to obtain an orbit solution, all launched satellites need to be acquirable and trackable by the SSN

from deployment until their demise so that they can be cataloged and maintained using SSN 

capabilities alone. Launching an untrackable spacecraft increases risk to all operators. 

Objects are trackable if they have a large enough radar or optical cross section to be tracked by at 

least two SSN sensor assets. Analytical evaluations of trackability consider both object size and 

material properties, so there is no absolute size threshold that is determinative. But as a rule of 

thumb, satellites need to have characteristic dimensions of 10 cm in each major dimension for 

spacecraft with perigee less than 2000 km and greater than 50 cm in each major dimension for 

spacecraft with perigee greater than 2000 km. 

If a satellite exceeds the above dimensions, then there is a reasonable expectation of its being 

tracked by the existing SSN, and typically no further concern with trackability is needed. If a 

satellite is smaller than the above dimensions, then additional arrangements should be made to 

see to its orbital maintenance should its onboard navigation fail. Such arrangements could 

include an agreement with a commercial SSA company to provide tracking and construct a 

predicted ephemeris until re-entry or to add a trackability enhancement or autonomously

powered beacon device to allow the satellite’s position to be determined for the whole of its 

7 Aerospace is an independent, nonprofit corporation operating the only Federally Funded Research and 

Development Center (FFRDC) for the space enterprise.
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orbital life. For objects that will regularly occupy a large number of altitudes, such as a HEO 

object, special examination of the situation is required. For example, the object might be 

trackable at the lower altitudes but not the higher ones, and the orbit might be eccentric enough 

and with low enough perigee that good orbital modeling will require tracking at both apogee and 

perigee; in such a case, the larger spacecraft dimension would need to be met to guarantee 

trackability along the whole of the orbit. 

To address this topic, the following specific practices are recommended:

A. Through selection of physical design and materials, ensure that the satellite is

trackable by SSN from deployment until demise.

a. For spacecraft with perigee heights less than 2000 km, the spacecraft should 

have characteristic dimensions of at least 10 cm in each major dimension.

b. For spacecraft with perigee heights greater than 2000 km, the spacecraft 

should have characteristic dimensions of at least 50 cm in each major 

dimension.

c. If the spacecraft cannot meet these dimension constraints, use a proven 

detectability enhancement.

d. For spacecraft having orbits that span a large range of altitudes, ensure that the 

spacecraft is trackable at all altitudes.

Spacecraft Reliability

Studies related to active debris removal strategies have shown that the greatest contributor to 

long-term space debris growth is derelict spacecraft left on orbit. Such spacecraft produce 

opportunities for collision with smaller debris objects that cannot be mitigated, which will then 

generally produce large amounts of debris. So, it is important to ensure that spacecraft survive 

until they can be disposed of by using appropriate disposal as described in the OMDSP and by

ensuring that the probability of successful post-mission disposal meets or exceeds 99%.

To address this topic, the following specific practices are recommended:

A. Ensure that spacecraft reliability is high enough that the likelihood of each 

spacecraft remaining fully functional until it can be disposed of meets or 

exceeds 99%.

B. Reassess the 99% analysis whenever the underlying assumptions change; for 

example, extending operations beyond design life or failures in key systems.

Development of Capabilities for Ephemeris Generation and 

Conjunction Risk Assessment and Mitigation

Conjunction assessment capabilities are needed immediately after launch. The software and 

process components of the conjunction risk assessment and mitigation capabilities should be 

fully developed and tested before launch including elements of both the flight hardware and the 

ground system.
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Three main capabilities should be developed:

1. Predicted ephemeris capability. Predicted ephemeris data that can be shared with other

O/Os is needed to assess the potential for collisions between space objects. The current 

U.S. Government conjunction assessment process uses two predicted ephemeris solutions 

for the asset: one generated using non-cooperative SSN tracking data and one shared with 

18 and 19 SDS by the O/O. For active, maneuverable spacecraft, the O/O-generated 

ephemeris is often the best representation of the future position because the O/O usually 

has access to more cooperative tracking data to feed the orbit-determination process (for 

example, from onboard Global Positioning System (GPS) receivers); has an accurate

model of the spacecraft’s drag coefficient and frontal area; and, most importantly, can 

model planned future maneuvers in the predicted trajectory. To enable the conjunction 

assessment process, predicted ephemerides must be furnished frequently, span an 

appropriate period of predictive time, employ point spacing close enough to enable 

interpolation, provide a full state (position and velocity) for each ephemeris point, and 

provide a realistic 6 x 6 covariance matrix (with both variance and covariance terms) for 

each ephemeris point. (See Appendix I for more details about covariance realism 

characterization and evaluation.)

2. Risk assessment capability. The results of satellite conjunction screening analyses are 

sent from USSPACECOM to O/Os in the form of CDMs that contain the states, 

covariances, and amplifying orbit determination information for the primary and 

secondary object at the Time of Closest Approach (TCA). These messages, however, are 

only a notification of a predicted potential close approach. For a robust safety-of-flight 

process, additional risk assessment analysis is needed to determine whether the close 

approach warrants mitigation. Conjunction risk assessment tools are needed to perform 

this risk assessment, which includes calculation of Pc and other relevant information such 

as expected collision consequence (addressed in Appendix O) and whether the state and 

covariance information is sufficiently accurate to subtend the risk assessment process 

(addressed in Appendix P). For conjunction events in which the Pc exceeds a severity 

threshold, mitigation action planning is necessary to plan a mitigation option that will 

lower the Pc to below an acceptable threshold, usually conducted with the aid of tradespace plots that give conjunction Pc reduction as a function of spacecraft trajectory 

modification size and execution time. Validating these tools is important well before 

flight. (See Appendix J.) Some commercial vendors offer risk assessment services.

Spacecraft operators who choose to purchase risk assessment services should make these 

arrangements well before launch to ensure adequate time for testing and development 

of a corresponding process for choosing a mitigation option given the risk assessment 

results received from the service.

3. Mitigation capability. A spacecraft can mitigate a close approach in several ways:

• Propulsive maneuvers (e.g., performed using thrusters).

• Attitude changes to take advantage of altered drag coefficients from altered 

frontal areas to effect a relative velocity change between the two objects.
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• Changing the spacecraft attitude to present a minimal frontal area to the relative 

velocity vector to minimize the likelihood of collision.

• Sharing ephemeris data with the operator of the other spacecraft involved in the 

close approach so that they can perform an avoidance maneuver.

Because the design of the spacecraft and/or ground system needs to accommodate the 

ability to perform these actions, spacecraft operators should choose a mitigation option 

when they select their mission orbit and ensure that the capability is built into the system 

appropriately in time for testing and use.

To address this topic, the following specific practices are recommended:

A. Develop and implement a capability to generate and share accurate predicted 

spacecraft ephemerides including any planned maneuvers. (See Section 3.1 for a 

discussion of ephemeris sharing for screening. See Section 6.2 for specific 

guidance on ephemeris generation frequency, length, point spacing, formatting, 

and contents.)

B. Determine during spacecraft design what risk mitigation approaches are possible 

for the spacecraft. While trajectory modification via thrusting maneuver is the 

most common approach, other approaches such as differential drag orbit 

modification are possible.

C. Develop and implement or arrange to acquire a capability to process CDMs and to 

compute conjunction risk assessment parameters such as the Pc.

D. Develop and implement or arrange to acquire a risk analysis capability to select 

mitigation actions that will lower the Pc for dangerous conjunctions to a userselected value.

E. Validate conjunction assessment tools well before flight, typically 6-12 months 

prior.
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5.0 Pre-Launch Preparation and Early Launch Activities 23

5.0 Pre-Launch Preparation and Early Launch Activities

The pre-launch and launch/early orbit phase of a satellite’s lifetime is the period during which 

safety-related policy decisions are rendered and associated data interfaces established. Safetyrelated policy decisions carry forward as precedent and actual operational arrangement to form 

the O/O’s safety posture over the satellite’s orbital lifetime. 

Many pre-launch activities such as establishing interfaces, data sharing agreements, and a

Concept of Operations (CONOPS) require coordination. Other activities pertaining to the launch 

and early orbit period such as outlining particular practices and reporting are needed to conduct 

conjunction assessment activities during this phase of orbital life and to facilitate a smooth 

transition into on-orbit conjunction assessment. Each activity is treated individually in this 

section.

CONOPS Discussions and Arrangements with USSPACECOM

Pertaining to Launch Phase

A spacecraft’s journey from the launch facility to its on-station positioning in its service orbit is 

complicated and open to mishaps that can damage both the launching spacecraft and other 

spacecraft in proximity. The U.S. Government performs required activities in support of the 

launch enterprise including cataloging the spacecraft and any other space objects, debris and 

otherwise, related to the launch. To meet these responsibilities and provide a safe exercise of the 

launch process, the spacecraft operator needs to execute several pre-launch activities and points 

of coordination. This is best done by coordinating with USSPACECOM to discuss all the related 

issues, exchange information, and generate a comprehensive launch and deployment plan so that 

all affected agencies can exercise their proper roles. 

First, early cataloging is extremely important to enable the conjunction assessment process to 

protect all other on-orbit assets. To assist the cataloging function, all aspects of the launch 

delivery and deployment methodology need to be fully documented and communicated to 

USSPACECOM so that those performing the launch cataloging process know what to expect at 

each point and can respond appropriately. 

Aspects of the launch delivery that may affect cataloging and should be documented would 

include the launch vehicle configuration (rocket versus air launch) and the launch phases 

(parking orbits, transfer orbits, injection, and post-injection transiting to on-station locations). 

The deployment methodology includes timing post-separation and number of objects deployed. 

Examples of unusual deployment features that might create cataloging issues include highvelocity deployments, non-immediate deployments (i.e., subsequent deployment of a satellite 

from one of the deployed satellites), and tethered satellites. Multiple nearly simultaneous 

deployments are a challenge for tracking and will delay cataloging which in turn poses a safetyof-flight risk. Deployments should be spaced to allow acquisition of each object. For multiple 

nearly simultaneous deployments, the expected range of deployment speeds and directions 

should be provided.
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Input for the R-15 launch form (launch plan and orbital parameters) should also be discussed 

with USSPACECOM so that they may render any necessary clarification or aid. The launch 

provider is responsible for completing and submitting the R-15 form; however, the O/O should 

discuss the content with USSPACECOM well in advance of the launch. (See Appendix K for 

more information.)

Second, detailed launch trajectory information for all launch objects needs to be submitted to 

USSPACECOM with a Form-22 (on space-track.org) well before the launch date so that a 

colocation and object avoidance analysis for the launch sequence can be conducted and, if 

necessary, adjustments made to ensure safety. To avoid close approaches with the ISS and other 

active spacecraft, it may be necessary to modify the launch sequence slightly and eliminate 

certain launch times from the launch window. Launch providers frequently take responsibility 

for these activities, but it is important for O/Os to be aware of the availability and benefits of this 

service.

Third, to avoid any data transfer failures while the launch is in progress, the required exchange of 

data between O/O and USSPACECOM during the launch process and the associated formats and 

timelines need to be established, understood, and exercised prior to launch. 

To address this topic, the following specific practices are recommended:

A. Establish contact with USSPACECOM to describe and discuss all aspects of the 

launch including delivery and deployment methodologies. 

B. Space the deployment of multiple spacecraft in a way that enhances the ability of 

USSPACECOM to quickly identify and differentiate the spacecraft using the

SSN.

C. Discuss the preparation of the R-15 launch form with USSPACECOM so that 

they understand its contents and any implications for safety of flight.

D. Ensure that the launch provider submits the Form 22 and launch trajectory 

information to USSPACECOM, including ephemerides for the powered flight 

portions and orbital elements for the parking orbits, so that potential colocation 

and deconfliction potentialities can be discovered. 

E. Provide to USSPACECOM as soon as possible launch-related information (e.g.,

injection vectors and initial ephemerides for deployed spacecraft) that can be used 

to assist with the cataloging process, especially to confirm the identity of launchrelated objects. Coordinate a satellite numbering scheme (potentially including 

temporary satellite numbers) appropriate to the launch type and expected degree 

of cataloging difficulty.

F. Coordinate with USSPACECOM any potential launch anomaly diagnostic 

products that can be provided if issues arise during the launch and early orbit 

sequence.
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CONOPS Discussions and Arrangements with USSPACECOM 

and NASA Pertaining to On-Orbit Mission Phase

USSPACECOM is required to maintain orbit determination solutions on all objects arising from 

the launch as part of its military space object custody responsibilities. USSPACECOM also 

provides conjunction assessment information to O/Os for safety of flight. In order for 

USSPACECOM to maintain the catalog most easily for safety of flight for all, the O/O should 

provide relevant details about its assets. The pre-launch period is the appropriate time to conduct 

exchanges of information that facilitate these activities.

1. Provide operational contact information. It is important for the satellite operator to 

provide operational point-of-contact information so that USSPACECOM can coordinate 

spacecraft tracking, cataloging, identification, and provision of space flight safety data for 

the satellite. Submitting this information allows expeditious contact if issues arise during 

the launch and on-orbit periods of the satellite’s lifespan and provides the information 

necessary for USSPACECOM to arrange for the delivery of basic space flight safety 

services.

2. Provide information about satellite construction and operation. Basic information 

about the satellite to be deployed, such as satellite dimensions, presence of deployable

structures (e.g., solar panels, antennae), satellite material properties, and expected 

satellite regular attitude, needs to be communicated to USSPACECOM. These aspects of 

satellite construction and operation affect trackability, and an understanding of these 

construction features allows USSPACECOM to assemble a tracking approach, assign 

appropriate sensors, and predict the regularity of attempted tracking success. 

3. Provide satellite orbit maintenance strategy. The orbit maintenance strategy for the 

satellite should be communicated, at least at a high level. Information such as the logic 

for determining orbit maintenance maneuvers, the maneuver thruster technology, and the 

frequency/size/duration of orbit maintenance burns will help USSPACECOM to set up 

the orbit maintenance parameters properly for each satellite to perform the most reliable 

orbit maintenance possible. 

4. Provide the satellite flight control and navigation paradigm. Understanding the flight 

control and navigation paradigm of the satellite is needed, especially whether a traditional 

ground-control paradigm has been followed or whether autonomous navigation is used. If 

the latter, the amount of ground-knowledge of satellite activities, such as whether there is 

foreknowledge of maneuvers and an opportunity to override these maneuvers from the 

ground before they are executed, is important to understand the degree to which the 

satellite’s navigation can be manually influenced if necessary. In addition to setting 

general expectations for the satellite’s flight dynamics, this information is helpful in 

determining the degree of expected fidelity for regularly generated satellite O/O 

ephemerides.
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5.0 Pre-Launch Preparation and Early Launch Activities 26

To address this topic, the following specific practices are recommended:

A. Register the spacecraft with USSPACECOM using the Satellite Registration form 

on space-track.org.

B. Provide USSPACECOM with basic construction and mission information about 

the satellite such as stowed dimensions; deployable structures such as solar 

panels, antennae, booms, including all their (rough) dimensions; satellite material 

properties and colors; regular satellite attitude; and registered operational radio 

frequencies. 

C. Provide USSPACECOM with a basic overview of the satellite’s orbit 

maintenance strategy including the paradigm for determining when orbit 

maintenance maneuvers are required; the maneuver technology used (as this 

relates to burn duration and expected accuracy); and the frequency, duration, and 

magnitude of typical burns. 

D. Provide USSPACECOM with an understanding of the flight control and 

navigation paradigm, principally whether a ground-based control approach is 

followed or some degree of (or full) autonomous control is used. If the satellite 

control does include some autonomous flight dynamics or control features, 

indicate how much (if any) foreknowledge ground controllers have of 

autonomous maneuver actions, the amount of information that is communicated 

to the ground both before and after the maneuver (e.g., maneuver time, delta-V, 

direction), and whether ground-based overrides are possible.

CONOPS Discussions and Arrangements with USSPACECOM 

and NASA Pertaining to Conjunction Assessment

On-orbit conjunction assessment is needed to protect the satellite and keep valuable orbital 

corridors free of debris pollution and sustainable for the indefinite future. The screening process 

is the first step in completing a risk analysis for a potential conjunction.

Conjunction assessment screenings typically use O/O ephemerides as a statement of the primary 

object’s position. Ephemeris formats, delivery mechanisms, and screening timetables need to be 

coordinated with the screening provider. The screening provider should use this information to 

monitor the satellite’s projected position over time and identify potential conjunctions. The O/O 

needs to choose which screening service provider will be used (i.e., the USSPACECOM free 

service, a validated commercial conjunction assessment service, or both) and establish a robust 

interface prior to launch.

USSPACECOM currently provides a free conjunction assessment service that performs 

conjunction assessment screenings on behalf of an O/O and sends proximity warnings (CDMs) 

for each situation in which the distance between the O/O’s satellite and another cataloged object 

is smaller than a set threshold. These messages give O/Os the data they need to assess the 

collision likelihood of a particular conjunction and, if necessary, plan and take mitigative action. 

As noted in Section 3.1, NASA recommends at a minimum using the USSPACECOM 
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5.0 Pre-Launch Preparation and Early Launch Activities 27

conjunction assessment service, which can be augmented with validated commercial conjunction 

assessment services when desired. (See the USSPACECOM Spaceflight Safety Handbook for 

additional information regarding the USSPACECOM conjunction assessment service.)

Commercial providers should provide equivalent support and data formats. Many commercial 

conjunction assessment services work from the USSPACECOM conjunction assessment data 

and not from separate or unique commercial SSA data.

Based on satellite orbit and mission characteristics, a screening volume size will need to be 

assigned. (See the USSPACECOM Spaceflight Safety Handbook for more details.) The 

screening volume is the physical volume (generally an ellipsoid) that is “flown” along the 

primary’s orbit during the screening process, with any objects found within this volume 

considered to be conjunctions and associated CDMs generated. If a commercial conjunction 

assessment provider is selected, the O/O will need to work directly with the provider to discuss 

the type, timing, and format of the information needed. (See Appendix L for Information about 

how NASA validates and uses commercial data.)

USSPACECOM distributes CDMs through space-track.org. An O/O needs to register on spacetrack.org and provide contact information to USSPACECOM to receive the basic level of 

CDMs. If desired, a test instantiation of space-track.org is available to allow O/Os to practice 

generating, receiving, and processing the conjunction assessment data products. 

Finally, a formal Orbital Data Request (ODR) for any of the desired USSPACECOM-generated 

conjunction assessment information beyond the most basic products will need to be submitted to 

USSPACECOM and adjudicated before information exchange can begin. An ODR form is a 

method to request data and services beyond the basic ones. The form and instructions for filling 

it out are posted on space-track.org. Non-U.S. Government entities are strongly encouraged to 

sign SSA sharing agreements with USSPACECOM, which expedites the ODR process. For 

NASA missions, ODRs are sent to CARA and JSC FOD, who submit them on behalf of the 

mission. ODRs are used to request permission to redistribute USSPACECOM data to other 

entities, obtain specialized one-time analyses, and make other specific requests.

Large constellations may require special considerations such as quantity or timeframe of data 

used for screening and risk analysis. NASA has considerable operational experience with 

conjunction risk assessment and has assisted previous large constellation operators in designing a 

conjunction risk assessment process that scales appropriately.
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To address this topic, the following specific practices are recommended:

A. Decide whether the USSPACECOM free service, a validated commercial 

conjunction assessment service, or both will be used by the mission. 

B. Establish a service with the selected service provider.

C. Implement a SSA sharing agreement with USSPACECOM to receive advanced 

data support and services.

D. Through the registration of the satellite with USSPACECOM, begin the process 

of arranging for conjunction analysis data exchange including O/O ephemerides, 

maneuver notification reports, and CDMs. USSPACECOM uses the spacetrack.org account as the mechanism for product exchange. 

E. If needed, complete an Orbital Data Request (ODR) form to arrange for delivery 

of USSPACECOM advanced conjunction analysis products.

F. For large constellations, coordinate with NASA and the screening provider to 

identify and address any special considerations. 

In situ Launch Products and Processes

Once liftoff is achieved, the foci become those of a safe journey to the final on-station 

destinations of the spacecraft and the efficient performance of the launch cataloging process. To 

determine whether the launch is nominal and has deposited its spacecraft as expected, the initial 

injection vector should be provided to USSPACECOM as soon as it is available. Additionally, 

once initial contact has been made with each spacecraft and initial position information has been 

downlinked, the generation and forwarding to USSPACECOM of associated predicted 

ephemerides is very helpful in properly identifying the new spacecraft and, in some cases, 

finding them in the first place. Finally, to render any desired anomaly support and to assume the 

appropriate conjunction assessment posture for non-functional spacecraft, it is important to

forward (or update on space-track.org) spacecraft status information, especially in the era of 

“disposable” satellites in which infant mortality is higher.
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To address this topic, the following specific practices are recommended:

A. To aid in satellite tracking and identification, provide injection vector(s) to 

USSPACECOM as soon as they are available.

B. To assist in spacecraft identification for the cataloging process and provide 

general awareness among all O/Os, generate and forward predicted ephemerides 

for the spacecraft to USSPACECOM and publish the ephemerides (and all 

subsequent ephemeris updates) publicly as soon as contact is established with 

each deployed spacecraft.

C. If USSPACECOM has issued TLEs for launched objects, notify USSPACECOM 

of the TLE and object number associated with your spacecraft.

D. Provide early reporting to USSPACECOM of any spacecraft failures or other 

operational difficulties, both to obtain any available anomaly support and to 

assign the appropriate conjunction assessment approach to the spacecraft (i.e.,

inactive and thus handled in a manner equivalent to a debris object).

E. If using a commercial provider, make sure it has access to information from items 

A-D.
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6.0 On-Orbit Collision Avoidance 30

6.0 On-Orbit Collision Avoidance

For nearly all spacecraft, the on-orbit phase of their life cycle is the longest, meaning that the 

conjunction assessment practices and CONOPS in place during this phase will have the greatest 

impact on the satellite’s overall risk exposure. 

As explained in Section 3, the conjunction assessment process as presently structured comprises 

three phases:

1. Conjunction assessment screenings identify close approaches between a protected 

asset, called the primary satellite, and any other space objects, called (from the vantage 

point of the primary) “secondaries.”

2. Conjunction risk assessment examines each of the close approaches produced by the 

screening activity to determine which may represent dangerous situations and therefore 

require a mitigation action. 

3. Conjunction mitigation constructs a mitigation action, usually a trajectory change for 

the primary object, that will both reduce the collision risk of the close approach to an 

acceptable level and not create any new high-risk conjunction events. 

Before any of these three activities can take place, certain satellite data and position information 

needs to be produced and made available to the conjunction assessment process. 

These four aspects of conjunction assessment (required input data and the three phases of the 

conjunction assessment process) are each treated separately below.

Spacecraft Information and Orbital Data Needed for Conjunction 

Assessments

Because conjunction assessment identifies (and if necessary, mitigates) close approaches 

between spacecraft, it requires access to a comprehensive space catalog of orbital information. 

The USSPACECOM space catalog is the base catalog used by nearly all conjunction assessment

practitioners. Earlier sections of this document described the pre-launch registration and 

coordination process with USSPACECOM to receive basic launch and on-orbit conjunction 

assessment services. Several commercial conjunction assessment service providers offer 

conjunction assessment products derived from alternative space catalogs. O/Os are encouraged to 

pursue commercial services, particularly when such services offer improvements and innovations 

above and beyond what is available from USSPACECOM. However, NASA recommends O/Os 

use the service offered by USSPACECOM as both a baseline and a supplement to commercially

procured services. This is because the objects contained in the commercial catalog may not be 

the same as those in the DOD catalog and because the commercial vendor may provide 

conjunction assessment services based on publicly available TLEs8 along with solutions for the 

objects in their own catalog. These TLE-based solutions are not sufficiently accurate to be used 

8 See Appendix E for more information about the use of TLEs.
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6.0 On-Orbit Collision Avoidance 31

for conjunction assessment. (See Appendix L for information about how NASA validates and 

uses commercial data.)

The USSPACECOM space catalog used for conjunction assessment contains position and 

uncertainty information for the primary object. 

• If the primary object is not maneuverable, it is in principle possible to perform 

conjunction assessment on its behalf entirely from catalog-based information. However, 

satellite O/Os generally have a better understanding of the spacecraft’s construction and 

thus its non-conservative force parameters such as the ballistic coefficient and solar 

radiation pressure coefficient. So, the O/Os’ prediction of the satellite’s future position, 

captured in a predictive ephemeris, is often more reliable or at the least an important 

adjoining datum to the future position information calculated from a space catalog entry. 

• For satellites that do maneuver, future position calculations from catalog information 

alone will not capture any planned trajectory changes and thus will leave undiscovered 

any satellite conjunctions that could arise from the modified trajectory. 

Therefore, for both non-maneuverable and maneuverable spacecraft, but especially for the latter, 

it is necessary that O/Os furnish predicted satellite state and uncertainty information, usually in 

the form of an ephemeris that includes state covariance at each ephemeris point. The details of 

the generation of such ephemerides that result in the most useful product for conjunction 

assessment are described in the details portion that concludes this section. 

While it is most important to submit such ephemerides to the screening entity, it is also helpful to 

place them on a public-facing website for any space operator to download and process. Mutual 

sharing of expected future positions is the best way for active satellites to avoid collisions with 

each other. Claims that predicted ephemerides contain proprietary information of any 

consequence are simply not compelling and, in any case, are outweighed by the safety benefit of 

exchanging such information. Such ephemerides should be recomputed and reissued/reposted as 

soon as a change to a spacecraft’s intended trajectory is planned.

In determining how to react when a primary satellite is found to be in conjunction with a 

secondary, the logic path is governed heavily by whether the secondary object is an active, 

maneuverable spacecraft. 

• If the object is non-maneuverable, then the object will follow a Keplerian orbit without 

unexpected perturbations. Future positions can be predicted in a straightforward way 

using a dynamical model. 

• If the object is an active spacecraft that either has shown a history of maneuvering or is 

believed to be maneuverable, then it is quite possible that trajectory-changing maneuvers 

are planned and the assumption of a Keplerian orbit is not appropriate. 

For this reason, it is important to know whether any given spacecraft is active, capable of 

maneuvering, and presently in a phase of satellite life in which maneuvering is possible. This 

status can be documented and communicated by the O/Os’ setting of the spacecraft’s active/dead 

and maneuverable/non-maneuverable flags in its space-track.org record. This allows other O/Os 
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to determine whether the satellite can or will change its trajectory in a non-Keplerian manner and 

thus consider this possibility in conjunction assessment.

O/Os of active, maneuverable spacecraft should provide USSPACECOM with information

outlining basic information about each planned maneuver. This data should be uploaded to 

www.space-track.org for the most efficient use. While in principle such information could be 

reconstructed from submitted ephemerides, it is simpler and more accurate to provide the 

information directly in this form. Providing maneuver notifications assists USSPACECOM in 

updating their own catalog as they know when to look for maneuver activity and, if discovered 

(and subsequently tracked), can expeditiously update the satellite’s catalog entry to reflect the 

new trajectory. Of course, forwarding maneuver notifications is not a substitute for sending 

updated ephemerides that contain the intended maneuvers. Rather, it is an accompanying 

notification that allows better use of the received ephemerides and facilitates the 

USSPACECOM mission.

More O/Os are considering or are including autonomous flight control features, especially in 

large constellations in which the constellation management functions are complex. Autonomous 

flight control features may include orbit maintenance maneuvers and, in some cases, even 

conjunction risk mitigation maneuvers that are developed, scheduled, and executed from the 

onboard control system without any active ground-based participation. While such approaches 

can offer improved efficiencies, they present their own challenges. 

Even if satellite maneuvers are planned and executed autonomously, these planned maneuvers 

must be included in ephemerides and made available in near real time both to the screening 

provider and more broadly. This is because, recognizing the latencies of the download and 

distribution mechanisms, satellite maneuvers must not be executed without sufficient advance 

notice to allow the conjunction assessment process to become aware of the intended maneuver 

and ensure its safety. The amount of advance notice required is governed by the latencies in the 

selected conjunction assessment process, which includes the O/O infrastructure to receive and 

react to conjunction assessment information from the screening provider. The principal difficulty 

is notifying other active, maneuverable satellites that may be contemplating their own 

maneuvers. Maneuver intentions must be shared with other such O/Os in a satellite’s vicinity to

ensure that intended maneuvers by either or both operators, if executed, do not place both 

satellites on a collision course.
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To address this topic, the following specific practices are recommended:

A. Actively maintain the space-track.org record for the satellite, updating the 

active/dead and maneuverable/non-maneuverable flags to reflect the satellite’s 

current status. 

B. Furnish predicted ephemerides that include state covariances to USSPACECOM 

(and any additional commercial screening provider) and set the privileges to allow 

any interested party to access and download this information. 

C. Furnished ephemerides should possess the following characteristics:

a. Be of a 7-day predictive duration for LEO and 14 days for other orbits;

b. Be issued at least at the following frequencies:

i. Three times daily for spacecraft with perigee heights less than 500 km;

ii. Daily for other LEO orbits; and

iii. Twice weekly for other orbits.

c. Include all known maneuvers within the ephemerides’ prediction duration.

d. Provide ephemeris point spacing of approximately 1/100th of an orbit, in either 

time or true anomaly. (Certain scientific missions with extremely long orbits or 

high eccentricities may require more specialized approaches.)

e. Contain a realistic covariance at each ephemeris point for at least the six 

estimated state parameters. (Appendix I provides a practical guide for assessing 

covariance realism, as well as some general principles for tuning the covariance 

production process.)

f. Be formatted and distributed in the Consultative Committee for Space Data 

Systems (CCSDS) standard Orbital Ephemeris Message (OEM) format, 

preferably in the J2000 reference frame.

D. Furnish maneuver reports to USSPACECOM for any trajectory-altering satellite 

maneuvers sufficiently in advance of maneuver execution to enable an O/O 

evaluation of the maneuver’s safety. Employ the standard maneuver reporting 

message for this notification.

E. When a maneuver becomes part of a satellite’s trajectory plan, generate and 

submit to the screening provider an updated ephemeris that contains this new 

maneuver as early as is feasible but certainly with sufficient advance notice to 

enable an O/O evaluation of the maneuver’s safety. 

Conjunction Assessment Screenings

The first step in the conjunction assessment process is to find close approaches between 

protected (primary) objects and other objects, with the latter object set’s positions represented 

either by ephemerides (if they are active spacecraft) or space catalog entries. Finding these close 

approaches is accomplished by conjunction assessment screenings in which the predicted 

positions of the primary object and all other space objects that survive a pre-filtering process are 

compared. 
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At USSPACECOM, conjunction assessment screenings are executed using a volumetric-based 

approach: a physical screening volume (usually an ellipsoid) is “flown” along the primary 

object’s trajectory, and any secondary trajectories that penetrate this volume are considered 

conjuncting objects. This screening is accomplished using a tool called the Astrodynamics 

Support Workstation (ASW).

Volumetric screenings generate more close approaches than probabilistic or “covariance-based” 

methods but are preferable because they essentially give a snapshot of the satellite catalog in the 

vicinity of the primary’s ephemeris. If the screening volume is large enough, the conjunction 

information can be used to determine the safety of not just the nominal trajectory but also any 

reasonably sized maneuvers that the primary may choose to make. 

Once these close approach objects are identified, further processing is invoked to determine the 

precise time of closest approach between the two objects and the two objects’ states and 

covariances at that time.

A protected asset should be screened for close approaches against a comprehensive satellite 

catalog at least daily with the results of this process obtained and processed by the O/O, also at 

least daily. For active, maneuverable satellites that submit ephemerides to the screening process 

as a way of including their planned maneuvers into their predicted trajectories, these 

ephemerides should be screened against each other (subject to appropriate pre-filtering) in near

real time whenever an O/O submits an updated ephemeris. These “O/O vs O/O” screenings are 

the best way to ensure that maneuver plans are communicated among O/Os to prevent 

simultaneous maneuvers from causing a collision.

Current USSPACECOM practice is to conduct three screenings per day. Each screening predicts 

close approaches between:

1. The ASW solution for each protected (active) asset against the full catalog;

2. O/O ephemerides submitted after the last screening against the full catalog; and

3. O/O ephemerides submitted after the last screening against all other unexpired 

O/O-submitted ephemerides.

In other words, O/O-submitted ephemerides are screened against the full catalog when initially 

submitted, then retained and screened against other O/O ephemerides until they expire.

Three screenings per day is a minimum frequency for higher-drag orbit regimes such as LEO 

orbits with perigee heights below 500 km; daily screenings for other orbit regimes yields 

sufficient accuracy. 

(See the USSPACECOM Spaceflight Safety Handbook for details about the cadence and conduct 

of conjunction assessment screenings.)
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To address this topic, the following specific practices are recommended:

A. Submit predicted ephemerides for the spacecraft to a screening provider to be 

screened for conjunctions at least daily with spacecraft in higher-drag orbit 

regimes screened at least three times per day.

B. Ensure that an O/O ephemeris for an active, maneuverable spacecraft is screened 

against other ephemerides from active, maneuverable spacecraft in near real time 

after any such ephemeris is submitted to the screening provider. 

C. Obtain and process these screening results from the screening provider at the 

same frequency at which they are produced for both the full-catalog and O/O vs 

O/O screening cases described above.

Conjunction Risk Assessment

Satellite conjunctions are approaches between two satellites closer than a specified set of 

distances, which is often chosen to be much larger than the set that would pose an actual 

collision threat. A key next step, therefore, is to evaluate each conjunction to determine if it 

poses, or is likely to pose, a substantial risk of collision. This evaluation activity, called 

conjunction risk assessment, comprises both the key calculations that feed the concept of risk 

(that is, both collision likelihood and collision consequence) and the evaluations of the input data 

that subtend these calculations to ensure that they constitute a basis for decision making. Only 

conjunctions that are determined to be high risk merit the consideration of mitigation actions.

Methods proposed in the scientific literature for calculating and assessing satellite collision 

likelihood have different merits and different risk tolerance orientations. Of all the possibilities,

Pc is the oldest, most straightforward, and most widely embraced collision likelihood parameter. 

Because it is a present industry standard, NASA recommends that operators employ Pc as the 

foundational element of their collision likelihood assessment. (See Appendix M for an extended 

treatment of the recommendation for the use of Pc as the collision likelihood parameter.)

Two approaches to calculating the Pc are:

1. The “two-dimensional” Pc (2D-Pc) calculation approach, which was originally 

introduced by Foster and Estes in 1992 with theoretical clarifications by Alfano (2005b) 

and Chan (2008). This method is a durable simplification of the calculation that is valid 

in most instances, but there are situations in which it does not perform accurately. 

2. The “three-dimensional” Pc (3D-Pc) calculation method, which was originally 

formulated by Coppola (2012) and “repaired” and extended by CARA. Once it has 

completed final NASA validation, it is expected to be the recommended analytic 

approach. This method is accurate for nearly every situation, tests exist to identify those 

very few cases in which it may not be fully adequate, and it is computationally efficient. 

Additionally, the primary and secondary object covariances for some orbit regimes can contain 

significant correlated error, thus introducing inaccuracy in the calculated Pc. (See Appendix N 

for a more detailed discussion of Pc calculation methods and related issues.)
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Software (including source code, test cases, and documentation) to calculate the Pc using both 

the traditional two-dimensional and (when validated) the presently recommended threedimensional technique and to remove correlated error between the primary and secondary 

covariances can be obtained free of charge at the public-facing CARA software repository. (See 

Section 7 in this document for the specific URL.)

The value of the Pc threshold at which an O/O would choose to mitigate a conjunction is a 

function of both the O/O’s risk tolerance and the volume of conjunctions that the O/O is able to 

mitigate. In the conjunction assessment mission area, however, there has been broad 

convergence on a per-event Pc mitigation threshold value of 1E-04, meaning that remediation 

actions are recommended when the likelihood of collision is greater than 1 in 10,000. Missions 

that wish a more conservative risk posture can select a more demanding Pc threshold such as 

1E-05. This infused conservatism may allow more streamlined risk assessment techniques in 

other areas. 

Finally, some practitioners like to include an additional imperative to mitigate when the 

predicted miss distance is smaller than the hard-body radius or a distance close to the hard-body

radius value. This predicted miss distance approach would need to be invoked only rarely 

because a small miss distance typically produces a Pc that violates most commonly accepted Pc

mitigation thresholds. (See Appendix N for more information about the hard-body radius

calculation.)

Other risk assessment methods exist (e.g., Alfano 2005b, Carpenter and Markey 2014, Balch et 

al. 2019) and are generally considered to be more conservative than the Pc-based methodology 

advocated above. O/Os are encouraged to employ a more conservative conjunction assessment

approach if it suits their risk posture. However, the Pc method and the mitigation threshold of 

1E-04 enjoy wide acceptance in the conjunction assessment industry and historically have 

provided a sustainable balance between safety and mission impact.

Risk is the product of the likelihood of an unfavorable event and the consequence of that event, 

should it occur. For some time, it has been presumed that any satellite collision is a catastrophic 

event that is to be avoided by any means possible. In most cases, such events will render an 

active satellite unusable, presenting a very serious risk to the O/O. Therefore, the likelihood (Pc) 

was computed, and the consequence was not factored into the computation.

However, as the orbit environment grows, there may come a point when an O/O is faced with too 

many conjunctions to avoid individually. In this case, one method to triage the conjunctions to 

determine which should be mitigated to best protect both the spacecraft and the orbital 

environment is computation and application of the consequence as part of the risk determination. 

Satellite collisions, depending on satellite masses and relative velocity, can produce wildly 

different amounts of orbital debris from a handful of pieces to many thousands of pieces large 

enough to critically damage a spacecraft. To be sure, introducing any debris at all into the space 

environment is to be avoided. Conjunctions that, if they were to result in a collision, would 

produce only a small amount of debris (maybe fewer than 50 pieces) could be addressed using a

more lenient mitigation threshold to prioritize them appropriately against those that would create 

more debris. A threshold that is an order of magnitude more lenient than what is used for high-
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debris conjunctions would align in magnitude with other situations in which relaxing the 

mitigation threshold is warranted (Hejduk et al. 2017). (See Appendix O for a more expansive 

treatment of the assessment of a conjunction’s debris production potential. See the CARA 

software repository for software to calculate debris production potential; see Section 7 in this 

document for the specific URL.)

Finally, the data used to calculate the parameters that feed the risk assessment decision, namely 

the state estimates and accompanying uncertainty volumes (covariances) for the primary and 

secondary objects, must be examined to determine whether they manifest problematic elements 

that would prevent the calculated parameters from serving as a basis for conjunction mitigation 

actions. In such cases, it is possible that executing a mitigation action based on those data could 

make the conjunction situation worse rather than better. 

A non-actionability situation with USSPACECOM conjunction assessment products occurs 

occasionally. For example, an object whose state has been propagated longer than the orbit 

determination fit-span in order to reach TCA is considered under most conditions to be 

insufficiently tracked and over-propagated and thus not suitable as a basis for conjunction

mitigation actions. (See Appendix P for a recommended procedure to evaluate USSPACECOM 

conjunction assessment products for actionability.) Occasionally one of the two objects in a 

conjunction lacks a covariance, making probabilistic conjunction assessment impossible but still 

enabling other risk assessment methods. (See Appendix P for a discussion of such situations.)
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To address this topic, the following specific practices are recommended:

A. Use the Probability of Collision (Pc) as the principal collision likelihood 

assessment metric.

B. Pursue mitigation if the Pc value exceeds 1E-04 (1 in 10,000). 

C. Pursue mitigation if the estimated total miss distance is less than the hard-body

radius value.

D. Employ the current operational NASA Pc calculation methodology for routine Pc

calculation. Consider removing correlated error from the primary and secondary 

object joint covariance. 

E. As a prioritization method for situations in which the number of conjunctions 

meeting mitigation criteria exceeds the ability of the O/O to mitigate, estimate the 

amount of debris that a conjunction would produce if it were to result in a 

collision. A less stringent Pc an order of magnitude lower could be appropriate in 

such cases.

F. If employing USSPACECOM data products for conjunction assessment, use the 

procedure given in Appendix P to determine whether the data for a particular 

conjunction are actionable and thus constitute a basis for conjunction assessmentrelated decisions.

G. If a different conjunction assessment product provider is chosen, develop and 

employ data actionability criteria for this provider’s conjunction assessment

information to determine conjunction assessment event actionability.

Conjunction Risk Mitigation

O/Os with satellites that possess the ability to mitigate conjunctions have a responsibility to 

perform mitigation actions when required. In practical terms, this means that a mitigation action 

should be tendered when a conjunction’s risk parameter, usually the Pc, exceeds the mitigation 

threshold at the “maneuver commitment point,” which is that point in time before the TCA when

a decision to mitigate is needed in order for the mitigation action to be in place before the TCA 

actually occurs. The most typical (and effective) mitigation action is changing the satellite’s

trajectory to avoid a possible collision with the secondary either by thrusting to effect a satellite 

maneuver or, in some cases, changing the satellite’s attitude to alter its drag coefficient and thus 

its trajectory. An additional, although generally much less effective approach is to change the 

satellite’s attitude simply to reduce the satellite’s cross-sectional area in the direction of the 

oncoming secondary. This does not fully mitigate the close approach but reduces the likelihood 

of an actual collision between the two objects.

When planning a mitigation action, the general practice is to choose a trajectory alteration that 

reduces the Pc for the conjunction by 1 to 2 orders of magnitude. A recent study (Hall 2019a) 

showed that a Pc reduction by 1.5 orders of magnitude (that is, by a factor of ~0.03) marked the 

beginning of diminishing return with regard to lifetime satellite collision risk. Therefore, NASA 

recommends a minimum of 1.5 orders of magnitude reduction in Pc as a post-mitigation Pc goal;
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i.e., if the recommended mitigation threshold of 1E-04 is used, the post-mitigation goal would be 

~3.2E-06 or lower. 

In general, there is a trade-off between mitigation maneuver size and maneuver execution time. 

To mitigate a conjunction adequately, smaller maneuvers can be used if the maneuver is made 

earlier; that is, farther in advance of TCA. Waiting until closer to TCA will typically require a 

larger maneuver to achieve the same Pc reduction. However, because most conjunction events 

drop off to a low level of risk before TCA (due to additional tracking and improved state 

estimates and covariances), waiting until closer to TCA to perform a mitigation action increases 

the likelihood that it can be determined not to be necessary. Thus, O/Os must decide in each case 

whether they wish to act earlier with a less invasive action required or whether they wish to wait 

until closer to TCA in the hopes of observing the collision likelihood drop below the mitigation 

threshold and thus being able to waive off the maneuver, but knowing that, if an action is still 

required, it will be larger and more disruptive. There is no clear rubric for how to proceed in such 

cases, but external considerations, such as staffing availability for a later maneuver and amount 

of disruption that a large maneuver would require, often govern the decision.

When performing a trajectory-changing mitigation action, “new” conjunctions and/or elevated

Pc values of existing conjunctions often occur. O/Os should ensure any mitigation action does 

not render the overall safety-of-flight evaluation worse by producing a more dangerous situation 

than would have existed without the mitigation action. One could examine the amalgamated risk 

of all the conjunctions in the near future and conduct mitigation planning on this basis, but it is 

generally acceptable to pursue mitigation of the one conjunction that violates the threshold (and 

remediate it to a Pc 1.5 orders of magnitude below the threshold) while ensuring that no new 

conjunctions are produced that exceed the threshold. Using the thresholds recommended here, 

this means bringing the violating conjunction down to a Pc of 3.2E-06 without introducing or 

raising any other conjunction Pc values above 1E-04. The best way to ensure that these standards 

are met is to generate an ephemeris that includes the mitigation action and submit it to the 

screening provider for a special screening action. This will produce a fresh set of CDMs against 

the planned mitigation action and allow easy and reliable verification that the Pc values for both 

the principal conjunction and any ancillary conjunctions remain below the desired levels. 

Using larger screening volumes and analyzing the maneuver against the resulting CDMs is 

another method of determining whether the maneuver creates close approaches. This method 

creates CDMs for conjunctions that are somewhat far away from the nominal trajectory but 

might constitute worrisome conjunctions after a maneuver. This method for ensuring the safety 

of the post-maneuver trajectory is serviceable for debris objects, which will not alter their orbits 

beyond Keplerian models. However, this method does not protect against potential, yet-to-bedisclosed trajectory changes by other maneuverable satellites.

Choosing a mitigation action for a conjunction against a non-maneuverable secondary is 

generally straightforward, but the situation is much more complicated when the secondary object 

is an active, maneuverable spacecraft. While submitted ephemerides from that secondary’s O/O

is a statement of that spacecraft’s intended trajectory at the time of production, it is likely that the 

secondary’s O/O has also noticed the conjunction and may be planning a mitigation action of its 

own. In addition to the fact that two mitigation actions for the same close approach are 
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unnecessary, there is a real danger that the two mitigation actions could place the two satellites 

on even more of a collision course than taking no action at all. 

Establishing contact with the O/O of an active secondary is critical to jointly establishing a way 

forward for the particular conjunction. The O/Os should jointly decide which satellite will pursue 

mitigation (should it remain necessary at the maneuver commitment point) and what the 

mitigation action will be and constrain the trajectory of the non-mitigating satellite to that given 

in its published ephemeris until after the TCA has passed. 

Given the recent industry trend to extremely large satellite constellations, the individual reaching

out to other O/Os is unlikely to scale adequately as such constellations continue to grow. A more 

automated mechanism for exchanging maneuver intentions among O/Os will likely be necessary. 

SPD-3 directs the movement of conjunction assessment activities away from DOD to a Federal 

civil agency by 2024, so it makes sense for this new entity to develop an architecture and 

protocol for the exchange of this type of information. For the present, O/Os need to share their

maneuver intentions with other O/Os through direct contact or a third-party organization, such as 

the Space Data Association9 with some amount of manual interaction required.

9 An international organization that brings together satellite operators to support the controlled, reliable, and efficient 

sharing of data critical to the safety and integrity of the space environment. The Space Data Association membership 

includes the world’s major satellite communications companies.
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To address this topic, the following specific practices are recommended:

A. When a conjunction’s Pc at the mitigation action commitment point exceeds the 

mitigation threshold (recommended to be 1E-04), pursue a mitigation action that 

will reduce the Pc by at least 1.5 orders of magnitude from the remediation 

threshold. 

B. Ensure that an ephemeris containing the mitigation action is screened against the 

full catalog, not a large screening volume collection of CDMs.

C. Ensure that the mitigation action does not create any additional conjunctions with 

a Pc value above the mitigation threshold (for which the recommended value is 

1E-04).

D. When the secondary object is an active, maneuverable spacecraft, reach out to the 

secondary’s O/O and jointly establish a way forward for the particular 

conjunction, including deciding which spacecraft will maneuver and freezing the 

other spacecraft’s planned trajectory until the TCA has passed.

E. Use space-track.org contact information to engage other O/Os.

Automated Trajectory Guidance and Maneuvering

Satellite designers are increasingly taking advantage of the automation of maneuver planning and 

execution to simplify mission operations. Particularly with large constellations of satellites, 

automation can substantially increase efficiency over traditional flight control techniques. 

However, the automation processes in which flight dynamics computations and decision making 

occur largely or even entirely without human intervention, and especially when they are executed

on board the satellites themselves, can present real concerns related to space traffic management 

and the prevention of collisions between satellites. 

With traditional ground-computed and executed trajectory adjustments that have humans in the 

loop, satellite operators can compute maneuvers, produce predicted ephemeris data to transmit to 

the rest of the community to be screened for conjunctions, and command the execution of safe

maneuvers to effect that advertised trajectory. Admittedly, such a technique does not scale easily 

for large constellations, but it has proven reliable and serviceable for securing safety of flight 

over years of experience.

However, highly automated systems can now be designed in which satellites, using onboard

navigation and a programmed target, can compute their own maneuvers and execute them 

without notification to, or pre-coordination with, their ground control; in such a case, explicit 

screening of the maneuver by USSPACECOM or some other screening authority, as well as 

notification to the rest of the space community, would frequently not be possible. If other space 

operators are not aware that a satellite is planning a maneuver, the other operators may also plan 

a maneuver and the two maneuvers taken together may cause a collision. 

Operators of automated satellite systems should ensure that, when contemplating a maneuver, the 

intended time, direction, and magnitude of that maneuver (as well as other event-related data for 

conjunction risk maneuvers) be communicated to the screening authority at a sufficient interval 
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of time before the maneuver so that the maneuver ephemeris can be screened before execution.

This communication is most important in ensuring safety of flight between active maneuverable 

spacecraft, each of which may be generating maneuver plans that, if executed as intended, will 

create a collision. Maneuver plans should be shared with the screening authority as a predicted 

ephemeris and, if possible, a maneuver notification report; and it is highly desirable that this 

information be shared without restriction, perhaps by posting predicted ephemerides so that any 

interested party can download them, without restriction. 

One method that some operators use to facilitate maneuver planning is to request from the 

screening authority the use of a screening volume size that encompasses a large amount of 

orbital space, ensuring that they receive a large set of CDMs that is representative of all the 

spacecraft operating nearby. The operators then use these CDMs to internally plan maneuvers 

and screen them against this set of CDMs to ensure that the planned maneuver does not cause a 

close approach with any of the objects for which they have CDM data. While largely effective 

against non-maneuvering objects, this practice cannot fully account for the fact that the other 

objects may themselves be maneuverable spacecraft also altering their trajectories. So, if both 

maneuverable spacecraft do not send their predicted trajectories back to the screening authority 

for reconciliation, they will not be aware of each other’s plan and may in fact cause a collision.

At some point in the future, an automated clearinghouse may be in place for such information to 

allow near real time receipt and circulation of ephemerides containing maneuver plans to other 

O/Os. There is work underway at NASA in partnership with industry to design and prototype a 

ground node that includes near-real-time screening of submitted ephemerides, as well as 

mechanisms for the two spacecraft to assign responsibility for mitigating a specific conjunction. 

Hopefully, this capability will be available as part of the Office of Space Commerce’s future 

space traffic coordination system. Quick and efficient screening of planned maneuvers generated 

by onboard systems requires the creation and operation of this central, low-latency ephemeris 

“clearinghouse.” So, to achieve this future vision of safe operations, both industrial and 

governmental action is necessary. 

At present, however, the USSPACECOM screening process is performed only once every 8 

hours. It is possible that a file received from an operator may just miss a screening opportunity, 

and therefore it may take up to16 hours to screen the predicted trajectory. Therefore, spacecraft 

using this information to plan onboard maneuvers are obligated to allow this much time in 

advance for screening their maneuver prior to executing to ensure safety of other on-orbit 

neighbors. This timeline also affects non-autonomous spacecraft, as they want to ensure that 

their planned trajectory is taken into account by the autonomous spacecraft, so they also must 

include the 16 hour advance notice, although that timeline is more typical for traditional groundbased flight dynamics processes.

Once a maneuver is autonomously planned and submitted for screening, the maneuver should be 

executed as designed unless an alteration is required for safety of flight. Remaining with the 

communicated plan, even if more efficient possibilities arise in the interval leading up to 

maneuver execution, enables the rest of the space community to use the submitted ephemeris as 

the basis for their own trajectory planning.
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There may be situations in which a satellite should not execute an intended maneuver that the 

automation computes, such as in the presence of a surprise post-maneuver conjunction or a 

conjunction with an active satellite involving cooperative, human-in-the-loop conjunction event 

management. It is thus imperative for safety reasons that automated systems include the ability to 

pause or abort any maneuver planned for execution in response to ground command.

To address this topic, the following specific practices are recommended for use by operators 

of constellations with automated flight dynamics systems:

A. When an onboard flight dynamics system computes any maneuver to alter the 

satellite’s orbit for mission or conjunction mitigation purposes, communicate 

maneuver details to the operating ground control early enough to enable a

USSPACECOM screening and appropriate action in response to the screening 

results.

B. Share maneuver plans with USSPACECOM both as a predicted ephemeris with 

realistic covariance and, when possible, as a maneuver report. Allow these 

notifications to be publicly viewed and downloaded by any interested party. 

C. Execute a maneuver as intended once a maneuver is autonomously planned and 

externally communicated unless an alteration is required for safety of flight. 

D. Include the ability to pause or abort, for safety reasons, any maneuver planned by 

the automated system, regardless of whether the maneuver is planned by a ground 

system or on board the satellite.

E. Ensure an automated maneuvering system can temporarily suspend automatic 

conjunction assessment activities to allow another operator to maneuver. 

F. Rapidly submit a new ephemeris for screening if a maneuver is not executed as 

planned in the original file sent for screening, such as if a maneuver fails.

G. Keep spacecraft maneuverability status on space-track.org up-to-date so other 

O/Os know whether any particular satellite is capable of maneuvering.

H. If onboard flight dynamics planning is used, be able to communicate back to 

operational secondary satellite O/Os that the relevant information to enable a 

maneuver to mitigate a conjunction between them is on board the satellite and 

will be acted upon.

I. Request a larger-than-average screening volume from your screening provider to 

ensure that the “snapshot” of the space catalog available to your satellites is 

broadly inclusive and thus allows maneuver planning to take cognizance of all 

possible hazards in choosing a new trajectory. This maximizes the chances that, 

when screened before execution, the chosen maneuver will be safe.

Other Considerations

The items in this section are best practices that affect orbit design and so, while not directly 

related to the conjunction assessment process, are appropriate to consider.
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Light Pollution. After the launch of the initial portion of the SpaceX Starlink constellation, 

astronomers noticed that their observing campaigns were being affected by extremely bright, 

detector-saturating streaks due to the Starlink vehicles. To minimize interference with Earthbased astronomy, O/Os should ensure that spacecraft are built and flown in such a way as to 

minimize the creation of light pollution. 

Adverse astronomical effects arise from satellites reflecting sunlight (e.g., in the visible and nearinfrared (IR) spectral bands) and emitting radiation (e.g., in the thermal-IR and radio bands), as 

well as from occultations in which satellites block the light from astronomical objects. Groundbased sensors in the visible and near-IR bands are most challenged by constellations with 

satellites that are brighter than about 7

th stellar magnitude and that glint brightly in reflected 

sunlight, especially if deployed at inclinations close to the observatory latitude, and, 

counterintuitively, at higher orbital altitudes (Walker et al. 2020; Bassa et al. 2022). Comparable

orbit inclinations and observatory latitudes result in significantly more frequent crossings of the 

telescope’s field of view. Higher altitudes result in a lower relative velocity between satellite and 

telescope, which increases dwell-time on each sensor pixel, causing saturation that irreparably 

contaminates data. Lower altitude satellites also tend to enter Earth’s shadow earlier during 

astronomical nighttime periods, decreasing the duration of their adverse effects, even though 

they still can cause light pollution during twilight periods. 

To preserve the appearance of the night sky and limit adverse effects on ground-based 

observations, the consensus recommendation of the astronomical community is to keep satellites 

fainter than the recommended V-band magnitude limit of MV = 7 + 2.5 log10(h/550km), with 

h indicating the altitude (Walker et al. 2020). This corresponds to MV = 7 for the population of 

Starlink constellation satellites currently deployed at 550 km altitude, and MV = 7.85 for the 

OneWeb satellites at 1,200 km. Factors that affect the brightness of individual satellites include 

size, albedo, surface characteristics, degree of specular vs diffuse reflection, self-shadowing, and 

orientation, as well as observation and illumination ranges and angles. Both a constellation’s 

overall population and individual satellite brightnesses are important considerations because 

ground-based observations will be affected significantly by the existence of large numbers of 

bright satellites during astronomical nighttime observing conditions. Hall (2022) describes a 

method of evaluating light pollution levels for proposed or nascent constellations that

incorporates a constellation’s population, orbital distribution, and empirical or modeled 

brightness distribution to estimate the number of brighter-than-recommended satellites 

statistically expected to exist above observatories distributed over the Earth and throughout a 

year. Notably, using this method, if all of a constellation’s satellites are consistently fainter than 

the recommended MV limit given above, then even a large constellation could be evaluated to 

have acceptable visible and near-IR band light pollution levels. (This evaluation method is 

included in the EvaluateConstellation function of the Software Development Kit (SDK) in the 

NASA CARA software repository. See Section 7, Contact Information in this document for the 

specific URL.)

For constellations duplicating the same (or similar) manufacturing design for a large satellite 

population, O/Os should not rely on rough analyses or first-order assumptions about expected 

brightnesses. Instead, a full satellite brightness model that includes Bidirectional Reflectance 
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Distribution Function (BRDF) characterization of surface materials should be undertaken during 

the design phase to estimate the brightness distributions of the deployed constellation. O/Os 

should consider all mission phases including launch, ascent, and descent (Seitzer 2020). The 

SATCON-1 Workshop10 Report (Walker et al. 2020) provides the following four specific 

recommendations for constellation O/Os to encourage careful up-front design to minimize 

brightness and avoid glints to the greatest extent possible:

• LEO constellation operators should perform adequate laboratory BRDF measurements as 

part of their satellite design and development phase. This would be particularly effective 

when paired with a reflectance simulation analysis.

• Reflected sunlight ideally should vary slowly with orbital phase as recorded by high 

etendue (effective area  field of view), large-aperture ground-based telescopes to be 

fainter than 7 + 2.5 log10(h/550km), equivalent to 44  (550km/h) W/steradian.

• Operators should make their best effort to avoid specular reflection (flares) in the 

direction of observatories. If such flares do occur, accurate timing information from 

ground-based observing will be required for avoidance.

• Pointing avoidance by observatories is achieved most readily if the immediate postlaunch satellite configuration is clumped as tightly as possible consistent with safety, 

affording rapid passage of the train through a given pointing area. In addition, satellite 

attitudes should be adjusted to minimize reflected light on the ground track.

If possible, brightness distributions should also be measured using ground-based photometric 

observations of actual satellites (if already orbiting for partially deployed constellations) or 

scaled from observations of orbiting prototype/analog satellites based on a similar manufacturing 

design (if available). Hall (2022) describes how such empirical, ground-based brightness 

distributions can be used to estimate astronomical light pollution levels, even for constellations 

deployed in multiple altitude shells and with different inclinations. The SATCON-2 Workshop 

Report (Walker et al. 2021) describes the on-going effort to establish the “Sathub” repository of 

photometric observations of constellation satellites, as well as several software tools to aid both 

astronomers and constellation O/Os in the effort to mitigate astronomical light pollution.

10 The National Science Foundation’s (NSF’s) National Optical-Infrared Astronomy Research Laboratory

(NOIRLab) and the American Astronomical Society, with support from NSF, hosted the Satellite Constellations 1 

(SATCON1) workshop virtually from 29 June to 2 July 2020.
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To address this topic, the following specific practices are recommended:

A. As part of spacecraft physical design and orbit selection, perform a spacecraft 

photometric brightness analysis to determine whether the spacecraft is likely to 

present an impediment to ground-based astronomy. Consider changes to the 

satellite’s construction, materials, or operating attitudes to reduce expected 

photometric brightness to levels that will not impede ground-based astronomy. 

B. If a large constellation is being planned, either use a full BRDF-based 

photometric model or ground-based observations of actual orbiting satellites, if 

available, to obtain a durable estimate of the entire constellation’s expected 

brightness distribution as deployed on orbit.

C. If the constellation, given its population, orbit, and constituent satellites, is likely 

to affect ground-based astronomy, reassign the satellite orbits or modify the 

satellite construction to eliminate this effect.
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7.0 Contact Information

Below is the contact information for the resources mentioned in this handbook.

Table 7-1 NASA Contact and Reference Information

NASA JSC FOD Human Space Flight Conjunction Assessment Operations

jsc-dl-topo-iwg@mail.nasa.gov

NASA CARA NASA CARA Operations 

cara-management@lists.nasa.gov

NASA CARA 

Software 

Repository

https://github.com/nasa/CARA_Analysis_Tools

For NASA personnel, CARA or JSC FOD serves as the single point of contact between NASA 

and DOD (e.g., 18 SDS and USSPACECOM) for SSA data and support required for conjunction 

assessment and risk analysis of NASA missions. The roles of CARA and JSC FOD are defined 

in NPR 8079.1. 

For non-NASA personnel, Table 7-2 provides useful points of contacts.

Table 7-2 Contact and Reference Information for Non-NASA Personnel

Organization Contact Information and URLs of Interest

USSPACECOM / 

18 SDS

Diana McKissock; Cynthia Wilson

18SPCS.DOO.CustomerService@us.af.mil

+1-805-606-2675

Spaceflight Safety Handbook for Satellite Operators

https://www.spacetrack.org/documents/Spaceflight_Safety_Handbook_for_Operators.pdf

Launch Conjunction Assessment Handbook

https://www.space-track.org/documents/LCA_Handbook.pdf

Space-Track Handbook for Operators

https://www.spacetrack.org/documents/Spacetrack_Handbook_for_Operators.pdf
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Organization Contact Information and URLs of Interest

Description of Space Situational Awareness Sharing basic and advanced 

services, forms, and data examples: 

https://www.space-track.org/documentation#/odr

USSPACECOM USSPACECOM.SSA.Agreement-Requests@us.af.mil

NASA Examples NASA Examples of Information to Expedite Review of Commercial 

Operator Applications to Regulatory Agencies: 

https://www.nasa.gov/recommendations-commercial-space-operators

To provide feedback on this handbook, email: ca-handbook-feedback@nasa.onmicrosoft.com
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Appendix A. Acronyms 49

Appendix A. Acronyms

2D Two-Dimensional

3D Three-Dimensional

ASW Astrodynamics Support Workstation (tool)

BC Ballistic Coefficient

BRDF Bidirectional Reflectance Distribution Function

CARA Conjunction Assessment Risk Analysis (Program)

CCSDS Consultative Committee for Space Data Systems

CDF Cumulative Distribution Function

CDM Conjunction Data Message

COLA Collision on Launch Assessment

COMBO Computation of Miss Between Orbits (algorithm)

CONOPS Concept of Operations

DISCOS Database and Information System Characterising Objects in Space

DOD Department of Defense

EDR Energy Dissipation Rate

FOD Flight Operations Directorate at NASA JSC

GEO Geosynchronous Orbit

GPS Global Positioning System

HAC High Accuracy Catalog

HBR Hard-Body Radius

HEO High Earth Orbit

HST Hubble Space Telescope

ISS International Space Station

JSC Johnson Space Center

LCOLA Launch Collision Avoidance 

LEO Low Earth Orbit

LUPI Length of Update Interval

MC Monte Carlo
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MVN Multi-Variate Normal (function)

Nc Number of Collisions (statistically expected)

NASA National Aeronautics and Space Administration

Nmc Number of Monte Carlo (trials)

NPR NASA Procedural Requirements

ODM Orbit Data Messages (CCSDS standard)

ODMSP Orbital Debris Mitigation Standard Practices

ODPO Orbital Debris Program Office

O/O Owner/Operator

Pc Probability of Collision

PDF Probability Density Function

R-15 Ready Minus 15 (days, message format)

RCS Radar Cross Section

SDK Software Development Kit

SDS Space Defense Squadron (U.S. Space Force)

SGP4 Simplified General Perturbation Theory #4

SPD-3 Space Policy Directive-3, the National Space Traffic Management 

Policy

SRP Solar Radiation Pressure

SRPC Solar Radiation Pressure Coefficient

SSA Space Situational Awareness

SSN Space Surveillance Network

SWTS Space Weather Trade Space

TBMC Two-Body Monte Carlo 

TCA Time of Closest Approach

TLE Two-Line Element

URL Uniform Resource Locator

U.S. United States

USSPACECOM U.S. Space Command

VIM Vehicle Information Message
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Appendix A. Acronyms 51

VSFB Vandenberg Space Force Base

WRMS Weighted Root Mean Square
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Appendix B. Glossary 52

Appendix B. Glossary

Cislunar Space. Cislunar space is the three-dimensional volume of space beyond Earth’s 

geosynchronous orbit that is mainly under the gravitational influence of the Earth and/or the 

Moon. Cislunar space includes the Earth-Moon Lagrange point regions (defined below), 

trajectories utilizing those regions, and the Lunar surface. (Taken from the “National Cislunar 

Science & Technology Strategy” from the National Science & Technology Council’s Cislunar 

technology strategy Interagency Working Group.)

COLA Gap. The period between when traditional LCOLA ends and an on-orbit asset can 

mitigate a risk using standard on-orbit conjunction assessment methods (i.e., until the object can 

be cataloged and is available for conjunction assessment screening).

Collision Avoidance. The planning and execution of risk mitigation strategies to avoid a 

collision between two space objects. (See also conjunction mitigation.).

Colocation. Being in the vicinity of another operational spacecraft close enough that systematic 

conjunctions occur.

Conjunction. A close approach between two objects that is predicted to occur because the 

secondary object passes within a chosen geometric or statistical safety volume about the 

protected asset (also called “primary object”).

Conjunction analysis. The process of predicting a close-approach event by screening the 

ephemeris of the protected asset against the space object catalog (i.e., conjunction assessment) 

and then analyzing the event to determine the associated threat to the asset (risk assessment).

Conjunction Assessment. The identification of close approaches using ephemeris screening 

against a catalog of resident space objects.

Conjunction Mitigation. An action taken to remediate conjunction risk, including a propulsive 

maneuver, an attitude adjustment (e.g., for differential drag or to minimize frontal area), or 

providing ephemeris data to secondary owner/operators so that they can perform an avoidance

maneuver.

Conjunction Risk Assessment. The process of assessing a conjunction (predicted close 

approach) to determine the likelihood of two space objects colliding and to determine the 

expected consequence if they collide in terms of spacecraft inoperability and expected debris 

production.

Covariance. Characterization of uncertainty components and their interactions surrounding a 

space object’s estimated state at a given time.

Demise. When a spacecraft is no longer in space such as a complete burn up on reentry. 

Spacecraft passivation and migration to disposal orbits occur prior to demise.

Disposal. An end-of-mission process involving a spacecraft’s passivation and reentry into the 

atmosphere for its ultimate demise or its movement (if necessary) to an orbit or trajectory 

considered acceptable for orbital debris limitation. For purposes of this NPR, “disposal” includes 
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Appendix B. Glossary 53

the reorbiting or deorbiting of a spacecraft at the end of mission. Disposal occurs prior to 

spacecraft demise.

Ephemeris (plural: ephemerides). A file containing a time-ordered set of position and velocity 

measurements describing an object's predicted trajectory.

Geosynchronous Orbit (GEO). An orbit with period between 1300 and 1800 minutes, 

eccentricity (e) <0.25, and inclination (i) <35 degrees. Note that this definition is chosen to align 

with the definition used by USSPACECOM, which provides conjunction assessment screenings.

Hard-body radius. The radius of a circle equal to the sum of the circumscribing radii of both the 

protected plus the secondary spacecraft.

High Earth Orbit (HEO). An orbit with period greater than 225 minutes and eccentricity 

greater than 0.25. Note that this definition is chosen to align with the definition used by 

USSPACECOM, which provides conjunction assessment screenings.

Low Earth Orbit (LEO). An orbit with an orbital period less than 225 minutes and eccentricity 

less than 0.25. Note that this definition is chosen to align with the definition used by 

USSPACECOM, which provides conjunction assessment screenings. 

Maneuver Plan. The specific parameters that represent a planned spacecraft maneuver, 

including execution time, burn duration, and delta-v. The position and velocity of a single object

at a specified epoch is specified in an Orbit Parameter Message (OPM). The industry message 

standard for communicating maneuver plans is the Consultative Committee for Space Data 

Systems (CCSDS) standard CCSDS 502.0-B-2, “Orbit Data Messages,” Section 3 located at 

https://public.ccsds.org/Pubs/502x0b2c1e2.pdf.

Maneuverable. Capability to carefully and skillfully guide or manipulate a spacecraft, such as to

avoid an orbital conjunction.

Maneuverable spacecraft. A spacecraft that has capability permitting the manipulation of the 

spacecraft’s trajectory in a non-Keplerian fashion.

Non-cooperative tracking data. Data obtained describing the location of space objects that do

not themselves actively provide location data. For example, a piece of orbital debris that has no 

transponder could not provide ephemeris data. Other examples include natural objects such as 

asteroids, and spacecraft belonging to operators who do not choose to share an ephemeris for 

their spacecraft.

Non-Human Space Flight Mission. A NASA space flight mission that is not related to human 

space flight, i.e., non-human space flight. These space flight missions are supported by the 

CARA Program.

Orbit Regime. The general location of an orbit in space, such as the perigee height and whether 

the orbit is eccentric, used to assign it to a general orbit category.

Orbital debris. In this NPR, orbital debris is defined as any object placed in space by humans 

that no longer serves any useful function. Objects range from spacecraft to spent launch vehicle 
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Appendix B. Glossary 54

stages to components and include materials, fragments, trash, or other objects that are 

intentionally or inadvertently cast off or generated. (Derived from NPR 8715.6.) 

Payload. A specific complement of instruments, sensors, equipment, and support hardware 

carried into space to accomplish a mission or a discrete activity in outer space. Personnel are not 

considered a payload or a part of a payload. 

Protected asset. The asset of focus (also called “primary object”) for which risk assessments of 

potential collisions are being performed and collision avoidance mitigation activities are being 

considered and possibly performed. 

Resident space object. An artificial object that orbits Earth.

Safety volume. A volume defined around a protected asset as a zone for predicting close 

approaches with a “secondary” space object entering that volume.

Secondary object. Any cataloged object residing in space that passes through the safety volume 

of a protected (i.e., primary) asset when the protected asset with its safety volume is flown along 

its trajectory. The resident space object is identified as a “secondary object” and is the 

conjuncting object in a predicted future close-approach event. The secondary object may be an 

operated spacecraft.

Secondary payload. A payload that is manifested subordinate to a primary or co-manifested 

payload and is, therefore, subordinate in launch date and orbit selection. (See also “payload,” 

“primary payload,” and “rideshare.”)

Space Flight Mission. NASA space flight programs, projects, and activities (including 

spacecraft, launch vehicles, payloads, and instruments developed for space flight programs and 

projects, some research and technology developments funded by and to be incorporated into 

space flight programs and projects.

Space situational awareness. The knowledge and characterization of space objects and their 

operational environment to support safe, stable, and sustainable space activities. (From Space 

Policy Directive-3.)

Space Surveillance Network. A network of radar and optical sensors used by DOD to track 

space objects. Tracking data is used to perform orbit determination and maintain the space object 

catalog.

Systematic Conjunction. A situation in which two space objects repeatedly experience close 

approaches with each other due to their similar orbits.
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Appendix C. Best Practices List 55

Appendix C. Best Practices List

This appendix contains a summary list of the best practices found in this document. NASA 

missions should use Appendix D, Best Practices for NASA Missions, instead for a list that 

integrates internal NASA services and requirements.

Table C-1 Best Practices Summary

Section Best Practice Comment

3.0 History

3.2 USSPACECOM Conjunction Assessment Process

3.2.A Obtain a space-track.org account.

3.2.B Become familiar with the Spaceflight Safety Handbook

contents.

3.2.C Use USSPACECOM conjunction assessment service as a 

minimum for screenings, even if additional commercial data or 

services are used.

3.2.1.A Provide seven (7) days of predicted ephemeris (including 

maneuvers) to USSPACECOM for screening for LEO 

spacecraft, and provide 14 days for other Earth orbits; e.g., High 

Earth Orbit (HEO)/Geosynchronous Orbit (GEO).

3.2.2.A Provide at least one ephemeris per day to be screened and three 

ephemerides per day in the lower-drag LEO regime (perigee 

height less than 500 km).

3.2.2.B Determine whether the O/O’s process for obtaining screening 

results and performing conjunction risk assessment aligns with 

the timeline of the USSPACECOM process. If the timelines do 

not align in such a way as to enable timely and efficient 

screening support, pursue a rearrangement of the O/O’s process 

to minimize data latency and optimize screening efficiency.

3.2.3.A Populate and maintain the point-of-contact section on spacetrack.org with your operations contact data. Be sure that the 

operations contact can be reached 24/7 due to time zone 

differences between operators and the immediate nature of 

certain conjunction assessment emergencies.

3.2.3.B Use standard ephemeris, CDM, and maneuver notification 

formats defined by the Consultative Committee for Space Data 

Systems (CCSDS).

3.3 NASA Partnership with USSPACECOM

3.3.A Develop a robust safety-of-flight process that includes both 

conjunction assessment screening and risk assessment to inform 

close approach mitigation decisions.
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Section Best Practice Comment

3.3.B Large constellation operators should work with USSPACECOM 

pre-launch to determine if variations from the standard approach 

are necessary and, if so, to define a tailored screening process.

3.3.C Large constellation operators should consider working with 

NASA to define a risk assessment process. NASA is an 

experienced representative operator. Including NASA in 

discussions regarding establishing a conjunction assessment

process will ensure that the process will work with most 

operators for risk assessment purposes. 

3.4.2.A Owner/operators should conform to recommendations in the 

NASA Technical Publication “Astrodynamics Convention and 

Modeling Reference for Lunar, Cislunar, and Libration Point 

Orbits.”

3.4.2.B Cislunar mission support entities (sensors, catalog maintainers, 

etc.) should conform to the enhanced SSA message set (Butt 

2021) when creating cislunar SSA architectures.

3.4.2.C Owner/operators should maintain accurate orbit determination 

solutions and predicted covariance for objects in cislunar space.

3.4.2.D Owner/operators should deliver predicted ephemeris with 

covariance in the CCSDS format to space-track.org and to the 

DSN SPS portal.

4.0 Spacecraft and Constellation Design

4.1 Ascent to/Disposal from the Constellation’s Operational Orbit

4.1.A Perform a study to compute the number of expected close 

approaches anticipated during ascent and descent as well as the 

imputed additional satellite reliability that will be required to 

meet satellite disposal requirements at the chosen operational 

orbit. 

4.1.B If the results of the study show a large burden, consider 

choosing a different mission orbit with a lower burden. 

4.1.C All missions should review and follow the ODMSP guidance 

standards.

4.1.D When practicable, pursue active disposal using the fastest 

disposal option available.

4.1.E Recognize that transiting spacecraft should yield way to onstation spacecraft and thus take responsibility for any 

conjunction risk mitigation maneuvers or transient trajectory 

alterations that may be required.

4.1.F When planning descent using thrusters, if not planning an 

approach of circular-orbit altitude reduction, coordinate with the 

NASA JSC TOPO to ensure that perigee-lowering approaches 
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Section Best Practice Comment

do not present persistent and problematic orbital crossings with 

the ISS and other human space flight assets.

4.2 General Orbit Selection: Debris Object Density

4.2.A Include considerations of orbital debris density when selecting 

candidate mission orbits. Debris density diagrams, indexed by 

object size, are published by the NASA Orbital Debris Program 

Office (ODPO). (See Appendix G for more information and 

examples.)

4.2.B When choosing from the final set of candidate orbits, perform a 

conjunction frequency analysis to determine the number of

conjunction assessment high interest events per spacecraft per 

year that can be expected in each of the proposed orbital areas. 

4.3 Vehicle- and Constellation-Specific Orbit Selection: Spacecraft Colocation

4.3.A During orbit selection, perform an orbit colocation analysis to 

determine whether any of the proposed orbits is likely to create 

systematic conjunctions with existing actively maintained 

satellites. 

4.3.B If the orbit colocation analysis identifies systematic 

conjunctions, consider modifying the proposed orbit(s) slightly 

to eliminate this possibility. Optimizing orbit placement may be 

appropriate.

4.3.C If the selected orbit is likely to present systematic conjunctions 

with a pre-existing spacecraft, then coordinate with the other 

operator(s) to arrange a process to coordinate maneuver plans 

routinely during the life of the mission.

4.4 Launch-Related Conjunction Assessment

4.4.A Protect human space flight assets from close approaches during 

the COLA gap using stand-off distance or statistical measures. 

4.4.B Conform to additional LCOLA requirements that the launch 

range may impose.

4.5 Spacecraft Trackability

4.5.A Through selection of physical design and materials, ensure that 

the satellite is trackable by SSN from deployment until demise.

a. For spacecraft with perigee heights less than 2000 km, the 

spacecraft should have characteristic dimensions of at least 

10 cm in each major dimension.

b. For spacecraft with perigee heights greater than 2000 km, 

the spacecraft should have characteristic dimensions of at 

least 50 cm in each major dimension.
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Section Best Practice Comment

c. If the spacecraft cannot meet these dimension constraints, 

use a proven detectability enhancement. 

d. For spacecraft having orbits that span a large range of 

altitudes, ensure that the spacecraft is trackable at all 

altitudes.

4.6 Spacecraft Reliability

4.6.A Ensure that spacecraft reliability is high enough that the 

likelihood of each spacecraft remaining fully functional until it 

can be disposed of meets or exceeds 99%.

4.6.B Reassess the 99% analysis whenever the underlying 

assumptions change; for example, extending operations beyond 

design life or failures in key systems.

4.7 Development of Capabilities for Ephemeris Generation and Conjunction Risk Assessment 

and Mitigation

4.7.A Develop and implement a capability to generate and share 

accurate predicted spacecraft ephemerides including any 

planned maneuvers. (See Section 3.1 for a discussion of 

ephemeris sharing for screening. See Section 6.2 for specific 

guidance on ephemeris generation frequency, length, point

spacing, formatting, and contents.)

4.7.B Determine during spacecraft design what risk mitigation 

approaches are possible for the spacecraft. While trajectory 

modification via thrusting maneuver is the most common

approach, other approaches such as differential drag orbit 

modification are possible.

4.7.C Develop and implement or arrange to acquire a capability to 

process CDMs and to compute conjunction risk assessment 

parameters such as the Pc.

4.7.D Develop and implement or arrange to acquire a risk analysis 

capability to select mitigation actions that will lower the Pc for 

dangerous conjunctions to a user-selected value.

4.7.E Validate conjunction assessment tools well before flight, 

typically 6-12 months prior.

5.0 Pre-Launch Preparation and Early Launch Activities

5.1 CONOPS Discussions and Arrangements with USSPACECOM Pertaining to Launch 

Phase

5.1.A Establish contact with USSPACECOM to describe and discuss 

all aspects of the launch including delivery and deployment 

methodologies. 
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Section Best Practice Comment

5.1.B Space the deployment of multiple spacecraft in a way that 

enhances the ability of USSPACECOM to quickly identify and 

differentiate the spacecraft using the SSN.

5.1.C Discuss the preparation of the R-15 launch form with 

USSPACECOM so that they understand its contents and any 

implications for safety of flight.

5.1.D Ensure that the launch provider submits the Form 22 and launch 

trajectory information to USSPACECOM, including 

ephemerides for the powered-flight portions and orbital 

elements for the parking orbits, so that potential colocation and 

deconfliction potentialities can be discovered. 

5.1.E Provide to USSPACECOM as soon as possible launch-related 

information (e.g., injection vectors and initial ephemerides for 

deployed spacecraft) that can be used to assist with the 

cataloging process, especially to confirm the identity of launchrelated objects. Coordinate a satellite numbering scheme 

(potentially including temporary satellite numbers) appropriate 

to the launch type and expected degree of cataloging difficulty.

5.1.F Coordinate with USSPACECOM any potential launch anomaly 

diagnostic products that can be provided if issues arise during 

the launch and early orbit sequence.

5.2 CONOPS Discussions and Arrangements with USSPACECOM and NASA Pertaining to 

On-Orbit Mission Phase

5.2.A Register the spacecraft with USSPACECOM using the Satellite 

Registration form on space-track.org. 

5.2.B Provide USSPACECOM with basic construction and mission 

information about the satellite such as stowed dimensions; 

deployable structures such as solar panels, antennae, booms, 

including all their (rough) dimensions; satellite material 

properties and colors; regular satellite attitude; and registered 

operational radio frequencies. 

5.2.C Provide USSPACECOM with a basic overview of the satellite’s 

orbit maintenance strategy including the paradigm for 

determining when orbit maintenance maneuvers are required; 

the maneuver technology used (as this relates to burn duration 

and expected accuracy); and the frequency, duration, and 

magnitude of typical burns. 

5.2.D Provide USSPACECOM with an understanding of the flight 

control and navigation paradigm, principally whether a groundbased control approach is followed or some degree of (or full) 

autonomous control is used. If the satellite control does include 

some autonomous flight dynamics or control features, indicate 
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Section Best Practice Comment

how much (if any) foreknowledge ground controllers have of 

autonomous maneuver actions, the amount of information that is 

communicated to the ground both before and after the maneuver 

(e.g., maneuver time, delta-V, direction), and whether groundbased overrides are possible.

5.3 CONOPS Discussions and Arrangements with USSPACECOM and NASA Pertaining to 

Conjunction Assessment

5.3.A Decide whether the USSPACECOM free service, a validated 

commercial conjunction assessment service, or both will be used 

by the mission. 

5.3.B Establish a service with the selected service provider.

5.3.C Implement a SSA sharing agreement with USSPACECOM to 

receive advanced data support and services.

5.3.D Through the registration of the satellite with USSPACECOM, 

begin the process of arranging for conjunction analysis data 

exchange including O/O ephemerides, maneuver notification 

reports, and CDMs. USSPACECOM uses the space-track.org

account as the mechanism for product exchange.

5.3.E If needed, complete an Orbital Data Request (ODR) form to 

arrange for delivery of USSPACECOM advanced conjunction 

analysis products.

5.3.F For large constellations, coordinate with NASA and the 

screening provider to identify and address any special 

considerations. 

5.4 In situ Launch Products and Processes

5.4.A To aid in satellite tracking and identification, provide injection 

vector(s) to USSPACECOM as soon as they are available.

5.4.B To assist in spacecraft identification for the cataloging process 

and provide general awareness among all O/Os, generate and 

forward predicted ephemerides for the spacecraft to 

USSPACECOM and publish the ephemerides (and all 

subsequent ephemeris updates) publicly as soon as contact is 

established with each deployed spacecraft.

5.4.C If USSPACECOM has issued TLEs for launched objects, notify 

USSPACECOM of the TLE and object number associated with

your spacecraft.

5.4.D Provide early reporting to USSPACECOM of any spacecraft 

failures or other operational difficulties, both to obtain any 

available anomaly support and to assign the appropriate 

conjunction assessment approach to the spacecraft (i.e., inactive 

and thus handled in a manner equivalent to a debris object).
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Section Best Practice Comment

5.4.E If using a commercial provider, make sure it has access to 

information from items A-D.

6.0 On-Orbit Collision Avoidance

6.1 Spacecraft Information and Orbital Data Needed for Conjunction Assessments

6.1.A Actively maintain the space-track.org record for the satellite, 

updating the active/dead and maneuverable/non-maneuverable 

flags to reflect the satellite’s current status. 

6.1.B Furnish predicted ephemerides that include state covariances to 

USSPACECOM (and any additional commercial screening 

provider) and set the privileges to allow any interested party to 

access and download this information. 

6.1.C Furnished ephemerides should possess the following 

characteristics:

a. Be of a 7-day predictive duration for LEO and 14 days for 

other orbits;

b. Be issued at least at the following frequencies:

i. Three times daily for spacecraft with perigee 

heights less than 500 km;

ii. Daily for other LEO orbits; and

iii. Twice weekly for other orbits.

c. Include all known maneuvers within the ephemerides’ 

prediction duration.

d. Provide ephemeris point spacing of approximately 1/100th

of an orbit, in either time or true anomaly. (Certain 

scientific missions with extremely long orbits or high 

eccentricities may require more specialized approaches).

e. Contain a realistic covariance at each ephemeris point for 

at least the six estimated state parameters. (Appendix I 

provides a practical guide for assessing covariance realism, 

as well as some general principles for tuning the 

covariance production process.)

f. Be formatted and distributed in the Consultative 

Committee for Space Data Systems (CCSDS) standard 

Orbital Ephemeris Message (OEM) ephemeris format, 

preferably in the J2000 reference frame.

6.1.D Furnish maneuver reports to USSPACECOM for any 

trajectory-altering satellite maneuvers sufficiently in advance of 

maneuver execution to enable an O/O evaluation of the 

maneuver’s safety. Employ the standard maneuver reporting 

message for this notification.
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Section Best Practice Comment

6.1.E When a maneuver becomes part of a satellite’s trajectory plan, 

generate and submit to the screening provider an updated 

ephemeris that contains this new maneuver as early as is feasible 

but certainly with sufficient advance notice to enable an O/O 

evaluation of the maneuver’s safety. 

6.2 Conjunction Assessment Screenings

6.2.A Submit predicted ephemerides for the spacecraft to a screening 

provider to be screened for conjunctions at least daily with 

spacecraft in higher-drag orbit regimes screened at least three 

times per day. 

6.2.B Ensure that an O/O ephemeris for an active, maneuverable 

spacecraft is screened against other ephemerides from active, 

maneuverable spacecraft in near real time after any such 

ephemeris is submitted to the screening provider. 

6.2.C Obtain and process these screening results from the screening 

provider at the same frequency at which they are produced for 

both the full-catalog and O/O vs O/O screening cases described 

above.

6.3 Conjunction Risk Assessment

6.3.A Use the Probability of Collision (Pc) as the principal collision 

likelihood assessment metric. 

6.3.B Pursue mitigation if the Pc value exceeds 1E-04 (1 in 10,000).

6.3.C Pursue mitigation if the estimated total miss distance is less 

than the hard-body radius value.

6.3.D Employ the current operational NASA Pc calculation 

methodology for routine Pc calculation. Consider removing 

correlated error from the primary and secondary object joint 

covariance. 

6.3.E As a prioritization method for situations in which the number of 

conjunctions meeting mitigation criteria exceeds the ability of 

the O/O to mitigate, estimate the amount of debris that a 

conjunction would produce if it were to result in a collision. A 

less stringent Pc an order of magnitude lower could be

appropriate in such cases.

6.3.F If employing USSPACECOM data products for conjunction 

assessment, use the procedure given in Appendix P to 

determine whether the data for a particular conjunction are 

actionable and thus constitute a basis for conjunction 

assessment-related decisions.
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Section Best Practice Comment

6.3.G If a different conjunction assessment product provider is 

chosen, develop and employ data actionability criteria for this 

provider’s conjunction assessment information to determine 

conjunction assessment event actionability.

6.4 Conjunction Risk Mitigation

6.4.A When a conjunction’s Pc at the mitigation action commitment 

point exceeds the mitigation threshold (recommended to be 

1E-04), pursue a mitigation action that will reduce the Pc by at 

least 1.5 orders of magnitude from the remediation threshold. 

6.4.B Ensure that an ephemeris containing the mitigation action is 

screened against the full catalog, not a large screening volume 

collection of CDMs.

6.4.C Ensure that the mitigation action does not create any additional 

conjunctions with a Pc value above the mitigation threshold (for 

which the recommended value is 1E-04).

6.4.D When the secondary object is an active, maneuverable 

spacecraft, reach out to the secondary’s O/O and jointly 

establish a way forward for the particular conjunction, including 

deciding which spacecraft will maneuver and freezing the other 

spacecraft’s planned trajectory until the TCA has passed.

6.4.E Use space-track.org contact information to engage other O/Os.

6.5 Automated Trajectory Guidance and Maneuvering

6.5.A When an onboard flight dynamics system computes any 

maneuver to alter the satellite’s orbit for mission or conjunction 

mitigation purposes, communicate maneuver details to the 

operating ground control early enough to enable a

USSPACECOM screening and appropriate action in response to 

the screening results.

6.5.B Share maneuver plans with USSPACECOM both as a predicted 

ephemeris with realistic covariance and, when possible, as a 

maneuver report. Allow these notifications to be publicly 

viewed and downloaded by any interested party.

6.5.C Execute a maneuver as intended once a maneuver is 

autonomously planned and externally communicated unless an 

alteration is required for safety of flight.

6.5.D Include the ability to pause or abort, for safety reasons, any 

maneuver planned by the automated system, regardless of 

whether the maneuver is planned by a ground system or on 

board the satellite.
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Section Best Practice Comment

6.5.E Ensure an automated maneuvering system can temporarily 

suspend automatic conjunction assessment activities to allow 

another operator to maneuver.

6.5.F Rapidly submit a new ephemeris for screening if a maneuver is 

not executed as planned in the original file sent for screening, 

such as if a maneuver fails.

6.5.G Keep spacecraft maneuverability status on space-track.org upto-date so other O/Os know whether any particular satellite is 

capable of maneuvering.

6.5.H If onboard flight dynamics planning is used, be able to 

communicate back to operational secondary satellite O/Os that 

the relevant information to enable a maneuver to mitigate a 

conjunction between them is on board the satellite and will be 

acted upon.

6.5.I Request a larger-than-average screening volume from your 

screening provider to ensure that the “snapshot” of the space 

catalog available to your satellites is broadly inclusive and thus 

allows maneuver planning to take cognizance of all possible 

hazards in choosing a new trajectory. This maximizes the 

chances that, when screened before execution, the chosen 

maneuver will be safe

6.6 Other Considerations

6.6.A As part of spacecraft physical design and orbit selection, 

perform a spacecraft photometric brightness analysis to 

determine whether the spacecraft is likely to present an 

impediment to ground-based astronomy. Consider changes to 

the satellite’s construction, materials, or operating attitudes to 

reduce expected photometric brightness to levels that will not 

impede ground-based astronomy. 

6.6.B If a large constellation is being planned, either use a full BRDFbased photometric model or ground-based observations of actual 

orbiting satellites, if available, to obtain a durable estimate of 

the entire constellation’s expected brightness distribution as 

deployed on orbit. 

6.6.C If the constellation, given its population, orbit, and constituent 

satellites, is likely to affect ground-based astronomy, reassign 

the satellite orbits or modify the satellite construction to 

eliminate this effect.
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Appendix D. Best Practices for NASA Missions 65

Appendix D. Best Practices for NASA Missions

This appendix contains a summary list of the best practices for NASA space flight missions (i.e., projects). It uses the NASA term 

“project” and “mission” interchangeably. NASA uses dedicated staff to perform conjunction risk assessment: NASA Johnson Space 

Center (JSC) Flight Operations Directorate (FOD) for human space flight assets and visiting vehicles and NASA Conjunction 

Assessment Risk Analysis (CARA) Program for all other spacecraft. The table below differentiates between actions recommended for 

the project and actions taken by JSC FOD or CARA on the project’s behalf.

• The numbers of the best practices in the list below correspond to the section in the main document where they are fully 

described.

• A check mark in the “Project” column indicates that the project performs the best practice. 

• A check mark in the “CARA/JSC FOD Interfaces” column indicates that the project performs the best practice but will use 

CARA or JSC FOD as their interface with USSPACECOM.

• A check mark in the “CARA/JSC FOD” column indicates that CARA or JSC FOD will perform the best practice on behalf of

the project. 

• Check marks in parenthesis indicate the best practice is optional.

Table D-1 Best Practices for NASA Projects

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

3.0 History

3.2 USSPACECOM Conjunction Assessment Process

3.2.A Obtain a space-track.org account. Can optionally 

be done by 

project

3.2.B Become familiar with the Spaceflight Safety Handbook contents.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 66

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

3.2.C Use USSPACECOM conjunction assessment service as a 

minimum for screenings, even if additional commercial data or 

services are used.

3.2.1.A Provide seven (7) days of predicted ephemeris (including 

maneuvers) to USSPACECOM for screening for LEO spacecraft, 

and provide 14 days for other Earth orbits; e.g., High Earth Orbit 

(HEO)/Geosynchronous Orbit (GEO).

3.2.2.A Provide at least one ephemeris per day to be screened and three 

ephemerides per day in the lower-drag LEO regime (perigee height 

less than 500 km).

3.2.2.B Determine whether the O/O’s process for obtaining screening 

results and performing conjunction risk assessment aligns with the 

timeline of the USSPACECOM process. If the timelines do not 

align in such a way as to enable timely and efficient screening 

support, pursue a rearrangement of the O/O’s process to minimize 

data latency and optimize screening efficiency.

3.2.3.A Populate and maintain the point-of-contact section on spacetrack.org with your operations contact data. Be sure that the 

operations contact can be reached 24/7 due to time zone 

differences between operators and the immediate nature of certain 

conjunction assessment emergencies.

3.2.3.B Use standard ephemeris, CDM, and maneuver notification formats 

defined by the Consultative Committee for Space Data Systems 

(CCSDS).

3.3 NASA Partnership with USSPACECOM

3.3.A Develop a robust safety-of-flight process that includes both

conjunction assessment screening and risk assessment to inform 

close approach mitigation decisions
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 67

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

3.3.B Large constellation operators should work with USSPACECOM 

pre-launch to determine if variations from the standard approach 

are necessary and, if so, to define a tailored screening process.

3.3.C Large constellation operators should consider working with NASA 

to define a risk assessment process. NASA is an experienced 

representative operator. Including NASA in discussions regarding 

establishing a conjunction assessment process will ensure that 

the process will work with most operators for risk assessment 

purposes. 

3.4.2.A Owner/operators should conform to recommendations in the 

NASA Technical Publication “Astrodynamics Convention and 

Modeling Reference for Lunar, Cislunar, and Libration Point 

Orbits.”

3.4.2.B Cislunar mission support entities (sensors, catalog maintainers, 

etc.) should conform to the enhanced SSA message set (Butt 2021) 

when creating cislunar SSA architectures.

3.4.2.C Owner/operators should maintain accurate orbit determination 

solutions and predicted covariance for objects in cislunar space.

3.4.2.D Owner/operators should deliver predicted ephemeris with 

covariance in the CCSDS format to space-track.org and to the 

DSN SPS portal.

4.0 Spacecraft and Constellation Design

4.1 Ascent to/Disposal from the Constellation’s Operational Orbit

4.1.A Perform a study to compute the number of expected close 

approaches anticipated during ascent and descent as well as the 

imputed additional satellite reliability that will be required to meet 

satellite disposal requirements at the chosen operational orbit. 
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 68

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

4.1.B If the results of the study show a large burden, consider choosing a 

different mission orbit with a lower burden. 

4.1.C All missions should review and follow the ODMSP guidance 

standards.

4.1.D When practicable, pursue active disposal using the fastest disposal 

option available.

4.1.E Recognize that transiting spacecraft should yield way to on-station 

spacecraft and thus take responsibility for any conjunction risk 

mitigation maneuvers or transient trajectory alterations that may be 

required.

4.1.F When planning descent using thrusters, if not planning an 

approach of circular-orbit altitude reduction, coordinate with the 

NASA JSC TOPO to ensure that perigee-lowering approaches do 

not present persistent and problematic orbital crossings with the 

ISS and other human space flight assets.

4.2 General Orbit Selection: Debris Object Density

4.2.A Include considerations of orbital debris density when selecting 

candidate mission orbits. Debris density diagrams, indexed by 

object size, are published by the NASA Orbital Debris Program 

Office (ODPO). (See Appendix G for more information and 

examples.)

4.2.B When choosing from the final set of candidate orbits, perform a 

conjunction frequency analysis to determine the number of 

conjunction assessment high-interest events per spacecraft per year 

that can be expected in each of the proposed orbital areas. 
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 69

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

4.3 Vehicle and Constellation Specific Orbit Selection: Spacecraft Colocation

4.3.A During orbit selection, perform an orbit colocation analysis to 

determine whether any of the proposed orbits is likely to create 

systematic conjunctions with existing actively maintained 

satellites. 

4.3.B If the orbit colocation analysis identifies systematic conjunctions, 

consider modifying the proposed orbit(s) slightly to eliminate this 

possibility. Optimizing orbit placement may be appropriate.

4.3.C If the selected orbit is likely to present systematic conjunctions 

with a pre-existing spacecraft, then coordinate with the other 

operator(s) to arrange a process to coordinate maneuver plans 

routinely during the life of the mission.

Include CARA 

in initial contact 

with other 

operator

4.4 Launch-Related Conjunction Assessment

4.4.A Protect human space flight assets from close approaches during the 

COLA gap using stand-off distance or statistical measures. 

4.4.B Conform to additional LCOLA requirements that the launch range 

may impose.

4.5 Spacecraft Trackability

4.5.A Through selection of physical design and materials, ensure that the 

satellite is trackable by SSN from deployment until demise.

a. For spacecraft with perigee heights less than 2000 km, the 

spacecraft should have characteristic dimensions of at least 10 

cm in each major dimension.

b. For spacecraft with perigee heights greater than 2000 km, the 

spacecraft should have characteristic dimensions of at least 50 

cm in each major dimension.

c. If the spacecraft cannot meet these dimension constraints, use 

a proven detectability enhancement.

CARA can 

perform 

trackability 

analysis for 

NASA missions
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 70

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

d. For spacecraft having orbits that span a large range of 

altitudes, ensure that the spacecraft is trackable at all altitudes.

4.6 Spacecraft Reliability

4.6.A Ensure that spacecraft reliability is high enough that the likelihood 

of each spacecraft remaining fully functional until it can be 

disposed of meets or exceeds 99%.

4.6.B Reassess the 99% analysis whenever the underlying assumptions 

change; for example, extending operations beyond design life or 

failures in key systems.

4.6 Development of Capabilities for Ephemeris Generation and Conjunction Risk Assessment and Mitigation

4.7.A Develop and implement a capability to generate and share accurate 

predicted spacecraft ephemerides including any planned 

maneuvers. (See Section 3.1 for a discussion of ephemeris sharing 

for screening. See Section 6.2 for specific guidance on ephemeris 

generation frequency, length, point spacing, formatting, and 

contents.)

4.7.B Determine during spacecraft design what risk mitigation 

approaches are possible for the spacecraft. While trajectory 

modification via thrusting maneuver is the most common 

approach, other approaches such as differential drag orbit 

modification are possible.

4.7.C Develop and implement or arrange to acquire a capability to 

process CDMs and to compute conjunction risk assessment 

parameters such as the Pc.

4.7.D Develop and implement or arrange to acquire a risk analysis 

capability to select mitigation actions that will lower the Pc for 

dangerous conjunctions to a user-selected value.

CARA to review 

project-selected 

mitigation 

actions 
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 71

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

4.7.E Validate conjunction assessment tools well before flight, typically 

6-12 months prior.

5.0 Pre-Launch Preparation and Early Launch Activities

5.1 CONOPS Discussions and Arrangements with USSPACECOM Pertaining to the Launch Phase

5.1.A Establish contact with USSPACECOM to describe and discuss all 

aspects of the launch including delivery and deployment 

methodologies. 

5.1.B Space the deployment of multiple spacecraft in a way that 

enhances the ability of USSPACECOM to quickly identify and 

differentiate the spacecraft using the SSN.

5.1.C Discuss the preparation of the R-15 launch form with 

USSPACECOM so that they understand its contents and any 

implications for safety of flight.

5.1.D Ensure that the launch provider submits the Form 22 and launch 

trajectory information to USSPACECOM, including ephemerides 

for the powered-flight portions and orbital elements for the parking 

orbits, so that potential colocation and deconfliction potentialities 

can be discovered. 

5.1.E Provide to USSPACECOM as soon as possible launch-related 

information (e.g., injection vectors and initial ephemerides for 

deployed spacecraft) that can be used to assist with the cataloging 

process, especially to confirm the identity of launch-related 

objects. Coordinate a satellite numbering scheme (potentially 

including temporary satellite numbers) appropriate to the launch 

type and expected degree of cataloging difficulty.

5.1.F Coordinate with USSPACECOM any potential launch anomaly 

diagnostic products that can be provided if issues arise during the 

launch and early orbit sequence.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 72

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

5.2 CONOPS Discussions and Arrangements with USSPACECOM and NASA Pertaining to 

On-Orbit Mission Phase

5.2.A Register the spacecraft with USSPACECOM using the Satellite 

Registration form on space-track.org. 

5.2.B Provide USSPACECOM with basic construction and mission 

information about the satellite such as stowed dimensions; 

deployable structures such as solar panels, antennae, booms, 

including all of their (rough) dimensions; satellite material 

properties and colors; regular satellite attitude; and registered 

operational radio frequencies. 

5.2.C Provide USSPACECOM with a basic overview of the satellite’s 

orbit maintenance strategy including the paradigm for determining 

when orbit maintenance maneuvers are required; the maneuver 

technology used (as this relates to burn duration and expected 

accuracy); and the frequency, duration, and magnitude of typical 

burns.

5.2.D Provide USSPACECOM with an understanding of the flight 

control and navigation paradigm, principally whether a groundbased control approach is followed or some degree of (or full) 

autonomous control is used. If the satellite control does include 

some autonomous flight dynamics or control features, indicate 

how much (if any) foreknowledge ground controllers have of 

autonomous maneuver actions, the amount of information that is 

communicated to the ground both before and after the maneuver 

(e.g., maneuver time, delta-V, direction), and whether groundbased overrides are possible.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 73

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

5.3 CONOPS Discussions and Arrangements with USSPACECOM and NASA Pertaining to Conjunction Assessment

5.3.A Decide whether the USSPACECOM free service, a validated 

commercial conjunction assessment service, or both will be used 

by the mission. 

5.3.B Establish a service with the selected service provider. CARA 

coordination 

required for use 

of commercial 

data

5.3.C Implement a SSA sharing agreement with USSPACECOM to 

receive advanced data support and services.

5.3.D Through the registration of the satellite with USSPACECOM, 

begin the process of arranging for conjunction analysis data 

exchange including O/O ephemerides, maneuver notification 

reports, and CDMs. USSPACECOM uses the space-track.org

account as the mechanism for product exchange.

5.3.E If needed, complete an Orbital Data Request (ODR) form to 

arrange for delivery of USSPACECOM advanced conjunction 

analysis products.

5.3.F For large constellations, coordinate with NASA and the screening 

provider to identify and address any special considerations. 

5.4 In situ Launch Products and Processes

5.4.A To aid in satellite tracking and identification, provide injection 

vector(s) to USSPACECOM as soon as they are available.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 74

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

5.4.B To assist in spacecraft identification for the cataloging process and 

provide general awareness among all O/Os, generate and forward 

predicted ephemerides for the spacecraft to USSPACECOM and 

publish the ephemerides (and all subsequent ephemeris updates) 

publicly as soon as contact is established with each deployed 

spacecraft.

5.4.C If USSPACECOM has issued TLEs for launched objects, notify 

USSPACECOM of the TLE and object number associated with

your spacecraft.

5.4.D Provide early reporting to USSPACECOM of any spacecraft 

failures or other operational difficulties, both to obtain any 

available anomaly support and to assign the appropriate 

conjunction assessment approach to the spacecraft (i.e., inactive 

and thus handled in a manner equivalent to a debris object).

5.4.E If using a commercial provider, make sure it has access to 

information from items A-D.

6.0 On-Orbit Collision Avoidance

6.1 Spacecraft Information and Orbital Data Needed for Conjunction Assessments

6.1.A Actively maintain the space-track.org record for the satellite, 

updating the active/dead and maneuverable/non-maneuverable 

flags to reflect the satellite’s current status. 

6.1.B Furnish predicted ephemerides that include state covariances to 

USSPACECOM (and any additional commercial screening 

provider) and set the privileges to allow any interested party to 

access and download this information.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 75

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

6.1.C Furnished ephemerides should possess the following 

characteristics:

a. Be of a 7-day predictive duration for LEO and 14 days for 

other orbits;

b. Be issued at least at the following frequencies:

i. Three times daily for spacecraft with perigee heights 

less than 500 km;

ii. Daily for other LEO orbits; and

iii. Twice weekly for other orbits.

c. Include all known maneuvers within the ephemerides’ 

prediction duration.

d. Provide ephemeris point spacing of approximately 1/100th of 

an orbit, in either time or true anomaly. (Certain scientific 

missions with extremely long orbits or high eccentricities may 

require more specialized approaches).

e. Contain a realistic covariance at each ephemeris point for at 

least the six estimated state parameters. (Appendix I provides 

a practical guide for assessing covariance realism, as well as 

some general principles for tuning the covariance production 

process.)

f. Be formatted and distributed in the Consultative Committee 

for Space Data Systems (CCSDS) standard Orbital Ephemeris 

Message (OEM) ephemeris format, preferably in the J2000 

reference frame.

6.1.D Furnish maneuver reports to USSPACECOM for any trajectoryaltering satellite maneuvers sufficiently in advance of maneuver 

execution to enable an O/O evaluation of the maneuver’s safety. 

Employ the standard maneuver reporting message for this 

notification.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 76

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

6.1.E When a maneuver becomes part of a satellite’s trajectory plan, 

generate and submit to the screening provider an updated 

ephemeris that contains this new maneuver as early as is feasible 

but certainly with sufficient advance notice to enable an O/O 

evaluation of the maneuver’s safety. 

6.2 Conjunction Assessment Screenings

6.2.A Submit predicted ephemerides for the spacecraft to a screening 

provider to be screened for conjunctions at least daily with 

spacecraft in higher-drag orbit regimes screened at least three 

times per day.

6.2.B Ensure that an O/O ephemeris for an active, maneuverable 

spacecraft is screened against other ephemerides from active, 

maneuverable spacecraft in near real time after any such ephemeris 

is submitted to the screening provider. 

6.2.C Obtain and process these screening results from the screening 

provider at the same frequency at which they are produced for 

both the full-catalog and O/O vs O/O screening cases described 

above.

6.3 Conjunction Risk Assessment

6.3.A Use the Probability of Collision (Pc) as the principal collision 

likelihood assessment metric. 

6.3.B Pursue mitigation if the Pc value exceeds 1E-04 (1 in 10,000).

6.3.C Pursue mitigation if the estimated total miss distance is less than 

the hard-body radius value.

6.3.D Employ the current operational NASA Pc calculation methodology 

for routine Pc calculation. Consider removing correlated error 

from the primary and secondary object joint covariance.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 77

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

6.3.E As a prioritization method for situations in which the number of 

conjunctions meeting mitigation criteria exceeds the ability of the 

O/O to mitigate, estimate the amount of debris that a conjunction 

would produce if it were to result in a collision. A less stringent 

Pc an order of magnitude lower could be appropriate in such 

cases.

6.3.F If employing USSPACECOM data products for conjunction 

assessment, use the procedure given in Appendix P to determine 

whether the data for a particular conjunction are actionable and 

thus constitute a basis for conjunction assessment-related 

decisions. 

6.3.G If a different conjunction assessment product provider is chosen, 

develop and employ data actionability criteria for this provider’s 

conjunction assessment information to determine conjunction 

assessment event actionability.

6.4 Conjunction Risk Mitigation

6.4.A When a conjunction’s Pc at the mitigation action commitment 

point exceeds the mitigation threshold (recommended to be 

1E-04), pursue a mitigation action that will reduce the Pc by at 

least 1.5 orders of magnitude from the remediation threshold. 

6.4.B Ensure that an ephemeris containing the mitigation action is 

screened against the full catalog, not a large screening volume 

collection of CDMs.

6.4.C Ensure that the mitigation action does not create any additional 

conjunctions with a Pc value above the mitigation threshold (for 

which the recommended value is 1E-04).
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 78

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

6.4.D When the secondary object is an active, maneuverable spacecraft, 

reach out to the secondary’s O/O and jointly establish a way 

forward for the particular conjunction, including deciding which 

spacecraft will maneuver and freezing the other spacecraft’s 

planned trajectory until the TCA has passed.

6.4.E Use space-track.org contact information to engage other O/Os.

6.5 Automated Trajectory Guidance and Maneuvering

6.5.A When an onboard flight dynamics system computes any 

maneuver to alter the satellite’s orbit for mission or 

conjunction mitigation purposes, communicate maneuver 

details to the operating ground control early enough to enable 

a USSPACECOM screening and appropriate action in 

response to the screening results

6.5.B Share maneuver plans with USSPACECOM both as a predicted 

ephemeris with realistic covariance and, when possible, as a 

maneuver report. Allow these notifications to be publicly viewed 

and downloaded by any interested party.

6.5.C Execute a maneuver as intended once a maneuver is 

autonomously planned and externally communicated unless 

an alteration is required for safety of flight. 

6.5.D Include the ability to pause or abort, for safety reasons, any 

maneuver planned by the automated system, regardless of 

whether the maneuver is planned by a ground system or on 

board the satellite.

6.5.E Ensure an automated maneuvering system can temporarily 

suspend automatic conjunction assessment activities to allow 

another operator to maneuver. 
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 79

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

6.5.F Rapidly submit a new ephemeris for screening if a maneuver 

is not executed as planned in the original file sent for 

screening, such as if a maneuver fails.

NASA O/Os 

submit to 

CARA/FOD

6.5.G Keep spacecraft maneuverability status on space-track.org

up-to-date so other O/Os know whether any particular 

satellite is capable of maneuvering.

6.5.H If onboard flight dynamics planning is used, be able to 

communicate back to operational secondary satellite O/Os that the 

relevant information to enable a maneuver to mitigate a 

conjunction between them is on board the satellite and will be 

acted upon.

6.5.I Request a larger-than-average screening volume from your 

screening provider to ensure that the “snapshot” of the space 

catalog available to your satellites is broadly inclusive and thus 

allows maneuver planning to take cognizance of all possible 

hazards in choosing a new trajectory. This maximizes the chances 

that, when screened before execution, the chosen maneuver will be 

safe.

6.6 Other Considerations

6.6.A As part of spacecraft physical design and orbit selection, perform a 

spacecraft photometric brightness analysis to determine whether 

the spacecraft is likely to present an impediment to ground-based 

astronomy. Consider changes to the satellite’s construction, 

materials, or operating attitudes to reduce expected photometric 

brightness to levels that will not impede ground-based astronomy.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix D. Best Practices for NASA Missions 80

Section Best Practice Project

Project with 

CARA/JSC FOD 

providing interface 

to USSPACECOM

CARA 

/JSC 

FOD

Comment

6.6.B If a large constellation is being planned, either use a full BRDFbased photometric model or ground-based observations of actual 

orbiting satellites, if available, to obtain a durable estimate of the 

entire constellation’s expected brightness distribution as deployed 

on orbit. 

6.6.C If the constellation, given its population, orbit, and constituent 

satellites, is likely to affect ground-based astronomy, reassign the 

satellite orbits or modify the satellite construction to eliminate this 

effect.
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix E. Use of Analytic Theory Orbital Data in Conjunction Assessment 81

Appendix E. Use of Analytic Theory Orbital Data in

Conjunction Assessment

The following is an amplification of a statement made by the Conjunction Assessment Technical 

Advisory Committee in 2016 on the use of analytic theory for conjunction assessment, and in 

particular the Two-Line Element (TLE) set publicly accessible catalog produced by 

USSPACECOM.

Due to enormous increases in computational capacity over the last twenty years, the space 

surveillance industry has been able to transition from analytic to higher-order theory approaches 

to space catalog maintenance. This transition brings a number of significant advantages to 

modern space catalogs such as the modeling of additional perturbations that were not typically 

represented in analytic theories (e.g., solar radiation pressure and solid earth tides), an improved 

fidelity in modeling the major perturbations (e.g., geopotential and atmospheric drag), and a 

durable covariance matrix to accompany each state estimate. Some of these features existed with 

previous analytic and semi-analytic theories, but it is only in recent times that all the additional 

attributes are routinely produced and available for space surveillance applications. This 

development has prompted the question of how data from analytic models (such as the 

Simplified General Perturbations Theory #4 [SGP4], which is used to produce the publicly

available TLE catalogs) and higher-order theory models (such as the USSPACECOM Special 

Perturbations (SP) Space Object Catalog, although higher-order theory data can also be furnished 

from other sources) should be employed in the conjunction risk assessment process.

Risk assessment, whether it is quotidian consumer risk, the extremely serious discipline of 

nuclear accident risk, or the present problem of satellite collision risk, must always contain 

within its calculus some determination of the likelihood of occurrence of the event in question. 

For CA, this determination is most commonly assessed by calculating the Probability of 

Collision (Pc; see Appendix I for a development of the calculation theory), and this calculation 

requires both the state estimates for the primary and secondary objects and the accompanying 

measures of these estimates’ uncertainties, typically through a covariance matrix, at the time of 

closest approach (TCA).

Most implementations of analytic orbital theories lack the ability to produce a meaningful 

covariance (this is true of the SGP4 TLEs), so they cannot enable a probabilistic conjunction 

assessment calculation and thus for conjunction assessment applications will yield only a miss 

distance at the time of the two objects’ TCA. Because no uncertainty information on this miss 

distance is provided, no probabilistic conclusion can be drawn. A miss-distance threshold can be 

(arbitrarily) selected to enable a binary “safe / not safe” conjunction evaluation, but there is no 

ability to determine, for example, how often the real miss distance, for which the nominal miss 

distance is only an estimated mean value, is actually likely to exceed or fall below such a 

threshold. No probabilistic assessment of whether a conjunction will be a dangerously close 

encounter is possible, so the likelihood of occurrence of a collision cannot be determined.

This dynamic is illustrated in Figure E-1, which gives a Cumulative Distribution Function (CDF) 

plot of miss distance distributions, both for critical (Pc > 1E-04) and non-critical (Pc < 1E-04) 
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix E. Use of Analytic Theory Orbital Data in Conjunction Assessment 82

events. The lack of any strong correlation between Pc and miss distance is clear: the span of miss 

distances for the critical events (less than 100 m to more than 10 km) is extremely broad and 

overlaps significantly with the results for the non-critical events. For example, to eliminate 95% 

of the high-Pc events using a miss-distance criterion alone, a 10 km miss-distance threshold

would need to be chosen—a value that would also include more than 50% of the non-worrisome 

events, creating a density of events to mitigate so great that an unsustainable number of such 

mitigation actions would be required. 

Figure E-1 Miss-Distance Distributions for Critical (Pc > 1E-04) and 

Non-critical (Pc < 1E-04) Events

Additionally, the inherent theory error in general perturbation approaches makes them ill-suited 

for even a risk-tolerant, miss-distance-based conjunction assessment. A published study (Hejduk 

et al. 2013) provided TLE accuracy information for the two methods presently used by 

USSPACECOM to generate them: traditional SGP4 orbit determination and Extrapolated 

General Perturbation (eGP) TLE generation, which performs the SGP4 orbit determination not 

against sensor measurements but against pseudo-observations generated from a higher-order 

theory trajectory for the object, which includes some forward prediction of the trajectory. Both 

methods are in use presently to generate the publicly-released TLE catalog, and it is not always 

easy to determine which method was used to produce any given TLE. Performance data for the 

orbital regime corresponding to Figure E-1 above (LEO with perigee heights greater than 500

km) are given in Figure E-2. These results show that, while the eGP methodology outperforms 

traditional SGP4 as expected, both are noisy in the epoch to 72-hour propagation states, which is 

the time-frame during which most conjunction risk mitigation decisions are made; errors from 

600 m to 3 km are observed. 
NASA Spacecraft Conjunction Assessment and Collision Avoidance 

Best Practices Handbook

Appendix E. Use of Analytic Theory Orbital Data in Conjunction Assessment 83

Figure E-2 eGP and Regular SGP4 Errors: LEO > 500 km (log scale)11

Figure E-3 below is an expansion of Figure E-1 to include CDF plots of miss-distance

distributions for events with both Pc > 1E-03 and, separately, 1E-02. Figure E-3 suggests that a 

miss-distance criterion of several hundred meters, or perhaps 1-2 km, could be used as a 

simplified method of performing a risk-tolerant conjunction assessment: remediate any 

conjunctions with a miss distance less that 1-2 km. This move is ill-advised because it would 

result in a huge number of unnecessary mitigations (as an example, for events with a miss 

distance less than 1 km, the number with a Pc less than 1E-03 and thus not serious is six times 

greater than the number with a Pc greater than 1E-03). In addition, the inherent theory error (600

m to 3 km, from above) is a substantial portion of the miss-distance threshold of 1-2 km that 

would be imposed—in some cases even greater than the threshold itself. So even under the very 

limited case described here, the use of general perturbation results for conjunction risk 

assessment is not tenable. Thus, analytic theory data, such as that contained in the public TLE 

catalogs, should not, taken alone, serve as a basis for risk assessment decisions and subsequent 

mitigation actions.

11 From Hejduk et al. 2015.

Epoch 18 hrs 72 hrs 7 days 15 days

10-1

100

101

102

Propagation Point

50ile Vmag Error (km)

eGP and GP Errors: LEO > 500 km

eGP

GP
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Appendix E. Use of Analytic Theory Orbital Data in Conjunction Assessment 84

Figure E-3 Expansion of Figure E-1 to Include CDFs for Pc Thresholds 

of 1E-03 and 1E-02

Nonetheless, analytic theory orbital data, usually furnished as TLEs, does have its uses in 

conjunction assessment; some of these have included the following:

• Mission planning activities such as the selection of satellite future orbits and final 

disposal orbits;

• General situational awareness information such as the positions of neighboring objects 

and the general effects of the basic perturbations (e.g., atmospheric drag);

• Pre-filtering of candidates for conjunction assessment screenings for which simple TLEbased filters can eliminate substantial numbers of candidate pairs from requiring explicit 

screening runs;

• Assessment of the status of a payload that appears as a conjuncting secondary, as active 

secondaries require special analysis and alerting when performing conjunction 

remediation; and

• Consistency checks of the higher-order theory data. While the higher-order theory data 

are typically more accurate, they themselves are vulnerable to updates with bad or 

inadequate tracking data, errors in force model and integration control settings, and

incorrect maneuver solutions. Comparisons with the analytic data can often identify such 

problems and, while not enabling their repair, can at least make clear that such cases 

constitute non-actionable conjunction assessment data.

Although the above uses of analytic theory data can be tangentially helpful to the conjunction 

assessment enterprise, these uses do not themselves directly support conjunction risk assessment,

for which more accurate state estimate data accompanied by uncertainty information is required.
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Appendix F. Expected Conjunction Event Rates 85

Appendix F. Expected Conjunction Event Rates

The conjunction assessment workload that a mission experiences is a function of:

• The total number of CDMs that it receives, 

• The number of associated events with risk levels high enough to require enhanced 

monitoring, and 

• The number of events that have a risk level so high as to require mitigation planning and 

potential execution. 

During mission planning and development, it is helpful to have a general idea of the frequency of 

such situations to model spacecraft fuel consumption, identify staffing needs, and determine the 

appropriate degree of conjunction assessment-related tool automation.

The following profiling of conjunction assessment event densities is intended to provide at least 

some first-order information to answer these questions. These data summarize three years’ recent 

conjunction assessment data history for the payloads that NASA protects in the LEO orbit 

regime (event densities in the non-LEO region are both low and highly dependent on the specific 

orbit, so summary information is not given here). In November 2021, Russia conducted a kinetic 

anti-satellite (ASAT) test that destroyed a derelict Russian satellite at approximately 480km, 

which generated an additional 1500 cataloged debris fragments in LEO. This increase is reflected 

in the three-year averages given below, although by 2024 most of these fragments will have 

decayed.

The graphs presented in Figure F-1 contain several component parts. 

The x-axis gives the hard-body radius for the conjunction, which is essentially the combined 

sizes of the primary and secondary objects. Although different methods are used to determine 

this size, perhaps the most common is to construct a circumscribing sphere about the primary 

object and add its radius to a standard radius size for the type of secondary object (i.e., payload, 

rocket body, or debris) in the conjunction (Mashiku and Hejduk 2019). Hard-body radius (HBR)

values of 20 m, 10 m, 5 m, 2 m, 1 m, and 0.1 m are used, the last few values included to give 

some statement of the expected situation for small satellites. All the CARA events were 

reprocessed with these different HBR values to produce these varied results. 

The y-axis gives the number of expected events per payload per year, shown on a logarithmic 

scale, with the type of event indicated by the color in the stacked bar charts, which are to be read 

in the following way:

• The height of the red bar indicates the frequency of red events, which are defined as 

events containing at least one CDM with a Pc value > 1E-04. These are the most serious 

events; they require detailed monitoring, mitigation planning, and in a minority of cases,

the actual execution of a mitigation action.

• The height of the yellow bar indicates the frequency of yellow events, which are defined 

as events containing at least one CDM with a Pc value > 1E-07. These events generally 

merit increased monitoring and attention, including in some situations, mitigation 
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Appendix F. Expected Conjunction Event Rates 86

planning (if they are close to the red threshold). Based on the definition above, all red 

events are also yellow events.

• The height of the green bar indicates the frequency of events of any type, including those 

that never manifest a Pc > 1E-07. Based on this definition, all red and yellow events are 

also green events.

The overall height of each bar thus indicates the CDM generation rate. Note that this number, 

while in some ways a useful loading figure, is a function of the size of the screening volume that 

is employed and thus is not that meaningful in itself. For a screening volume similar in size to 

those used by NASA CARA, the green event generation rates (which include the yellow and red 

events) are likely to be similar. Because they require relatively small miss distances, the yellow 

and red generation rates are expected to be largely independent of the screening volume size 

selected as long as the volume used is reasonably-sized.

Three different graphs are presented representing three different regions of LEO sorted by 

perigee height (p): a high-drag regime (p < 500 km), a low-drag regime (perigee height between 

500 and 750 km) that includes a large concentration of satellites somewhat higher than 700 km, 

and a second low-drag regime from 750 to 1400 km. There are moderate differences in event 

frequency among the three different regimes, although some of that variation may be due to the 

different levels of sampling among the three, given that NASA operates substantially different 

numbers of payloads in each of these three regions. These results are more notional than precise; 

nonetheless, they do give some level of orientation to the expected loading for each event type 

(green, yellow, and red). 
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Appendix F. Expected Conjunction Event Rates 87

Figure F-1 Conjunction Event Frequencies as a Function of Orbit Regime 

and Event Severity
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Appendix G. Orbital Debris Density 88

Appendix G. Orbital Debris Density

Orbital debris can be generated by a number of processes that have conspired to produce the 

present debris environment:

• Detritus cast off as part of the launch and injection activities; 

• Off-scourings from healthy satellites themselves, such as peeling of Mylar thermal 

insulation; 

• Collisions between satellites; 

• Explosions of satellites; and 

• Satellite debris-generating events in which (without any clear cause) a satellite is 

observed to break into more than one piece. 

Because of the orbital locations in which major debris-producing events have taken place, and 

due to the differences in efficiency of natural debris cleansing arising from varying drag at these 

different altitudes, orbital debris density is not uniform. It is thus helpful to examine the current 

debris density situation when choosing an operational orbit because the orbital debris density 

does influence the rate of close approach events as well as the likelihood of satellite damage due 

to collision with an object too small to be tracked.

The graphs in Figure G-1 are produced from the NASA Orbital Debris Engineering Model

(ORDEM) 3.2 release developed by the NASA Orbital Debris Program Office (ODPO). 

Generated for the 2023 debris environment, these graphs give debris flux (per satellite unit area 

and time on orbit) as a function of orbital altitude (a circular orbit is presumed) and inclination. 

Given that satellites often have many years of orbital lifetime, it could be argued that the graphs 

should be projected further forward in time and thus reflect debris generation events and natural 

debris depletion processes over as much as the next decade. However, such a prediction requires 

a stochastic execution of the model to try to guess at the number, severity, and location of future 

debris-producing events. Since the purpose here is to compare the relative debris densities of 

different regimes, the simplicity of a single rather than probabilistic presentation has been 

selected. 

The graphs are arranged by inclination, and while it is observed that the highest inclination band 

represented here does have a slightly higher debris density than the two lower bands, the 

differences in both absolute debris flux values and the overall curve morphology among the three 

inclination bands are not great, indicating that inclination is not a major contributor to debris 

density. However, variation with orbital altitude is more marked: the density peaks at about 850 

km and tails off in either direction from that peak at relatively equal rates. And the reduction is 

significant: about an order of magnitude in each direction within the bounds of the graphs (400 to 

1200 km orbital altitude). 

Three lines are shown on each graph:

• The amber line represents objects of sizes greater than 10 cm, which is the size of objects 

in the present space catalog without any contributions from the new Space Fence SSN 

radar and is thus related to satellite conjunctions presently tracked and reported. 
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Appendix G. Orbital Debris Density 89

• The reddish line is for objects of sizes greater than 5 cm, which is the size of objects that 

can be expected to be included in a catalog that does include tracking data from the new 

Space Fence radar, which should soon be contributing data to the conjunction assessment

enterprise. 

• The blue line is for objects of sizes greater than 1 cm, which is the size of objects large 

enough to be generally considered lethal to a satellite if there is a collision.

The gap between the reddish and blue lines thus represents the flux level of objects that are too 

small to be tracked yet large enough to potentially be lethally damaging. The gap represents a 

collision risk that, essentially, cannot be mitigated and so is simply accepted as the cost of 

operating a satellite in space.
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Appendix G. Orbital Debris Density 90

Figure G-1 Debris Flux as a Function of Orbit Inclination, Orbit Altitude, 

and Object Size
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Appendix G. Orbital Debris Density 91

In some cases, the flux densities between the 1 cm and 5 cm bands represent almost an order of 

magnitude difference. Considering this difference, some might question why conjunction 

assessment is pursued at all, given that so much of the collision risk cannot be remediated and 

simply must be accepted. To this question are two distinct responses:

1. First, within reasonable bounds, it makes sense to protect against safety-of-flight hazards 

that are known and that can, if necessary, be mitigated. NASA CARA’s statement of 

purpose is “to take prudent measures, at reasonable cost, to enhance safety of flight, 

without placing an undue burden on mission operations.” An unjustified over-investment 

in safety should be avoided, and mission objectives should not be regularly and 

substantially impaired by conjunction assessment considerations. But since it is not 

particularly expensive or difficult to identify high-risk conjunctions from the existing 

space catalog, and since such conjunctions are relatively infrequent, and furthermore, 

since the need for mitigation action for such conjunctions is less than an order of 

magnitude less frequent than that, it is good safety practice to conduct conjunction 

assessment operations according to the CARA mission statement. Space actors thus 

employ the conjunction assessment enterprise to “prevent the preventable.”

2. Second, the satellite conjunctions that occur between objects large enough to be in the 

space catalog are the ones that have the potential to generate large amounts of space 

debris. As the NASA ODPO has shown (Johnson et al. 2001), the debris production 

potential of a collision is a function of the two objects’ relative kinetic energy and 

masses: the ratio of their two masses and their relative velocity. Collisions in which the 

two objects’ masses are quite different will generally result in only the lighter of the two 

objects being fragmented with the heavier object being merely cratered. Objects in which 

the two masses are closer to each other will generally result in complete fragmentation of 

both objects and thus very large amounts of resultant debris. Extremely small secondary 

objects (i.e., a few centimeters in size and thus below the level of trackability), even at 

the large relative velocities of LEO conjunctions (~10,000 m/s), are quite unlikely to 

cause fragmentation of larger active payloads, so the amounts of debris produced by 

collisions with untracked objects will in almost all cases be relatively small. As stated 

previously, collisions with untracked objects can still be lethal to a satellite and do 

constitute an accepted risk simply of operating a satellite in space, but conjunction 

assessment against tracked and cataloged objects prevents the collisions that will produce 

large amounts of debris and thus makes a substantial contribution to space sustainability, 

even though it cannot protect payloads from debilitating conjunctions with very small 

objects. (Appendix O gives a more detailed treatment of the collision debris production 

topic.)

Choosing a mission trajectory that occupies a region of space with a lower debris density is thus 

a favorable selection for two reasons:

• It lowers the risk of a lethal collision with an untracked object; and 

• In general, it reduces the rate at which serious conjunctions with cataloged objects will 

occur. 
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Appendix G. Orbital Debris Density 92

In addition to achieving the above two goals (as the curves in Figure G-1 demonstrate), choosing 

orbits with lower orbital altitudes also facilitates compliance with the 25-year disposal 

guidelines.

While there may be a general correlation, it is important to recognize that there is not in fact a 

direct relationship between the debris flux for catalog-size objects and the actual rate at which 

conjunctions, even serious conjunctions, will be identified. The debris flux gives the expected 

frequency of penetration of the satellite’s cross-sectional area by some object in space. 

According to the curves in Figure G-1, a sun-synchronous object at 700 km, placed at the middle 

of a 20 m radius sphere (to employ an extremely conservative statement of its exposed area), 

would over a one-year period expect only 0.006 penetrations of this 20 m sphere. In other words,

it should take ~160 years on orbit for a penetration to occur. However, predicted close 

approaches for such an object are identified daily, yet mitigation actions would be warranted

only a few times per year. What is the meaning of this lack of alignment?

When a Pc for a specific event is calculated, it is interpreted as representing the likelihood that 

the “true” miss distance (which ultimately cannot be known) is smaller than the hard-body radius

(HBR) defined about the object (e.g., the 20 m radius of the constructed sphere described in the 

above paragraph). The “true” Pc corresponding to the “true” miss distance is either 0 or 1; i.e., 

either the satellites will pass within 20 m of each other or they will not. 

However, the orbit determination process does not predict future positions without error, so a Pc

value somewhere between 0 and 1 represents a calculation of the likelihood of a penetration 

given the uncertainties in the input measurement data to the orbit determination, lack of 

comprehensiveness of the dynamical model, and additional uncertainties expected in predicting 

the satellites’ epoch states to their TCA (such as atmospheric density forecast error). 

Generally, when the Pc is greater than 1E-04 (1 in 10,000 likelihood of a penetration), a 

mitigation action is recommended and executed, This threshold has emerged in the industry as an 

acceptable balance between safety-of-flight considerations and additional mission burden and 

encumbrance. Because mitigation actions are recommended when the likelihood of penetration 

exceeds 1 in 10,000, there is little surprise that the frequency of serious conjunction events 

exceeds that projected by the debris flux value: in only 1 out of 10,000 cases would the 

penetration actually occur if the mitigation action were not executed. Fortunately, a conservative 

approach such as this can be implemented and is still consistent with the mandates of prudent 

action, reasonable costs, and lack of undue burden on mission operations.

(See Appendix F for information on actual expected rates of serious conjunction events.)
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Appendix H. Long-Term Collision Risk and Satellite Colocation Analysis 93

Appendix H. Long-Term Collision Risk and Satellite 

Colocation Analysis

This section describes an approach developed by NASA CARA that uses long-term collision risk 

assessment methodologies applied to proposed satellites to predict: 

• Long-term average conjunction and collision rates that a new satellite can expect to 

experience; and 

• The potential frequency of repeating conjunctions experienced by a new satellite due to 

being colocated with another satellite.

These methods provide the means to avoid deploying new satellites into crowded regions of 

orbital space, and to prevent orbital collocation with one (or more) pre-existing satellites. 

Although the methods also apply to satellite mid-mission repositioning or end-of-life disposal 

efforts, they are demonstrated here using an example of a newly-proposed satellite. 

With the ongoing deployment of large constellations, such as the Starlink or OneWeb systems, 

avoiding overly crowded regions of space is becoming an increasingly important consideration. 

In addition, avoiding orbital colocation prevents problematic repeating conjunctions with other 

active satellites. To this end, when a new operational orbit is being selected, a long-term collision 

risk and orbit colocation analysis should be performed. Fortunately, it is often possible to make 

sufficient modifications to an intended nominal orbit to avoid these unfavorable situations, yet 

still meet mission objectives.

H.1 Long-Term Risk Assessment Theory and Algorithmic Description

Both semi-analytical and Monte Carlo methods provide the means to estimate statisticallyexpected long-term collision rates between satellites. Monte Carlo methods also provide 

estimates of the overall expected frequency of conjunctions, as well as the frequency of repeating 

conjunctions which can be used to identify potentially colocated satellites.

Analytic Long-term Collision Rate Analysis

The analytic theory developed by Kessler (1981) focuses on estimating collision rates between 

either spherical objects, or, for this application, circumscribing spheres. It provides estimates of 

such collision rates by neglecting all orbital perturbations except the orbital precession induced 

by Earth’s J2 gravitational term (see Vallado 1981 for a description of orbital precession). For 

each pair of analyzed satellites, the Kessler rate represents an average over six angles (Hall and 

Matney 2000). More specifically, the method averages collision rates over the three Keplerian 

orbital element angles for each of the two interacting objects. These three angles are the orbital 

right ascension of ascending node (RAAN, or Ω), the argument of perigee (ω), and the mean 

anomaly (M). In other words, Kessler rates represent six-dimensional phase space averages, 

which are equal to long-term temporal averages in idealized situations for which the ergodic 

hypothesis is valid. For this reason, Kessler rates are often referred to as “long-term” estimates, 

even when calculated in more realistic, non-idealized situations to which the ergodic hypothesis 

does not necessarily strictly apply.
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Appendix H. Long-Term Collision Risk and Satellite Colocation Analysis 94

The Kessler (1981) formulation expresses the average collision rate between two satellites as an 

integral over the volume of their overlapping orbital regions, as follows:

Ṅ

c

K = σ1,2 ∫ [S1S2vrel]dV

V

(H-1)

In this equation, V indicates the overlapping orbital volume shared by the primary and secondary 

satellites; σ1,2 = π(R1 + R2)

2

their combined collisional cross section; S1 and S2 their average 

spatial densities, respectively; and vrel their average relative velocity during conjunction events. 

(The superscript K indicates that the Kessler method has been used to estimate the collision rate, 

and the dot above the symbol Nc represents the first time derivative.) The Kessler collision rate is 

zero for orbits that do not cross one another at all over long-term J2-only propagations, for which 

the overlap volume V vanishes. The integrand factors within the square brackets of equation (H1) depend on first three Keplerian orbital elements of the primary and secondary satellite orbits, 

i.e., the semi-major axis (SMA), the eccentricity, and the inclination of each. Calculating the 

integral over volume in equation (H-1) entails two-dimensional numerical integration over 

geocentric latitude and radial distance.

Monte Carlo Colocation Conjunction Rate Analysis

Monte Carlo methods provide another means to estimate collision and conjunction rates, and 

allow for more generalities, including: 

• Trajectories that account for orbital perturbations other than just those induced by the J2

gravitational term; 

• Both spherical and non-spherical shapes, used to estimate conjunction rates that arise 

from ellipsoidal or box-shaped screening volumes; and 

• The ability to estimate the frequency of repeating conjunctions, used to assess satellite 

colocation.

The CARA Monte Carlo long-term rate estimation software uses the U.S. Space Force’s

Computation of Miss Between Orbits (COMBO) astrodynamics standards algorithm to 

determine close approaches between trajectories propagated using the SGP4 orbital theory. Input 

consists of a two-line element (TLE) set of mean orbital elements for the primary object plus a 

file of multiple TLEs for the secondary objects being considered. Each Monte Carlo trial entails 

propagating trajectories over a duration of several days (typically seven or ten), beginning each 

propagation at the epoch of the TLE catalog. The initial mean orbital elements for the trial 

propagations are the same as specified by the input TLEs, except that newly sampled (ω,Ω, M)

angles are generated for both objects, each randomly drawn from a uniform distribution spanning 

0 to 2. The Monte Carlo algorithm registers a “hit” for each instance that the trial trajectories 

approach one another close enough to penetrate a screening volume surrounding the primary 

object. For sufficiently large screening volumes, multiple hits can potentially occur per trial, so 

the algorithm also registers the earliest hit that occurs for each primary-secondary pair as a “firstcontact” event.
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Dividing the total number of hits by the product of the number of trials and the propagation 

duration yields the Monte Carlo estimate for the rate

Ṅ

c

MC =

Nhit

Ntrial Tprop

and ΔṄ

c

MC ≈

Ṅ

c

MC

√Nhit

(H-2)

The second equation above provides an approximation of the 1-sigma uncertainty of the estimate 

due to Monte Carlo counting uncertainties, which decreases as the number of registered hits 

increases. Rates of first-contact events are similarly calculated and are always less than or equal 

to the overall rate, i.e., Ṅ

fc

MC ≤ Ṅ

c

MC. As demonstrated later, for colocated orbits that produce 

mostly repeating conjunctions, the rate of first-contact conjunctions is significantly less than the 

total rate. 

H.2 Long-Term Risk Assessment Methodology Demonstration

To demonstrate long-term risk and satellite colocation assessments, this section introduces a 

hypothetical proposed satellite called “NewSat” with a nominal initial orbit intentionally 

designed to be colocated with that of the Hubble Space Telescope (HST). 

In this hypothetical scenario, NewSat has a hard-body radius of 3.5 m, and is to be launched and 

reach its mission orbit on 2022-11-18 00:00:00 UT. The mean orbit of HST at this epoch, 

propagated from a TLE cataloged shortly before that time, has a mean motion equal to 

15.11279168 revs/day, an eccentricity of 0.0002381, and an inclination of 28.4696 ⎯

corresponding to an equatorial perigee altitude of about 530.6 km and an apogee altitude of 

532.2 km. To create a colocated orbit for this demonstration, the TLE for NewSat’s nominal 

orbit has been made identical to that of HST in all respects except that the inclination has been 

rounded to the value of 28.5 and the eccentricity increased to 0.001. (These changes prevent the 

two orbits from being identical but are not sufficiently large to prevent them from being 

colocated, as will be demonstrated later.) This nominal NewSat deployment orbit corresponds to 

an equatorial perigee altitude of about 523.7 km and an apogee of 537.5 km, which is 13.8 km 

higher than perigee. However, for this hypothetical scenario, NewSat is given the flexibility to 

deploy into an alternate orbit with the same inclination, but with perigee altitudes anywhere from 

500 to 600 km, and with an apogee up to 20 km higher than perigee. As discussed below, the 

long-term risk assessment methodology estimates rates between NewSat and HST over this 

entire region of orbital parameter space, as well as for all the other satellites contained within the 

2022-11-18 TLE catalog, which represent a total of 36,368 potential secondary objects, a 

population that includes active and retired satellites, spent rocket-bodies, and orbital debris.

Figure H-1shows a plot of Kessler collision rates between NewSat and HST, calculated with 

equation (H-1), and using hard-body radii of 3.5 m and 10 m for the two satellites, respectively. 

Specifically, the plot shows the collision rate (on the color axis), as a function of perigee altitude 

(horizontal axis) and apogee-perigee difference (vertical axis). The white star marks NewSat’s 

nominal deployment orbit. However, as mentioned previously, NewSat could deploy into an 

alternate orbit at any location within the bounds of the plot. Unsurprisingly, the nominal orbit 

corresponds to a non-zero long-term collision rate between the NewSat and HST. However, 

much of the area on the plot corresponds to zero collision rate (shown as the darkest blue color 
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Appendix H. Long-Term Collision Risk and Satellite Colocation Analysis 96

on the plot); these regions represent candidate orbits for NewSat that do not overlap at all with 

HST’s orbit because they are sufficiently higher or lower in altitude. NewSat could change 

deployment plans by shifting its orbit into one of these regions, but that would only mitigate the 

long-term collisional threat due to HST and not necessarily that posed to the other cataloged 

satellites.

Figure H-1 Kessler Collision Rates between NewSat and HST

Figure H-2 shows collision rates summed over all the satellites contained within the full 2022-

11-18 TLE catalog. For the nominal NewSat orbit marked by the white star, a total of 2,183 

secondary objects were found to have non-zero Kessler rates among the 36,368 cataloged 

objects. The calculation uses hard-body radii for these secondary objects taken from a table of 

published dimensions for known satellites, when available, and based on radar cross section 

values for unknown objects such as orbital debris (Hall and Baars 2022). Figure H-2 shows that 

the nominal NewSat orbit is adjacent to (but not within) the region affected by the Starlink 

constellation satellites, which occupy several orbital shells at higher altitudes (the regions 

affected by three of these shells are marked in Figure H-2). So, if the NewSat mission were to 

change its deployment plans, doing so to avoid these already crowded regions would largely 

eliminate the expected number of Starlink conjunctions and associated risk mitigation actions. 

For clarity, Figure H-3 shows collision rates for all cataloged objects, but with Starlink 

constellation satellites excluded. A comparison of the color axis scales on Figures H-2 and H-3 

illustrates how relatively large the long-term rates due to the Starlink constellation are in this 

specific region of orbital space.
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Figure H-2 Total NewSat Collision Rates Among All Cataloged Satellites

Figure H-3 NewSat Collision Rates Excluding the Starlink Constellation
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Figures H-1, H-2, and H-3 graphically illustrate how long-term collision rate analyses can be 

used to avoid deploying satellites into crowded regions, and thereby help minimize the long-term 

collision risk among tracked objects. For the nominal deployment orbit, Figure H-2 indicates that 

NewSat’s predicted collision rate is ~610-4per year, corresponding to a statistically expected 

collisional “lifetime” (expected time until a collision) of ~1,700 years among cataloged satellites. 

(As mentioned previously, other physical effects such as active maneuvering, orbital decay, etc., 

are likely to occur on shorter timescales than this, meaning that the ergodic hypothesis does not 

strictly hold for this system; nevertheless, long-term collision rates and collisional lifetimes are 

still used in these situations as indicators of statistical risk.) Notably, shifting NewSat’s 

deployment orbit into one of the regions most affected by the Starlink constellation would lead to 

a significantly shorter collisional lifetime of 30 to 100 years⎯in the absence of any risk 

mitigation maneuvering, which fortunately is being performed by Starlink constellation satellites. 

However, a careful inspection of Figures H-1, H-2, and H-3 indicates that changing the planned 

NewSat deployment to an orbit with a mean equatorial perigee altitude of about 558 km and an 

apogee ≤7 km higher would avoid both the HST and Starlink regions simultaneously and extend 

NewSat’s collisional lifetime to ~3,000 years. Furthermore, an extended analysis that includes all 

future Starlink constellation deployments (as tabulated by Bassa et al. 2022) indicates that the 

collision rate predicted for this specific orbital region should remain relatively low, at least 

among currently cataloged objects and currently planned Starlink satellites.

H.3 Colocation Analysis Methodology

During their on-orbit residence, most spacecraft come into conjunction with other, secondary,

objects with some frequency. However, if two active satellites are maintained in similar orbits or 

in orbits that have consistent intersections, synodic alignment can occur that produces multiple 

close approaches on successive orbits. If the alignment is very close, such repeating conjunctions 

can persist over extended periods (e.g., much longer than typical seven- or ten-day conjunction 

screening durations) and could also recur periodically over a satellite’s entire orbital lifetime. 

Because conjunction management between active payloads is complex, requiring coordination of 

maneuver plans and joint decisions about near-term courses of action, it is desirable to minimize 

such situations. 

In the example introduced in the previous section, the nominal NewSat orbit was constructed 

specifically to be highly colocated with HST’s orbit. This section demonstrates how Monte Carlo

analysis can be used to identify such colocated orbits, which are characterized by a high 

frequency of repeating conjunctions, or, equivalently, a relatively low frequency of first-contact 

conjunctions. For this, the Monte Carlo method is used to predict the average rate of 

conjunctions and the fraction expected to be first-contact events. This specific analysis estimates 

conjunction rates averaged over a screening period of seven days (which is the same screening 

duration used for most LEO CARA satellites). Conjunctions occur in the Monte Carlo simulation 

when an ellipsoidal screening volume centered on the primary satellite is penetrated by the 

trajectory of a secondary satellite. The ellipsoid used for the present analysis has principal axes 

that measure 22525 km, aligned with the primary object’s radial, in-track and cross-track 

directions.
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Appendix H. Long-Term Collision Risk and Satellite Colocation Analysis 99

The goal of colocation analysis is to determine the orbital conditions that create repeating 

conjunctions, which can be accomplished by analyzing the frequency of first-contact events. As 

mentioned previously, first-contact conjunctions correspond to the initial instance that a 

conjunction screening volume is penetrated. This means that pairs of satellites that experience 

high frequencies of repeating conjunctions necessarily have low first-contact conjunction rates 

relative to their total conjunction rates. The colocation analysis graph in Figure H-4 demonstrates 

this effect by comparing total conjunction rates and first-contact rates, plotted as a function of 

∆a, which represents the offset of NewSat’s orbital semi-major axis (SMA, or a) from its 

nominal value. (Note, the analysis assumes that NewSat’s eccentricity and inclination remain at 

their nominal values of 0.001 and 24.5, respectively). The black dashed curve marked with 

circles in Figure H-4 plots the total conjunction rate, Ṅ

c

MC, calculated using equation (H-2). This 

total includes both first-contact conjunctions and any subsequent conjunctions (i.e., repetitions). 

The red dotted curve marked with diamonds plots the first-contact rate, Ṅ

fc

MC, which is always 

less than or equal to the total rate. The black curve shows that conjunctions of either type are 

predicted to occur for SMA offsets within about 10.5 km of the nominal deployment value, i.e., 

in the range -10.5 km ≤ ∆a ≤ +10.5 km. However, the red curve indicates that the rate of firstcontact conjunctions is noticeably lower than the total over the range -6.1 km ≤ ∆a ≤ +6.1 km. 

Furthermore, the first-contact rate is less than 50% of the total rate over the more restricted range 

of -2.2 km ≤ ∆a ≤ +2.2 km. 
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100

 Nmc = The number of Monte Carlo trials RIC = Radial – In-track – Cross-track 

Figure H-4 Predicted Rates for NewSat and HST Satellite Conjunctions

This analysis adopts this 50% reduction (i.e., Ṅ

fc

MC/Ṅ

c

MC < 0.5) as a means to identify highly 

colocated orbits, meaning that, for this specific screening volume and under these conditions, 

NewSat would need to shift its deployment SMA by at least 2.2 km in either direction from the 

nominal value to avoid a high level of colocation with HST. Notably, shifting by about 6.1 km 

would largely eliminate the occurrence of repeating conjunctions, but would not prevent all 

conjunctions between the two satellites. The one-dimensional analysis shown in Figure H-4 

assumes only SMA orbital adjustments, holding the deployment eccentricity and inclination 

constant at their nominal values. A similar two-dimensional analysis holding only the inclination 

constant can also be performed to determine how much the SMA and/or eccentricity would need 

to change to eliminate high levels of colocation (or, equivalently, how much the perigee and/or 

apogee altitudes would need to change). The generalized method can be extended to even higher 

dimensions to include all relevant, adjustable orbital elements.

If the NewSat mission were to change the planned deployment orbit to avoid colocation with 

HST, as described above, then it would be worthwhile to do so in a manner that does not result in 

it being collocated with any other high value satellites. For example, the Fermi Gamma-ray 

Space Telescope (FGST) and the Swift satellite, both NASA missions, occupy orbits similar to 

NewSat’s nominal proposed orbit, so it is conceivable that shifting the NewSat deployment orbit 
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101

could inadvertently create a high level of colocation with one of these satellites. Figures H-5 and 

H-6 demonstrate this by showing one-dimensional colocation analysis graphs for FGST and 

Swift, respectively (each made using the same assumptions as described above for Figure H-4). 

Figure H-5 shows that FGST’s red curve with diamonds is less than half of the black curve with 

circles for -7.0 km ≤ ∆a ≤ -2.5 km, so if NewSat were to shift into this range, then the analysis 

predicts it would become highly colocated with FGST. Similarly, Figure H-6 indicates that 

shifting NewSat’s orbit into the range +7.8 km ≤ ∆a ≤ +12.4 km would result in high colocation 

with the Swift satellite.

 Nmc = The number of Monte Carlo trials RIC = Radial – In-track – Cross-track 

Figure H-5 Predicted Rates for NewSat and FGST Satellite Conjunctions
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102

 

 Nmc = The number of Monte Carlo trials RIC = Radial – In-track – Cross-track 

Figure H-6 Predicted Rates for NewSat and Swift Satellite Conjunctions

H.4 Long-Term Conjunction Rate and Colocation Analysis Software

The NASA CARA software instantiation of the long-term risk and colocation analysis capability 

is an ongoing tool development effort, currently being refactored to execute faster (which is 

especially required for the Monte Carlo analysis modes), and eventually to be more portable 

(because it currently uses the U.S. Space Force COMBO tool, which has restricted distribution). 

The main CARA software tool entitled “LongTermRisk” uses TLE catalogs as input and allows 

users to estimate long-term Kessler collision rates as well as Monte Carlo conjunction rates and

associated first-contact rates. (The LongTermRisk tool was used to create all the figures shown in 

this appendix.) The tool also has the capability to ingest auxiliary TLE catalogs containing 

predicted future satellite constellation(s), for instance, or model populations of untracked orbital 

debris. Because the tool uses the limited-distribution AstroStandands version of the U.S. Space 

Force COMBO close approach analysis function, and because the associated execution 

environment is relatively complicated to set up, it is envisioned that the ability to run this tool 

will remain within the NASA CARA organization.
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Appendix I. Satellite Covariance Realism Assessment Procedures 103

Appendix I. Satellite Covariance Realism Assessment 

Procedures

I.1 Introduction

This section outlines standard methods for assessing the realism of a covariance produced as part 

of the state estimates for a spacecraft. Because probability-based methods for satellite 

conjunction risk assessment in almost all cases require a covariance for their calculation, realistic 

covariances for both the primary and secondary objects in a conjunction are important. 

The U.S. Space Force has pursued algorithmic improvements over the last twenty years to 

improve the realism and representativeness of their catalog’s covariance matrices, especially in 

LEO, so covariances that arise from this source have undergone efforts to assess and sustain their 

trustworthiness. For covariances produced for and contained in satellite O/O ephemerides, the 

situation is much more uneven. While it is true that in the majority of conjunctions the 

covariance for the secondary object predominates, in 5% of the conjunctions the primary 

covariance is larger than the secondary, meaning that it is likely to play a substantial role in 

collision likelihood assessment in over 10% of conjunctions. This is a large enough subset of a 

satellite’s conjunction history to make covariance realism for the primary object ephemeris an 

important consideration.

Because the focus of this section is more practical than theoretical, broader questions of 

covariance formation, methods of covariance propagation, or approaches within the orbit 

determination process to improve covariance realism are not addressed in detail. Modern orbit 

determination packages, such as the Ansys Orbit Determination Tool Kit, include features for 

covariance formation, propagation, and tuning, and their accompanying technical documentation 

is extensive. 

What this section does attempt to do is enumerate the data types needed for covariance realism 

investigations, introduce the appropriate test statistics, and give some guidance for the evaluation 

and interpretation of these tests. Most of the information here derives from NASA CARA’s 

practical experience with this problem, as there are few published studies on the subject and no 

practical guides. The particular focus is on determining the realism of predicted covariance 

generation for actively maintained spacecraft in the presence of precision position data (e.g.,

onboard GPS or telemetry tracking information) to use for a realism assessment because this is 

the particular situation presented to O/Os. 

Covariance realism assessment consists of three parts: collection/calculation of position error 

data, calculation of covariance realism test statistics, and proper assessment of those test 

statistics. After some introductory discussion, each of the three parts of this process will be 

addressed in detail.

I.2 General Remarks

It is important to recall that a spacecraft state estimate generated through an orbit determination

process is an estimate of a mean state (i.e., mean position and mean velocity), and a covariance is 
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Appendix I. Satellite Covariance Realism Assessment Procedures 104

a stochastic characterization of the expected errors about that mean state. The governing 

assumption is that these errors in the individual components conform to a Gaussian distribution; 

this is how a covariance matrix alone is able to represent the error distribution without requiring 

higher-order tensors. The activity of covariance realism is thus to determine how well actual 

state errors conform to the Gaussian distribution that the covariance specifies. Such a statement 

requires additional remarks. 

First, the present treatment focuses on the assessment of the realism of the position portion of the 

covariance, although in most cases the methods advanced here are applicable to a full 6 x 6 or 

even larger covariance matrix. There certainly are reasonable arguments for evaluating the 

covariance in element space (usually equinoctial elements) and considering all six elemental 

representations in any evaluation (Woodburn and Tanygin 2014). However, since the principal 

purpose of covariance generation at present is for conjunction assessment applications, and for 

many conjunction risk assessment approaches only the position portion of the covariance is used 

(typically to calculate the probability of collision employing the two-dimensional simplification 

of the situation; see Chan 2008), it is acceptable to limit oneself to a Cartesian representation of 

the covariance and focus only on its position portion. Furthermore, a previous study has 

demonstrated that potential non-Gaussian covariance behavior brought about by working in a 

Cartesian rather than curvilinear framework rarely affects the outcome of higher-probability 

conjunction events, namely those with Pc values greater than 1E-04 (Ghrist and Plakalovic 

2012). Given all of this, limiting the analysis to the position portion of the covariance is 

reasonable.

Second, because a covariance represents an error distribution, its adequacy as a representation 

can be evaluated only by examining a set of actual error data and determining whether these data 

conform to the distribution specified by the covariance. In actuality, this is usually not possible 

in a straightforward way because a particular covariance is propagated to a particular point in 

time and relevant only at that moment, and at that moment there is only one state estimate and 

thus only one error point. It is not possible to determine in any definitive way whether a single 

point conforms to a distribution; one can determine a percentile level for that point (e.g., for a 

normal distribution with mean 0 and standard deviation 1, absolute values of 3 or greater should 

occur only 0.13% of the time) and discern that such points will not occur frequently in such a 

distribution, but they will occur occasionally, and the situation in the above example may well be 

one such instance. Typically, this problem is addressed by generating a test statistic that 

compares each error point to its associated covariance, determining what the distribution of such 

test statistics should be, and evaluating the conformity of the set of test statistics to the expected 

distribution. More will be said about this in the following sections that directly address the 

calculation of test statistics and evaluation of their statistical properties.

Third, as stated in the previous paragraph, a covariance is always a covariance propagated to a 

particular time. If it is not propagated at all, it is an epoch covariance and is purported to reflect 

the error of the fit;

12 if it is propagated, it is intended to be a reflection of the state estimate error 

12 It is questionable whether the a priori covariance emerging from the batch process does indeed do this as it is 

produced by a calculation that involves only the amount of tracking, times of the tracks, and a priori error variances
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Appendix I. Satellite Covariance Realism Assessment Procedures 105

of that propagated state. Many different covariance propagation methods are available, each of 

which achieves a different level of fidelity, so one source of covariance irrealism can be the 

propagation method itself. It is thus important to group realism evaluations by propagation state; 

for example, all the calculated test statistics for covariances propagated from 1.5 to 2.5 days 

could be collected into a single pool and evaluated as a group, and the evaluation could be said to 

be applicable to covariances propagated about two days. It should also be pointed out that 

covariance irrealism, however it may be evaluated, is unlikely to correlate directly with 

propagation time in the sense that if the covariance is made realistic for a particular propagation 

state, it cannot necessarily be expected to be realistic for all propagation states. When pursuing 

covariance realism remediation, one frequently needs to decide whether some sort of omnibus 

improvement over all common propagation states is desired or whether it is preferable to focus 

on a particular propagation state or narrow ranges of states. Many aspects of the U.S. Space 

Force’s orbit determination process are tuned to optimize performance at 3 days’ propagation; 

this is not a terrible propagation state to choose for O/O covariance realism optimization for 

conjunction assessment applications, although one could also choose a somewhat shorter value if 

that were to align more closely with maneuver commitment timelines.

Fourth, in the context of a covariance error calculation, the individual state error values will need 

to be presumed to constitute independent samples, free of correlation between them. Such an 

assumption is common in most statistical processes, and it is not surprising to see it arise here. 

While true sampling independence is unlikely to be achieved, there are certain measures that can 

be taken to promote it. For example, if one has set up a covariance realism assessment scenario 

by comparing a predicted ephemeris (with covariance) to a definitive ephemeris, it would be best 

to take only one point of comparison for each propagation state bin that one wishes to evaluate. 

For example, in evaluating the two-day propagation state, there would be a temptation to take all 

of the ephemeris points from, say one hour before the two-day propagation point to one hour 

after that. If the ephemeris were generated with one-minute time steps, then this would produce 

120 points instead of just one, which on the surface would seem to give a nice sample set for a 

statistical evaluation. However, because the propagated and definitive ephemeris points are 

highly correlated, in fact little additional information is brought to the evaluation by including 

the entire dataset. Additionally, all of the statistical evaluation techniques that will be deployed 

to generate a realism evaluation assume sample independence; in such a case as the one 

described above, they will miscarry and produce what is likely to be an overly optimistic result. 

In the present scenario, it is best to limit oneself to a single comparison point per propagation 

state from this pair of ephemerides and seek out a group of such ephemeris pairs rather than use 

closely grouped data points from them to try to broaden the sample set.

The procedure recommended above eliminates a particular strain of correlation, but it leads 

naturally to the consideration of a second type: that between successive ephemerides. Definitive 

ephemerides are generally formed by piecing together sections of ephemeris from essentially the 

middle of the fit-spans of moving-window batch orbit determinations, and filters process data 

sequentially but with a forgetting-rate matrix that reduces the influence of older data as a 

for each observable. It does not give a statistical summary of the actual correction residuals. For this reason, some 

practitioners have argued for an alternative formulation of the covariance that considers residual error.
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Appendix I. Satellite Covariance Realism Assessment Procedures 106

function of data age. But in each case, a fair amount of time between ephemerides needs to pass 

before the generated points are statistically independent of a given predecessor set. The 

independence condition could be fulfilled by forcing the generation of products from entirely 

different datasets, but this is not a practical procedure. In past projects, trying to reduce the data 

overlap to less than 50%, meaning that subsequent ephemerides to be used in covariance realism 

evaluations need to be spaced so that they share less than 50% of the generating data with the 

previous ephemeris, has been considered acceptable in practice, although a lower figure would 

be desirable. One need not become overly fastidious about this issue, but it is important to take 

whatever practical steps one can to reduce the influence of sample data correlation on the realism 

assessment.

I.3 Part I: Error Computation

Satellite state errors are computed by comparing a predicted state estimate to some type of state 

truth source. The predicted data typically come from a predicted ephemeris with a predicted 

covariance associated with each ephemeris point. Truth data can come from a variety of sources:

onboard GPS precision position data, precision telemetry tracking data, or a precision ephemeris 

constructed from either of these. Ideally, both the predicted and truth data should align 

temporally (i.e., their time points should be exactly the same), and they should both possess 

covariance data at each time point. In actuality, it is rare that both of these conditions are met, 

and often neither is.

Covariance data are often not available for the truth data source. Precision tracking or GPS data 

can include covariance information as an output from a tracking or combinatorial filter; when 

precision ephemerides are constructed, sometimes covariances can be synthesized from the 

abutment differences observed between the joined “pieces” of ephemeris. However, it is 

frequently the case that even when this is theoretically possible, the construction software has 

failed to include this as a feature. If no covariance data are available for the truth source, one 

must then determine whether the errors in the truth data are so much smaller than the errors in 

the predicted ephemeris under evaluation that the errors in the truth data can safely be neglected. 

The degree of accuracy difference that would allow this assumption is a matter of opinion, but 

most commentators would probably agree that an order of magnitude difference would be an 

acceptable decrement; and in some cases, even smaller ratios could be tolerated. These 

differences, however, must be considered at the individual component level. If the error in one 

component tends to dominate the entire arrangement (as is often encountered with the in-track 

component due to inadequate drag modelling), then the overall normalized error of all three 

position points in the truth ephemeris can be much smaller than the overall error in each point in 

the predicted ephemeris, yet component errors for the cross-track and radial components could 

be of a similar magnitude in both truth and prediction. In such a case, the omnibus test statistic to 

be described in the next section would be distorted because it treats the normalized errors in each 

component essentially equally. 

If the time-points between truth and predicted data do not align, then some sort of intermediatevalue-determination scheme must be used for one of the two datasets. The highest-fidelity 

approach would be to use an actual numerical propagator to produce aligning values, but if the 

points for the source to be adjusted are spaced sufficiently closely, then a number of different 
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Appendix I. Satellite Covariance Realism Assessment Procedures 107

interpolation approaches produce results quite adequate for a covariance realism assessment. 

While the interpolation of state values is relatively straightforward and can be accomplished 

satisfactorily with different interpolation approaches (e.g., Lagrange, Hermite), the interpolation 

of covariances is much more problematic. Different interpolation methods appear to work better 

in different situations; there is no single accepted method to compare multiple covariances to 

evaluate their relative fidelity against each other, and there is a danger of certain interpolation 

methods producing non-positive-definite covariances, which do not make physical sense with the 

current problem. Given this situation, if both data sources (truth and prediction) can be 

interpolated, but only one of the two data sources possesses accompanying covariance data 

(presumably the predicted source), then it is usually preferable to interpolate the data source that 

lacks the covariance, for this eliminates the question of how to handle covariance interpolation. 

If both sources possess covariance, then one would in general interpolate the source with the 

closer point spacing. Alfano (2004) outlines certain covariance interpolation techniques and 

provides test results. There is also an interest in interpolating not the covariance, but the state 

transition matrices associated with the straddling ephemeris points. While this approach can in 

some cases produce slightly less desirable interpolated covariances, it does essentially guarantee 

that the interpolated result will be positive definite. 

Once position and covariance data for the predicted and truth datasets are aligned at the timepoint of interest, calculation of the error is straightforward: it is simply the (subtracted) 

difference between states as long as they both are rendered in the same coordinate system. The 

subtraction convention does not actually matter given the way the test statistic is computed, but 

for consistency, one can follow the “observed – expected,” or truth – prediction, paradigm. The 

two covariances for each comparison point (one for the truth position and one for the predicted 

position) are simply added together, presuming, of course, that they are in the same coordinate 

system. Thus, for each point of comparison, one will have a position difference (with three 

components) and a corresponding combined covariance (or just the predicted source’s 

covariance if the truth source’s errors are presumed to be extremely small). 

While one can conduct an entire covariance realism evaluation in the Earth-Centered Inertial 

(ECI) reference frame, it is often more meaningful to move it into the Radial – In-track – Crosstrack (RIC, which is also called the UVW) frame—a reference frame that is centered on the 

object itself. If only one of the evaluation data sources has an associated covariance, then it 

probably makes sense to make that source the center for the RIC coordinate frame. If a 

covariance is provided for both, then it does not really matter which is selected to ground the 

RIC frame. The use of the RIC frame is helpful in moving from a finding of irrealism to 

remediation suggestions.

I.4 Part II: Test Statistic Computation

As stated previously, a position covariance, which in this treatment is the portion of the matrix to 

be tested for proper error representation, describes a three-dimensional distribution of position 

errors about the object’s nominal estimated state, and the test procedure is to calculate a set of 

these state errors and determine whether their distribution matches that described for the position 

covariance matrix. To understand the test procedure, it is best to consider the problem first in one 

dimension, perhaps the in-track component of the state estimate error. Given a series of state 
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Appendix I. Satellite Covariance Realism Assessment Procedures 108

estimates for a given trajectory and an accompanying truth trajectory, one can calculate a set of 

in-track error values, here arranged in vector form and given the designation ε, as the differences 

between the estimated states and the actual true positions. According to the assumptions 

previously discussed about error distributions, this group of error values should conform to a 

Gaussian distribution. As such, one can proceed to make this a “standardized” normal 

distribution, as is taught in most introductory statistics classes, by subtracting the sample mean 

and dividing by the sample standard deviation: 



 − 

(I-1)

This should transform the distribution into a Gaussian distribution with a mean of 0 and a 

standard deviation of 1, a so-called “z-variable.” Since it is presumed from the beginning that the 

mean of this error distribution is 0 (because the state estimate is an estimate of the mean and is 

presumed to be unbiased), the subtraction as indicated in the numerator of Equation I-1 should be 

unnecessary, simplifying the expression to:





(I-2)

It will be recalled that the sum of the squares of n standardized Gaussian variables constitutes a 

chi-squared distribution of n degrees of freedom. As such, the square of Equation I-2 should 

constitute a one-degree-of-freedom chi-squared distribution. This particular approach of testing 

for normality—evaluating the square of the sum of one or more z-variables—is a convenient 

approach for the present problem, as all three state components can be evaluated as part of one 

calculation (εu represents the vector of state errors in the radial direction, εv the in-track direction, 

and εw the cross-track direction):

2

2 3

2

2

2

2

2

dof

w

w

v

v

u

u 













+ + =

(I-3)

One could calculate the standard deviation of the set of errors in each component and use this 

value to standardize the variable, but it is the covariance matrix that is providing, for each 

sample, the expected standard deviation of the distribution. Since the intention here is to test 

whether this covariance-supplied statistical information is correct, the test statistic should use the 

variances from the covariance matrix rather than a variance calculated from the actual sample of 

state estimate errors. For the present moment, it is helpful to presume that the errors align 

themselves such that there is no correlation among the three error components (for any given 

example, it is always possible to find a coordinate alignment where this is true, so the 

presumption here is not far-fetched; it is merely allowing that that particular coordinate 

alignment happens to be the RIC or UVW coordinate frame). In such a situation, the covariance 

matrix would lack any off-diagonal terms and thus look like the following:
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Appendix I. Satellite Covariance Realism Assessment Procedures 109





















=

2

2

2

0 0

0 0

0 0

w

v

u

C







(I-4)

and its inverse would be straightforward:

.

0 0 1

0 1 0

1 0 0

2

2

2

1





















=

−

w

v

u

C







(I-5)

If the errors for a single state are formulated as:

  u v w

 =   

(I-6)

then the pre-and post-multiplication of the covariance matrix inverse by the vector of errors 

(shown in Equations I-3 through I-6) will produce the expected chi-squared result:

 

2

2 3

2

2

2

2

2

2

2

2

1

0 0 1

0 1 0

1 0 0

dof

w

w

v

v

u

u

w

v

u

w

v

u

u v w

T C 

























     = + + =









































=

−

(I-7)

What is appealing about this formulation is that, as the covariance becomes more complex and 

takes on correlation terms, the calculation procedure need not change: the matrix inverse will 

formulate these terms so as properly to apportion the variances among the U, V, and W

directions, and the chi-squared variable can still be computed with the εC

-1

ε

T

formulary. For such 

a situation in two-dimensions (chosen here for illustrative purposes because the expression is less 

complex) in which the error quantities are εx and εy and the correlation coefficient is ρ, the entire 

equation, with correlation terms included, assumes the form:

( )

















+ −

−

=

−

x y

x y

y

y

x

T x C

 

 











 

2

1

1

2

2

2

2

2

1

(I-8)

One can observe that if the correlation coefficient is zero, the equation reduces to the twodimensional equivalent of the form shown in Equation I-7 above. As the correlation coefficient 

moves from zero to a more substantial value, the test statistic encounters a trade-off between the 

overall inflating effect of the (1-ρ) multiplier and the subtracted correlation term.

The quantity εC

-1

ε

T

is called the Mahalanobis distance (technically, it is the square of the 

Mahalanobis distance), named after the mathematician P.C. Mahalanobis (who, by the way, was 

a personal friend of the 20th-century mathematical genius Ramanujan). This construct is a 

convenient and useful way to calculate a normalized distance. 
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I.5 Part III: Test Statistic Evaluation

It is very well that a test statistic can be derived that, if the covariance is realistic, should 

conform to a known statistical distribution, but of course, there needs to be some method for 

testing a group of these test statistics to determine if in fact they do conform to the expected 

distribution. Such a desire leads the investigation to the statistical subdiscipline of “goodness of 

fit.”

Every student of college statistics learns about Analysis of Variance (ANOVA), the particular 

procedure for determining whether two groups of data can essentially be considered the same or 

different. More particularly, it is a procedure for determining whether the experimental 

distribution, produced by the research hypothesis, can be considered to come from the parent 

distribution represented by the null hypothesis, and the operative statistic arising from the 

analysis is the p-value: the likelihood that the research dataset can be considered a sample drawn 

from the null hypothesis’s parent distribution. If this value becomes small, such as only a few 

percent, it means that there are only about two or three chances in one hundred that the 

experimental dataset would have been generated from sampling from the null hypothesis dataset.

In this case, the research and the null hypothesis outcomes can be considered to be palpably 

different, which would be likely to lead to the rejection of the null hypothesis and the embrace of 

the research hypothesis. This procedure is a specific example of statistical hypothesis testing.

A similar procedure can be applied to evaluate goodness of fit, namely, to evaluate how well a 

sample distribution corresponds to a hypothesized parent distribution. In this case, the general 

approach is the reverse of the typical ANOVA situation: it is to posit for the null hypothesis that 

the sample distribution does indeed conform to the hypothesized parent distribution, with a low 

p-value result counseling the rejection of this hypothesis. This approach does favor the 

association of the sample and the hypothesized distribution, which is why it is often called 

“weak-hypothesis testing”. Although counterintuitive, this approach is not unreasonable: what is 

being sought is not necessarily the “true” parent distribution but rather an indication of whether it 

is reasonable to propose the hypothesized distribution as the parent distribution for the 

experimental data that one has generated or calculated. In the present case, the question to be 

posed is whether the observed squared Mahalanobis distance histories, calculated by the 

procedure in Part II, conform to a 3-degree-of-freedom chi-squared distribution, namely, whether 

they can be considered to have been drawn from a 3-degree-of-freedom chi-squared distribution 

as a parent distribution—if they do, then the covariance properly represents the actual observed 

error distribution.

There are several different mainstream techniques for goodness-of-fit weak-hypothesis testing:

moment-based approaches, chi-squared techniques (not in any way linked to the fact that the 

present application will be testing for conformity to a chi-squared distribution), regression 

approaches, and Empirical Distribution Function (EDF) methods. The easiest and most direct of 

these is simply a test of the first moment of the distribution (that is, the mean), which, if 

normalized by the degrees of freedom of the distribution, should be unity (or, in the present case, 

should take on an unnormalized value of 3). The square root of this mean, the so-called 

Mahalanobis distance, is a good estimate of a single-value scale factor describing the covariances 

departure from reality, and as such, it is a convenient way to compare the results from different 
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Appendix I. Satellite Covariance Realism Assessment Procedures 111

covariance correction techniques as well as estimate a single-value scale factor that could 

potentially be used to remediate an irrealism situation. 

While this test is easy to apply and expeditious for generating comparative results, in comparison 

to other goodness-of-fit tests it lacks power. Indeed, many different distributions could have the 

same mean yet be substantially different in the overall behavior or in the tails: a close match of 

the mean is a necessary but not sufficient condition for matching a distribution. To evaluate the 

match between entire distributions, the EDF methodology is generally considered to be both the 

most powerful and most fungible to different applications. For this reason, it does not make 

sense to apply formal goodness-of-fit tests to first-moment results (i.e., matching of the mean); 

these should be used merely as a methodology to compare performance for the corrected versus 

uncorrected cases and intra-correction-methodology performance.

The general EDF approach is to calculate and tabulate the differences between the Cumulative 

Distribution Function (CDF) of the sample distribution and that of the hypothesized distribution, 

to calculate a goodness-of-fit statistic from these differences, and to consult a published table of 

p-values for the particular goodness-of-fit statistic to determine a significance level. Specifically, 

there are two goodness-of-fit statistics in use with EDF techniques: supremum statistics, which 

draw inferences from the greatest deviation between the empirical and idealized CDF (the 

Kolmogorov-Smirnov statistics are perhaps the best known of these); and quadratic statistics, 

which involve a summation of a function of the squares of these deviations (the Cramér – von 

Mises and Anderson-Darling statistics are the most commonly used). It is claimed that the 

quadratic statistics are the more powerful approach, especially for samples in which outliers are 

suspected, so it is this set of goodness-of-fit statistics that are recommended for covariance 

realism evaluations. The basic formulation for both the Cramér – von Mises and AndersonDarling approaches is of the form:

 





−

Q = n F x − F x x dx n( ) ( ) ( )

2



(I-9)

The two differ only in the weighting function ψ that is applied. The Cramér – von Mises statistic 

is the simpler:

 (x) = 1

(I-10)

setting ψ to unity. The Anderson-Darling is the more complex, prescribing a function that 

weights data in the tails of the distribution more heavily than those nearer the center:

  

1

( ) ( ) 1 ( )

−

 x = F x − F x

(I-11)

The Anderson-Darling construct is thus more sensitive to outliers. Given NASA CARA’s 

experience that outliers frequently creep into covariance realism evaluations and introduce 

statistical processing issues, it is recommended to choose the somewhat more permissive 

Cramér – von Mises statistic for covariance realism investigation purposes.
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Appendix I. Satellite Covariance Realism Assessment Procedures 112

It is a straightforward exercise to calculate the statistic in Equation I-9, discretized for the actual 

individual points in the CDF for each trajectory (that is, changing the integral into a summation), 

and for convenience, this quantity is called the “Q-statistic.” The step after this is, for each 

Q-statistic result, to consult a published table of p-values (determined by Monte Carlo studies) 

for this test to determine the p-value associated with each Q-statistic (a good source for these 

tables as well as an excellent treatment of the overall subject is given in D’Agostino and 

Stephens 1986). The usual procedure is to set a p-value threshold (e.g., 5%, 2%, 1%) and then to 

determine whether the sample distribution produces a p-value greater than this threshold 

(counseling the retention of the null hypothesis: sample distribution conforms to hypothesized 

distribution) or less than this threshold (counseling rejection of the null hypothesis: sample 

distribution cannot be said to derive from the hypothesized distribution as a parent). One can also 

interpolate to determine the precise p-value for each test situation. NASA CARA has source 

code and test cases that perform all the above calculations and reside on the NASA CARA 

public-facing software repository for free download (See Section 7, Contact Information in this 

document for the specific URL.)

Finally, it should be noted that, even though there are normalization provisions within the EDF 

formulation, the results do, to some degree, depend on the size of the sample. In a way this is 

considered already by accommodation within the p-value tables for sample size, but because of

the quadratic-sum nature of the test statistic, the procedure can still be overwhelmed by large 

sample sizes. One approach to mitigating this situation is to pick a standard sample size—

perhaps somewhere in the neighborhood of 50 samples—and calculate the test statistic in a 

(with-replacement) resampled manner, producing a CDF of the p-values attained for each 

sample. As an example, suppose that for a particular evaluation there are 100 error vectors with 

associated covariance and therefore 100 test statistic (εC

-1

ε

T

) results. When running the 

goodness-of-fit test, one might choose 1000 random, 50-point samples (with replacement) from 

this set of 100 values and test each, producing a CDF chart of the 1000 p-values obtained from 

the resampling investigation. 

What is an acceptable level for a p-value result—one that would indicate that the error 

distribution matches that of the covariance? In goodness-of-fit practice, rarely is a significance 

level greater than 5% required, and levels of 2% or even 1% are often accepted. It probably can 

be said that values less than 1% cannot allow the conclusion that there is any real conformity to 

the hypothesized distribution. At the same time, it should be added that the calculation is rather 

sensitive to outliers and that this should be kept in mind when interpreting results.

If results from different remediation approaches match the hypothesized distribution closely 

enough, then comparison of different p-value levels can serve as a notional indication of the 

relative performance of these different approaches. However, if the performance is such that the 

hypothesized distribution is not approached all that closely by any of the correction mechanisms, 

then a situation can be encountered in which the results fall off the published tables of 

p-values, and it becomes extremely difficult to compare the results of the different methods 

conclusively. In such a case, it may be possible to draw some broad comparative results from 

looking at the Q-values rather than the associated p-values, but in all likelihood, it will be 

necessary to revert to simply a comparative-results set such as first-moment tests.
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Appendix I. Satellite Covariance Realism Assessment Procedures 113

I.6 Part IV: Data Outliers and Conditioning

As remarked in the above section, goodness-of-fit test results can be sensitive to outliers; this is 

true whether one interprets results visually or uses a formal technique. The deleterious impact on 

test results is mitigated somewhat using the resampling approach discussed previously, by which 

the contribution of the outliers to each individual test is lessened. However, the fact remains that 

bad data do enter the orbit determination process, and the failure to take some account of this 

reality can produce situations in which the covariance realism assessment problem becomes 

intractable. 

The entire covariance realism assessment process is grounded on the notion that individual 

component errors are normally distributed, and this situation allows for certain techniques to 

identify outliers. The usual “x-sigma” filter is a naïve and unscientific method for outlier 

identification and is especially difficult to justify for the Gaussian distribution, where there is 

some developed theory for outlier identification. A superior approach is the Grubbs outlier test, 

which provides a formal statistical test for outliers but works only in situations with a single 

outlier and cannot be applied recursively (Grubbs 1969). In the case of multiple outliers, the 

procedures of Rosner (1975, 1977) are applicable but must be applied with an a priori guess of 

the number of potential outliers. That is, one must first inspect the data to assemble a proposed 

set of outliers and then test this group as outliers for a particular significance level. Because only 

a single component can be assessed at a time, to use this approach it is probably best to design a 

tool that can examine a particular error point’s behavior in all three components (compared to the 

rest of the main distribution) to determine which set of points might constitute an outlier set and 

test that set. Several such attempts may be needed before a set of points can be identified as 

outliers to a given significance level. 

An extended example of the application of the technique described here is available in Zaidi and 

Hejduk (2016).
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Appendix J. CARA Conjunction Risk Assessment Tools Validation 114

Appendix J. CARA Conjunction Risk Assessment Tools 

Validation

CARA and JSC FOD are chartered to perform conjunction assessment screenings, risk 

assessment, and mitigation action guidance on behalf of NASA missions, so typically there is no 

particular need for missions to obtain or develop conjunction risk assessment evaluation tools. 

However, cases can occasionally arise in which it is not practical or desirable for CARA/JSC 

FOD to perform these calculations, such as for potential autonomously controlled missions that 

will perform onboard conjunction assessment. In such cases, the needed calculations or tools will 

be validated by CARA/JSC FOD before operational use. Methods used for validation include the 

following:

• Inspection. Used to verify that a particular datum or feature is present, that a display or 

graphic is properly constructed to convey a particular concept, etc.

• Analysis/Documentation. Used to ensure that a particular algorithm is theoretically or 

practically sound, that a needed parameter is properly converted to a different reference 

frame or units, etc.

• Formal Test. Used to ensure that critical calculations are performed correctly by 

executing a formal test with preconfigured input data and expected results, which are 

compared to the test article’s results and any differences satisfactorily explained.

Formal test is the most frequently used methodology within CARA validation. conjunction risk 

assessment calculations for which formal test cases with expected results presently exist include 

the following:

• Two-dimensional Pc calculation with and without covariance correlation correction and 

non-positive-definite covariance correction

• Two-dimensional Pc calculation when one covariance is missing (Frisbee method)

• Three-dimensional Pc calculation (Coppola-Hall method) with and without covariance 

correlation correction and non-positive-definite covariance correction

• Pc calculation by Brute Force Monte Carlo (from epoch)

• Pc sensitivity to space weather mismodeling

• Conjunction relative state comparison

• Collision consequence evaluation (anticipated number of resultant debris pieces above a 

certain size)

• Maneuver trade space calculations for single and multiple conjunctions

The NASA CARA software repository includes test cases for software validation. (See Section 

7, Contact Information in this document for the specific URL.)
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Appendix K. R-15 Message 115

Appendix K. R-15 Message

The Ready minus 15 (R-15) Vehicle Information Message (VIM) is a collection of launchrelated information that is distributed by the launch vehicle operator 15 days before launch to 

inform concerned parties about upcoming launch activity. It contains key information to support 

the tracking and early acquisition of the injected payloads as well as other launch-related objects 

such as rocket bodies. The extract below gives preparation instructions for this message. An 

official copy of the R-15 form can be obtained from the space-track.org website maintained by 

USSPACECOM. A sample structure for the R-15 is provided below for reference only.

K.1 R-15 Preparation Instructions

How to fill out a R-15/VIM report:

ITEM ENTRY

1 Launch site (Site, Pad, Country)

2 Launch date (Greenwich Mean Time (GMT))

3 Earliest launch time. (GMT, HH:MM:SS)

3A Latest launch time. (GMT, HH:MM:SS)

4 List the total number and name of each object to achieve orbit.

4A Payload(s) to achieve orbit. Include the nominal (operational) lifetime and operating 

position for each.

4B Rocket bodies (booster segments) to achieve orbit. If none achieve orbit, enter "none.”

4C All other objects achieving orbit, including debris, debris clusters, bolts, and so forth. If 

none will achieve orbit, enter "none."

5 Launch booster and sustainer description. If booster is augmented by strap-on motors, list 

the number and type.

6 Point of contact for the launch. 

7 Mission brief of payload(s).

8 Transmitting frequency and power of all devices (including booster segments and 

continuous radio transmissions) and schedule and power of all lights (if any) throughout 

the operational life. Statement of whether emission is fixed by program, command, or 

transponder tracking signal.
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Appendix K. R-15 Message 116

R-15/VIM REPORT ATTACHMENT A: Keplerian orbital parameters to include sequence of 

events from liftoff (HH:MM:SS = 00:00:00) to final injection into operational orbit. Require 

times for each in HH:MM:SS from liftoff. Events include: separation of booster(s)/stage(s), 

motor ignition(s)/cutoff(s), jettison of pieces (fairings etc.), maneuvers and reorientation, deorbit 

and ejections) of packages/booms and so forth.

K.2 R-15/VIM Report Structure

ITEM 1 Launch Site:

ITEM 2 Launch Date:

ITEM 3 Earliest and latest possible launch time (GMT):

ITEM 3A Latest possible launch time (GMT):

ITEM 4 List the total number and name of each object to achieve orbit.

ITEM 4A Payload(s) to achieve orbit. Include the nominal (operational) lifetime and 

operating position for each:

ITEM 4B Rocket bodies (booster segments) to achieve orbit. If none achieve orbit, enter 

"none.”

ITEM 4C All other objects achieving orbit, including debris, debris clusters, bolts, and so 

forth. If none will achieve orbit, enter "none."

ITEM 5 Launch booster and sustainer description. If booster is augmented by strap-on 

motors, list the number and type:

ITEM 6 Point of contact for the launch: 

ITEM 7 Mission brief of payload(s):

ITEM 8 Transmitting frequency and power of all devices (including booster segments and 

continuous radio transmissions) and schedule and power of all lights (if any) 

throughout the operational life. Statement of whether emission is fixed by 

program, command, or transponder tracking signal.
National Aeronautics and Space Administration K.3 R-15/VIM Report Attachment A Structure

MET (s) Event timeline

Altitudes (km)*** Inclination 

(deg)

EccentricitySMA 

(km)

Arg. of 

perigee 

(deg)

RAAN

** 

(deg)

True 

Anomaly 

(deg)

Latitude 

(deg)

Longitude

(deg)

Relative 

Velocity 

(m/s)

Current 

Altitude 

(km)

Period 

(min) Apogee Perigee

MET - Mission Elapsed Time

SMA - Semi-Major Axis 

RAAN - Right Ascension of the Ascending Node
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Appendix L. Commercial Data in NASA Conjunction Assessment 118

Appendix L. Commercial Data in NASA Conjunction 

Assessment

The breadth and quality of commercial SSA data has developed in the last decade from 

essentially no commercial presence at all to the presence of a number of different vendors, each 

specializing individually in radar, optical, or passive radio frequency satellite tracking. In

addition to tracking measurement data, vendor offerings now include additional SSA products 

such as vectors, ephemerides, and even conjunction risk assessment analysis outputs such as 

Conjunction Data Messages (CDMs). 

In examining and facilitating the use of commercial data in NASA conjunction risk assessment

calculations, CARA and JSC FOD adhere to the following principles:

1. Use raw observation (measurement) data only and combine with Space Surveillance 

Network (SSN) observations for a single solution

2. Validate all non-SSN data 

3. Undertake a cost/benefit analysis before purchasing commercial SSA data

More details on these principles are described below.

L.1 Use raw observation (measurement) data only and combine with 

SSN observations for a single solution 

Of all the data types offered by commercial providers, only the raw satellite tracking data are at 

present fully and unambiguously of use to the NASA conjunction assessment enterprise. 

Because NASA has access to both the USSPACECOM satellite tracking data from the SSN and 

the USSPACECOM space catalog maintenance operational system, NASA has the ability to 

include raw commercial observation data along with SSN tracking data into a combined close 

approach prediction. This process involves combining all of the measurement data on an object

of interest from both the SSN and commercial sources to perform a single orbit determination. 

The predicted close approaches can then be calculated from this combined source. The CARA 

and JSC FOD personnel who are embedded in the 18 SDS work center at VSFB presently have 

this capability in a “sandbox” area on the operational system that is not used for routine 

operations. The sandbox area enables CARA/JSC FOD operators to combine the SSN and 

commercial data in a native and compatible way to produce a single risk assessment solution that 

can be acted upon unambiguously. 

Work is also progressing on a regularization of the reception of commercial data into the 18 SDS 

enterprise; when such a capability is in place, conjunction assessment products deriving from 

combined commercial and DOD tracking data will be possible routinely. But receiving higherlevel products from commercial vendors, such as vectors or even conjunction assessment outputs 

like CDMs, introduces multiple solutions into the enterprise and creates significant operational 

difficulties in trying to adjudicate among them. 
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Appendix L. Commercial Data in NASA Conjunction Assessment 119

Event evaluation in the presence of multiple solutions

There is presently a debate within the industry regarding the best way to proceed with event 

evaluation in the presence of multiple solutions. CARA/JSC FOD encounters a version of this 

situation in miniature each day in that most conjunction events possess two solutions: one that 

uses the DOD predicted position for the primary object state and a second that uses the O/O 

predicted ephemeris for that state. Counterintuitively, it is not always clear which of these two 

sources for the primary object predicted state is superior. 

O/Os typically have more and better past position data on their satellite, either from telemetry 

tracking or onboard GPS fixes, and they also understand the configuration of their satellite better 

and thus should be able to calculate the components of the ballistic coefficient with more 

precision. The O/Os should then be able to come up with a better epoch solution on which to 

base prediction, and they are positioned to do a better job in prediction as well because they 

potentially possess a superior ballistic coefficient. However, O/O orbit determination software 

atmospheric density models often introduce more error into predicted states than the model used 

by the 18 SDS. 

In the situation that CARA faces, the choice of a preferred data source is thus not straightforward 

because a number of factors influence the selection: the capabilities of the O/O’s orbit 

determination software, the particular orbit that the satellite occupies, the degree to which the 

space weather situation is perturbed, and the span from the present time to TCA, among others.

Establishing a rubric of precedence

To reliably choose between these two information sources, CARA has performed a Verification 

and Validation (V&V) activity of the orbit determination products for selected NASA O/Os and 

has developed rubrics for selecting a particular solution (DOD- or O/O-based) source in 

particular contexts. A V&V activity of this type requires several months’ worth of data and is 

complicated to perform, necessitating specialized tools and subject matter expert interpretation of 

the results. With multiple providers of information for both the primary and secondary objects 

involved in a conjunction, the situation would be that much more complicated.

Assimilative solution selection

An alternative to establishing a rubric of precedence for the multi-solution situation is using an 

assimilative modeling approach similar to that used for hurricane modeling. 

The results from multiple providers are collected and comparatively analyzed, both visually and 

with formal clustering algorithms. Due to the large representation among the submissions (i.e., 

most of the individual results clustering around a single result), the hope is to be able to establish 

a supermajority result that suggests itself as the favored solution. Although such a procedure 

appears attractive at first, it encounters difficulties in implementation.

• First, it requires a sufficient number of providers supplying solutions to obtain 

meaningful data clusters. Clustering among, say, ten submitted solutions has the 

propensity to identify meaningful clusters and thus enable the drawing of certain 
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Appendix L. Commercial Data in NASA Conjunction Assessment 120

conclusions. With only two or three providers, this is not really possible. At present, the 

number of different providers is too small to use a clustering approach. 

• Second, because of explainable and therefore expected discontinuities in space 

surveillance data sets, it is not unusual for minority submissions to an assimilative 

framework to represent the superior solution. The common situation of satellite 

maneuvers is a good example: only one of a set of providers may have detected a 

maneuver for one of the spacecraft in a conjunction and updated that spacecraft’s state 

appropriately. This solution is clearly superior to other submissions that did not obtain 

tracking in time to identify the maneuver and correct the trajectory. But as a single 

solution representing this modified state, this solution will appear assimilatively as an 

outlier and is likely to be rejected. This scenario has played out repeatedly at the Sprint 

Advanced Concept Training (SAC-T) exercises conducted by the U.S. Space Force’s 

Joint Commercial Operations (JCO) cell: a single vendor’s submission differs 

appreciably from the other submissions yet is shown later to be the preferred solution. 

In short, while assimilative solution selection remains a potentially helpful construct for 

employing multiple solutions contemporaneously to guide a single operational decision, more 

research and refinement are required before such a paradigm can be employed in an 

operationally satisfactory manner to support conjunction risk assessment.

Direct fusion of orbital solutions

Finally, there are proposals in the academic literature for the direct fusion of different orbital 

solutions, including CDMs from different providers, into a single solution that in principle 

combines the information of all the individual submissions.

Carpenter (2020) represents the most promising of such proposals, which is also nicely tailored 

for the conjunction assessment problem. While the theoretical development is indisputable, a

couple of practical problems remain: 

• First, the combination methodology relies directly on realistic covariances accompanying 

each state estimate. If these covariances are not representative, then the fused product is 

errant not just in its own covariance but in its synthesized state estimate. Because 

covariance realism is an elusive achievement for many providers, and because a rigorous 

V&V effort is required to establish the abiding presence of realistic covariances in a 

provider’s product set, direct fusion is not a mechanism that can be easily or immediately 

employed.

• Additionally, the theory requires the cross-correlations between the covariance matrices 

arising from different providers to be characterized and deployed in the fusion paradigm, 

yet there is no obvious method for establishing these cross-correlations between the 

providers’ orbital determination uncertainties. There is an argument that, due to the use of 

different input data with different errors, the correlated error should be negligible; at the 

same time, it could reasonably be expected that some shared model error, such as 

geopotential error or atmospheric density forecast error, would appear in a crosscorrelation analysis.
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Appendix L. Commercial Data in NASA Conjunction Assessment 121

So, for the direct fusion methodology described here, more focused study is needed before an 

approach of this type can be employed operationally.

Conclusion about the use of commercial SSA data

Given the present difficulties with the presence of multiple SSA and conjunction assessment

products, NASA has concluded that it is necessary to limit the use of commercial SSA data to the 

combination of commercial and DOD tracking information.

L.2 Validate all non-SSN data 

All non-SSN sources supplying data to be used in orbit determination solutions to maintain the 

catalog must be regularly calibrated to ensure the removal of any data biases that might skew the 

conjunction assessment screening results. 

Using raw observation data from commercial vendors (as opposed to post-processed solutions) 

enables straightforward data characterization and numerical validation. 

Commercial vendors supporting NASA are regularly asked to track and submit the tracking data 

taken on calibration satellites for which precision ephemerides are available; these satellites can 

be both dedicated calibration spheres (such as those used by the International Laser Ranging 

Service) and U.S. Government payloads with stable orbits. The commercial tracking data are 

compared to the precision ephemerides and the residuals characterized for each observable: mean 

errors can be subtracted from the data themselves and thus do not affect the data quality, error 

variances can be used as sensor data weighting factors in the orbit determination process, and 

non-Gaussianity and variation of the means and variances with time can indicate an unstable 

situation that may render a particular commercial provider’s data unsuitable for use.

For stable commercial data sources, quantification of mean error and error variance allows the 

data to be combined with SSN data (which also have quantified error means and variances) to 

produce an orbit determination result that has weighted the constituent data correctly and thus 

properly considers the relative accuracy of the inputs in forming the desired single solution.

L.3 Undertake a cost/benefit analysis before purchasing commercial 

SSA data

While following the recommendations of L.1 and L.2 above would allow the introduction and 

proper use of commercial SSA data in NASA conjunction assessment, a third consideration 

focuses on whether the use of these data would in fact result in a significant operational benefit.

NASA, as a U.S. Government entity, follows the guidance of the National Space Policy to 

receive conjunction assessment services from the 18 SDS and 19 SDS, who maintain the U.S.

catalog of space objects. While it is true that adding properly calibrated commercial tracking data 

should result in a more reliable orbit determination solution with a smaller uncertainty, the effect 

may be such that the use of these additional data would rarely, if ever, result in a different 

operational decision regarding whether to require and execute a conjunction mitigation action. 
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Appendix L. Commercial Data in NASA Conjunction Assessment 122

Most conjunction situations receive adequate SSN tracking data to the degree that adding some 

additional data does not change the risk assessment appreciably and therefore does not alter the 

operational decisions. A complex cost-benefit analysis would need to be performed to 

understand the financial obligation appropriate to purchase commercial data to augment the 

existing NASA conjunction assessment process based on the risk mitigation expected. 

If, for example, having commercial data changed a conjunction Pc value from 5E-05 to 1E-04, 

this would cause a mitigation action to be taken when, without the data, it probably would not 

have been if the Pc threshold for maneuvering were set at 1E-04, so the operational outcome was 

changed to lower the risk. However, the risk exposure if the mitigation action were not taken is 

still very low: an actual risk of a 1 in 10,000 chance of a collision versus the 1 in 20,000 chance 

calculated with the SSN data alone. 

The benefit would depend on how many times per year these decisions would be altered and thus 

how much risk is mitigated. By some estimates, over 90% of the objects larger than 1cm and 

thus able to render a satellite inoperative in a collision are too small to be tracked and thus are 

not considered in the conjunction risk assessment process. Therefore, part of the trade space is to 

consider how much adding commercial data reduces collision risk compared to the background 

risk. This decision would likely vary by orbit altitude based on trackability of objects of various 

sizes and the existing debris population.
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Appendix M. Use Pc as the Risk Assessment Metric for Conjunction Assessment 123

Appendix M. Use of the Probability of Collision (Pc) as the

Risk Assessment Metric for Conjunction Assessment

M.1 Introduction

Satellite conjunction assessment comprises two principal goals: to protect important assets from 

premature and unplanned mission failure due to preventable collisions and to assist in the 

regulation and minimization of space debris production. The first of these goals is in its details 

largely left up to the individual O/O to adjudicate. After all, the particular “value” of any given 

on-orbit asset, and therefore the level of risk of its possible loss that one is willing to bear, are 

governed by the specifics of the situation including the age (and perhaps importance) of the 

satellite and mission, the degree to which the mission objectives have already been met, and 

mission redundancy provided by additional spacecraft. It is best left to the individual mission 

project office to choose appropriate conjunction assessment actions (or inactions) relating 

directly to mission preservation. However, the second goal of overall space debris production 

minimization is much broader in scope. Born of the desire to keep key orbital corridors free from 

debris pollution to allow their perpetual continued use by all space actors, this goal transcends 

the health and preservation of the individual mission. It is in response to this second goal that 

actual conjunction risk assessment and mitigation thresholds are articulated. Mission operators 

can always take a more conservative posture than what is appropriate for debris mitigation, but at 

the least they must embrace a minimum level of responsibility to preserve key orbital corridors 

for future use.

To this end, the purpose of satellite conjunction assessment and risk analysis is neither to 

maximize safety, nor fully to minimize risk of satellite conjunction with other objects, nor 

absolutely eliminate the likelihood of space debris production. Instead, the official CARA 

statement of purpose is more nuanced: to take prudent measures, at reasonable cost, to improve 

safety of flight, without placing an undue burden on mission performance. This statement 

includes a number of qualitative terms, such as “prudent,” “reasonable,” and “undue burden”; for 

ultimately, it is not a scientific conclusion but a series of prudential judgments to assemble 

guidelines that work to prevent space debris pollution while accommodating the competing 

claims of mission execution and inherent levels of risk assumed simply by launching a satellite at 

all.

It is this last consideration, namely the risk necessarily assumed simply by launching a satellite, 

that requires attention, especially in selecting a collision likelihood metric and evaluation 

paradigm. A 2020 NASA ODPO space debris catalog generated for CARA contained over 

300,000 objects larger than 1 cm in physical size, which is the level at which an object is 

typically considered able to penetrate a satellite’s shielding and render it inoperative. With 

tracking improvements and the launch of additional satellites, one can expect a regularly

maintained space catalog of perhaps 30,000 to 50,000 objects. This means that, roughly 

speaking, about five-sixths of the objects large enough to leave a satellite in a failed and 

uncontrolled state if a collision should occur with them will be untracked. Presumably, that same 

proportion of the close-approach events that actually occur are not discoverable with current 

sensor technology and cannot be mitigated. Given then that only about one-sixth of the close-
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Appendix M. Use Pc as the Risk Assessment Metric for Conjunction Assessment 124

approach events are trackable and in principle actionable, the overall conjunction risk analysis 

process (and the risk assessment parameters that drive it) should be commensurate with a 

situation in which greater than 85% of similarly likely collisions cannot be addressed at all and 

thus constitute a risk that simply has to be accepted. It is not reasonable to adopt an excessively

conservative risk management position for known conjunctions when so substantial a portion of 

the actual collision risk is accepted without any possible mitigation as part of the cost of space 

operations.

However, despite the large background collision likelihood that is accepted simply by launching 

a satellite at all, there is still great value to on-orbit conjunction analysis, risk assessment, and 

mitigation. First, because collisions between protected payloads and large secondary objects will 

produce, by several orders of magnitude, the most debris fragments, there is substantial benefit to 

avoiding collisions of this type. These large secondary objects are resident and well maintained 

in the present satellite catalog, so they represent rather straightforward cases for conjunction 

assessment. Second, when serious conjunctions of any type are identified and are well 

understood, these also represent straightforward situations for which due diligence counsels risk 

assessment and possible mitigation action. It is only when the situation is poorly determined—

when some information about a conjunction is present but not of the sufficiency needed to 

conclude that a problematic situation is in fact at hand—that requiring remediation actions 

through an overweening conservatism is not appropriate, given the size of the accepted 

background risk. 

The purpose of this appendix is to explain the selected risk assessment metric and interpretive 

framework for that metric, chosen to enable proper balance between mitigation of truly 

problematic conjunctions and an unnecessary conservatism that reduces spacecraft lifetime and 

unduly encumbers science mission objectives.

M.2 Point of Reference: Conjunction Risk Assessment Based on Miss 

Distance

In the early days of conjunction assessment, satellite position uncertainty data were not regularly 

available, so the only orbital data product on which to base conjunction risk mitigation decisions 

was the predicted miss distance at TCA between the two conjuncting satellites. If the miss 

distances were smaller than the combined sizes of the two objects (a quantity usually on the 

order of 10-20 meters), then it was clear that a mitigation action would be necessary to modify 

the primary satellite’s orbit to increase this miss distance to a safe level. But it was also known 

that there was often significant uncertainty in the two objects’ predicted state estimates, so miss 

distances that were larger than the objects’ combined size were also likely to be threatening—but 

how threatening, precisely? Similarly, if a mitigation action such as a maneuver were pursued, 

how large should such an action be to guarantee a desirable level of safety? Because the answers 

to these questions were not known, very conservative miss-distance thresholds were then 

embraced, often based on very little analysis, which led to a great deal of operational anxiety and 

unnecessary mitigation actions. For example, nearly all conjunctions with miss distances (at 

TCA) less than a value of 5 km present perfectly safe encounters, but all of these could be treated 

as worrisome and worthy of potential mitigation actions. Such a situation could not be sustained 

operationally: it went beyond prudence and presented an undue burden to mission operations. 
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Methods were thus developed that considered the characterized error in the state estimates to 

determine the likelihood that the two trajectories at TCA would have a close approach smaller 

than the combined sizes of the two satellites.

Approaches that view the problem in this way, namely those that give an actual likelihood that 

the miss distance will be small enough to cause a collision, are certainly an advance over the use 

of the miss distance alone. It is important to remember, however, that the probabilistic answer 

they produce is solely a function of the quality of the astrodynamics data that are used as input to 

the computation—the tracking information available and the errors encountered in predicting 

states from epoch to TCA. In truth, the probability of collision for any given conjunction is 

actually either 1 or 0: the conjunction is either going to result in a collision, or it is not. The 

probabilistic framing comes from the degree of predictive certainty of the outcome brought by 

the quality of the astrodynamics data in the particular case. There is no “definitive” collision 

likelihood value for a particular conjunction. Improvements in data and data quality will push the 

calculated answer further toward the values of 0 or 1 depending on whether the two satellites 

actually are on path to collide, and because satellite collisions are extremely rare events, in 

nearly every case the true likelihood of collision is 0. Sometimes interest is expressed in wishing 

to obtain sufficient tracking data to allow the “true” collision likelihood to be calculated, or after 

the event, to rework the solution using the tracking data collected ex post facto to establish what 

the “definitive” collision likelihood actually was. None of these considerations is in the end 

helpful, or for that matter even possible. In the first case, while more and better data will provide 

a superior answer, any value short of 0 or 1 is just an estimate constrained ultimately by the 

inadequacy of the tracking data. In the second case, the ex post facto solution is not definitive but 

is yet another estimate, this time with somewhat better input data. The probabilistic framework is 

helpful and desirable, but in the end, it reflects what is known about the conjunction situation 

rather than being a stand-alone, absolute assessment of collision likelihood.

M.3 Use of Pc for Conjunction Risk Assessment Requirements

Many conjunction risk assessment metrics that have been proposed in the critical literature; 

Hejduk and Snow (2019) give a useful overview, description, and attempted categorization. In 

choosing a particular collision likelihood metric for requirements specification purposes, 

different considerations, technical and otherwise, are relevant:

• Suitability to NASA’s risk posture regarding conjunction risk assessment;

• Ability to represent the collision likelihood in a manner commensurate with this risk 

posture;

• Straightforwardness and tractability of calculation;

• Ease of conceptual grasp of the metric and its origins; and

• Acceptance within the conjunction assessment industry.

From these considerations, CARA has chosen the Probability of Collision (Pc) as the metric for 

high-risk conjunction identification. Of the different options examined, this metric was the best 

candidate to evaluate collision risk given the desired context of balancing safety of flight with 

minimizing the disruption of mission objectives. It is straightforward to calculate and, with 

certain recent improvements, can be computed quite accurately in many astrodynamically 
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demanding circumstances. It can be explained relatively easily to, and be interpreted by, decision

makers. It can be turned into a statement about miss distances if this framework is desired. 

Finally, it is the emerging metric of choice among the military, civil, and commercial 

conjunction assessment industries.

The Pc metric, as calculated by analytic methods, was first explained formally in 1992 (Foster 

and Estes). A comprehensive treatment of the calculation and associated issues can be found in

Chan (2008), although this monograph is now somewhat dated and does not consider many of 

the newer collision likelihood calculation proposals. (See Appendix K for an explanation of the 

presently embraced calculation methods for this parameter, along with the tests that have to be 

performed to determine which calculation approach to use in any particular case. It may be 

helpful to the reader new to conjunction assessment to refer to Appendix K before proceeding as 

it gives a precise definition of terms used in the following treatment.)

M.4 Pc and Probability Dilution

Despite the previous section’s account of selecting a metric, the Pc is not a parameter without 

controversy. The main objection to the metric is a phenomenon called “probability dilution” in 

which low values of the Pc do not necessarily guarantee safety although they can offer support 

for refraining from a mitigation action. This section discusses the overall phenomenon of 

probability dilution and explains why it is viewed as a manageable issue when using the Pc in 

mitigation threshold development.

As stated previously, probabilistic conjunction assessment metrics take on their probabilistic 

nature from the uncertainties in the state estimation data used to characterize the miss distance at 

TCA. It is not difficult to understand the alignment of inputs that creates a high Pc value: the 

calculated miss distance between the two objects is small, and the primary and secondary object 

covariances (and thus the uncertainty on the miss distance) are reasonably small also, so one 

easily envisions that of the entire set of possible actual miss distances, some notable portion will 

be smaller than the hard-body radius. The Pc, which is the portion of the possible miss distances

smaller than the hard-body radius, will be relatively large. Imagine a similar situation for a small 

Pc: the nominal miss distance is large, and the covariances and miss-distance uncertainty are 

small, so the range of possible actual miss distances are nearly all rather large. One can conclude 

quite satisfactorily in such a case that there is little chance that the actual miss distance will be 

less than the hard-body radius. 

But what if, for either of the previous cases, one or both covariances are extremely large? This 

would happen if, for at least one of the satellites, the predicted position at TCA, due either to a 

poor orbit determination update or difficulties in accurate propagation, were extremely badly 

known. The predicted miss distance is by definition the expected value, but it is a poor proximate 

prediction of the miss distance because there is so much uncertainty in one or both of the 

satellites’ position at TCA. The range of possible miss distances now becomes extremely large. 

Therefore, a relatively smaller portion of the possible miss-distance values will be smaller than 

the hard-body radius, and the Pc will take on a small value. In the earlier case in which the 

nominal miss distance was large but the covariances small, one could with confidence conclude, 

based on the quality of the data, that a collision is unlikely. In this latter case, the likelihood of 
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collision is also small, but only because one has very little idea where one or both satellites 

actually will be at TCA, so one cannot conclude that a small miss distance is likely when so large 

a range of miss distances is possible. This latter case is called “probability dilution” (a term 

introduced by the first treatment of this subject in the literature (Alfano 2005b)) because the 

small value of the Pc is not achieved by the certainty of well-established state estimates but 

through “dilution” by relatively poor state estimates.

An analogy that is sometimes helpful is that of determining whether two cars parked in a large 

parking lot are parked next to each other. If one knew that one car was parked on the left side of 

the parking lot and the other on the right side of the parking lot, then one could conclude that it is 

unlikely that the two cars are parked next to each other: only if both cars park on the boundary 

between the left and right sides, and then only if they actually choose adjacent spaces, will the 

two cars be parked next to each other. This is a conclusion enabled by the definiteness of the 

data. Now, suppose that one knows nothing at all about where the two cars are parked in the 

parking lot; what is the likelihood of their being parked next to each other? It is also low, but in 

this case not because one knows that the cars have been placed in different parts of the lot but 

rather because, in a large parking lot, it is simply unlikely that any two cars will happen to be 

next to each other. It is a conclusion that follows not from what is known but rather from what is 

not known; one cannot conclude from the available data that the cars are probably far apart; but 

at the same time there is no evidence to indicate that they are close. If, therefore, one is required 

to hazard a guess, the large size of the parking lot makes the supposition that they are not 

adjacent reasonable.

So, what is the risk assessor to do in such a situation? One could embrace a very conservative 

position and require that, unless it can be demonstrated conclusively that the two satellites are 

virtually certain not to collide, a mitigation action is warranted. Some commentators have 

suggested this position as the natural one for advancing safety of flight (e.g., Balch et al. 2019). 

There are two sets of difficulties with such a position, one of which is practical and the other 

conceptual.

The practical difficulty centers on the number of increased mitigation actions and the magnitude 

of those actions if an extremely conservative risk analysis metric/approach were to be embraced 

operationally. An analysis by Hejduk et al. (2019) indicated that, for a protected asset in a 700 

km circular orbit, the adoption of the conservative “ellipse overlap” technique, for which the two 

covariances’ overlap has to be limited to a very small value to certify that a collision is extremely 

unlikely, would increase the number of mitigation actions by a factor of anywhere from 6 to 10. 

Most O/Os believe they are already assuming a relatively safe posture in that they have set the 

thresholds on the risk-assessment metrics they currently use to require mitigation actions close to 

the mitigation action rate that they believe they can sustain without unacceptable mission 

disruption. While perhaps a relatively bounded increase could be countenanced, any expansion 

beyond that would be extremely difficult to accept. Increases by a factor of as much as an order 

of magnitude simply cannot be borne without resulting in major disruption, if not nullification, of 

the mission activities that most satellites are launched to perform. Furthermore, remediation 

actions based on minimizing covariance ellipsoid overlap rather than reducing the Pc value to an 

acceptable level will need to be large—much larger than the typical satellite maneuvers that are 
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presently performed. Large maneuvers expend additional fuel and, if pursued more frequently, 

will also require subsequent response maneuvers to restore the orbital parameters that were 

violated by the initial mitigation action. An extremely conservative risk analysis approach such 

as the one described here is simply not seen as operationally viable for most missions.

In addition to these practical impediments, a conceptual dissonance is introduced in embracing 

an extremely conservative risk-assessment strategy given the much larger collision background 

risk from untracked/uncataloged objects. As previously explained, the dynamics of the dilution 

region result in a reduction in severity and therefore a reduction in perceived necessity to act as 

less is known about the conjunction. As the amount of tracking information (or, similarly, the 

amount of certainty in prediction) for a dilution-region conjunction is worsened, the satellite 

covariance(s) increase in size, and the Pc decreases until ultimately it results in a value of 0 (to 

machine precision). This asymptotic value of nullity aligns nicely with the zero-value Pc that is, 

at least indirectly, imputed to conjunctions with untracked/uncataloged objects and about which 

the risk-assessment analyst can do nothing at all. As one progresses from knowing a lot, to a 

little, to nothing at all about a conjunction, the Pc moves conceptually from a higher value, to a 

lower value, to a zero value. For an extremely conservative approach such as that of minimizing 

covariance ellipsoid overlap, an opposing and inconsistent dynamic is observed: the less one 

knows about the conjunction, the larger the covariance ellipsoids are, and therefore larger and 

more frequent maneuvers are required to achieve minimum ellipsoid overlap to ensure safety 

until one moves from knowing a small amount about a conjunction to knowing nothing at all, 

and then—there is a sudden disjunction from taking large and invasive actions to doing nothing. 

Given that, as stated previously, about 85% of the conjunctions that a satellite actually faces 

cannot be addressed at all because nothing is known about them, it does not make sense that, for 

the small number of conjunctions for which only poor data are available, large and disruptive 

mitigations are required. 

Instead, the use of the Pc, with the dilution region dynamic explicitly recognized, is a more 

natural fit for the situation that is actually encountered. When outside the dilution region, a 

satisfactory amount of orbital data and reasonably small covariances exist. In this situation, the 

Pc accurately reflects a situation that is either worrisome or safe, and one can be confident in the 

conclusion in either case. If in the dilution region the Pc is high despite the poor data quality and 

large covariances, a worrisome situation has very much been identified, so appropriate mitigation 

action should be taken. If in the dilution region the Pc is low, one cannot, as has been explained 

previously, necessarily infer that the situation is safe; the two satellites might actually be poised 

for a dangerous close approach with this fact obscured by poor data quality—a situation that 

could potentially be revealed by the summoning of additional tracking data. It is appropriate to 

recognize that this situation (state estimate with large covariance) is not dissimilar to that of a 

conjunction with an untracked/uncataloged object about which nothing is known (random state 

estimate and infinite covariance). It is thus acceptable to treat low-Pc dilution region cases as a 

small extension of the untracked/uncataloged object conjunctions and not pursue a mitigation 

action. Requiring conjunction remediation for low-Pc cases with poor data quality when such 

cases are truly very similar to the ~85% of conjunctions that are believed to exist but for which 

no mitigation is possible is not considered to be a prudent measure and thus runs counter to the 

CARA statement of purpose.
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While not appropriate for broad implementation, conservative approaches such as ellipsoid 

overlap minimization are not without merit. In situations in which the collision risk may be 

pushed higher by other factors, such as a high-consequence conjunction due to the potential to 

produce large amounts of debris, it may be desirable to employ a conservative method when in 

the dilution region. In such a case, one might first analyze the situation by manipulating the 

covariance and determining the highest Pc value that could be realized with the miss distance

(following Alfano 2005b); if that Pc is still below the threshold, then the conservative approach 

would be difficult to justify. But if this “maximum Pc” is above the threshold, then the 

conjunction could in fact be worrisome, and a conservative approach could be properly applied. 

At a minimum, if it were possible to marshal additional tracking data to improve the state 

estimate, then a situation such as this would be a good fit for employing such a capability.

Finally, it should be noted that there have been interesting proposals recently for risk assessment 

approaches based not on the probability of collision but on the (somewhat) related concept of 

examining confidence intervals on the miss distance; such proposals include those of Carpenter 

(2019) and Elkantassi and Davison (2022). These approaches, which are presently being 

evaluated formally, bring the advantage of avoiding situations in which, with relatively small 

miss distances, even risky conjunctions might be obscured by the inability, due to largish 

covariances, to integrate up enough risk to register as problematic events that require mitigation. 

However, the expectation is that using such approaches will produce unacceptably large false 

alarm rates, and the issue of “missing” high-risk events in low-miss-distance situations can be 

addressed by adding a miss distance mitigation criterion in addition to that based on the Pc. But 

any firm recommendations will need to wait for the completion of a full analysis.

M.5 Conclusion

It is emphasized that the above guidance describes and explains why Pc was chosen by NASA 

CARA as the risk-assessment metric to be used to determine the circumstances under which a 

mitigation action is required of missions to promote preservation of orbital corridors from debris 

pollution. O/Os may always pursue additional mitigation actions in a manner that increases the 

conservatism of their safety profile. For the case of low-Pc conjunctions in the dilution region, 

missions may elect to pursue mitigation actions. They may even use extremely conservative 

methods such as ellipsoid overlap minimization to size these mitigation actions. This guidance 

indicates that mitigation actions are required only when the Pc exceeds the appropriate 

mitigation threshold. Missions may always pursue additional such actions, either episodically or 

as part of a standing strategy, if they wish a more risk-adverse safety posture.
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Appendix N. Pc Calculation Approaches

N.1 Introduction

This appendix discusses the selection of the Probability of Collision (Pc) as the risk assessment 

parameter to use for conjunction assessment requirements compliance. While this parameter is 

widely used in the conjunction assessment industry, issues related to its calculation exist that 

merit extended discussion. The most frequently used analytical techniques to calculate the Pc are 

well established and computationally efficient but include assumptions that restrict their use and 

make the calculations vulnerable to error for a small fraction of conjunctions. Numerical 

techniques also exist, such as Monte Carlo Pc estimation. Predictably, these make fewer 

assumptions and are more widely applicable, but they are much more computationally 

demanding. There are also issues related to the regularization and interpretation of the input data 

to the Pc calculation, some of which are resolved by techniques that are now becoming standard 

practices. In calculating Pc estimates, it is necessary to examine and prepare the input datasets 

carefully and then to choose the calculation approach that is appropriate to the situation. The 

purpose of this appendix is to amplify the Pc calculation-related recommendations by providing 

an extended technical explanation of the data preparation and Pc calculation issues so that 

implementers and users of these calculations can proceed with a better understanding of the 

different options and resultant fidelities of Pc calculation. 

To accomplish this goal, this appendix will address the following technical areas:

• A step-by-step description of the conjunction plane two-dimensional Pc calculation, 

which is the most established and widely used analytical Pc computation technique, and 

its enabling simplifications and assumptions;

• Examination and repair/expansion of input data to the calculation, focusing mostly on the 

orbital state covariance matrices for the two objects in conjunction;

• Discussion of the use of Monte Carlo techniques, which is the numerical method used for 

high-fidelity Pc computation;

• A test to determine whether an analytical or numerical technique should be used for a 

particular conjunction;

• Approaches to choosing for the Pc calculation the hard-body radius, which gives a 

statement of the combined sizes of the primary and secondary objects; and

• Discussion of alternative analytic Pc calculation methods, specifically the two- and threedimensional “Nc” (as opposed to “Pc”) estimation methods that address conjunctions 

affected by curvilinear trajectories and non-Gaussian distribution effects.

N.2 Conjunction Plane Analytic Pc Calculation

The conjunction plane method of Pc calculation, which is by far the most widely used approach 

in the conjunction assessment industry, was developed for the Space Shuttle Program and first 

described in the literature in 1992 (Foster and Estes). There have been a number of important 
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Appendix N Pc Calculation Approaches 131

treatments since that time ⎯ e.g., Akella and Alfriend (2000), Patera (2001), Alfano (2005a), 

Chan (2008), Garcia-Pelayo (2016), and Elrod (2019) ⎯ but all rely on the same basic 

methodology: applying reasonable assumptions to enable analytical approximations. While the

particulars vary, these approaches all share the same concept of calculating the Pc estimate by 

integrating over a two-dimensional region on a conjunction encounter plane.

Conjunction plane Pc analysis begins with the states and covariances for the primary and 

secondary objects’ orbital states at TCA. An important set of questions should be addressed 

concerning whether these data, especially the covariances, are truly representative of the 

expected states and uncertainties at TCA or whether the propagation process has distorted them. 

These questions will be addressed in a subsequent section, once a more focused context for them 

has been established through the present discussion of the general procedure. 

The first step is to recognize that Pc calculations depend on the relative positions and 

uncertainties of the two objects, so moving to a framework that views the problem this way is 

helpful. Subtraction of the two objects’ positions produces a relative position vector, the 

magnitude of which is the miss distance between the two objects (at TCA). Similarly, because 

interest is in the relative rather than absolute position uncertainty, it is possible to combine the 

two objects’ covariances to form a joint (relative) covariance and allocate that, if desired, to one 

“end” of the relative position vector (by convention the end for the secondary object), as shown 

in Figure N-1. There are, of course, questions regarding whether the two covariances are 

independent and can be combined by simple addition; this question is addressed in a later 

section, but it is typically acceptable to presume independence and combine the covariances in 

this manner. 

Figure N-1 Relative Positions and Uncertainties of Two Objects

The second step relates to modeling the combined sizes of the primary and secondary objects. 

The general approach is to place a circumscribing sphere about the primary (whose size is well 

known by the O/O because it is their satellite) and then do the same thing for the secondary but 

often via an estimation technique as the secondary is usually a debris object for which there is no 

definitive size information. If these two spheres approach and begin to overlap one another at 

any point during the encounter, then a potential collision has been identified. Again, keeping in 

mind that a relative framework is useful here, the two objects’ size spheres can be combined into 

one super-sphere (also called the “collision sphere”) and placed at one end, by convention the 

primary object end, of the relative miss vector, as shown in Figure N-2. If the miss vector should 

shrink to be smaller than the radius of the collision sphere (also called the hard-body radius), that 

would be the equivalent of the two original spheres encroaching on each other at TCA. 
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Figure N-2 Combining the Sizes of the Primary and Secondary Objects

The third step is to envision the situation at TCA in which all the uncertainty is assigned to the 

secondary object’s end of the relative miss vector held in a fixed position in the mind. The 

primary object end of the relative miss vector is moving along through TCA and bringing with it 

the sphere representing both objects’ combined size. Even though the satellites follow curved 

trajectories and the covariance evolves and changes at each instant, if the encounter is presumed 

to take place extremely quickly—and this is in most conjunctions a good assumption because the 

satellites’ relative velocity usually exceeds 10 km/sec—then two assumptions can be made: the 

trajectories are essentially rectilinear during the encounter period, and the covariances (and thus 

the joint covariance) can be considered static. This means that the encounter can be envisioned as 

in Figure N-3:

Figure N-3 Geometry at TCA

The passing of the primary object by the secondary can be seen as following a “soda straw” 

straight trajectory whose cylindrical radius is the same as that for the hard-body radius and 

whose placement is one miss distance away from the position of the secondary at TCA. Since the 

joint covariance shown as the ellipsoid above represents the uncertainty of one “end” of the 

miss-distance vector (as shown by the central dot in the above diagram), this dot can be 

presumed to be potentially in any place within the ellipsoid, meaning that in some portion of 

those realizations, it will fall within the soda straw. When this is the case, a collision is 

presumed. The task is to determine the likelihood that the dot will, in the actual realization of this 
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Appendix N Pc Calculation Approaches 133

conjunction, fall within the cylindrical path (“soda straw”) swept out by the motion of the 

primary object. This probability can be decomposed to be rendered as the product of the 

individual probabilities that each component of the secondary object position (the dot) will fall 

within the soda straw pathway, i.e., if an orthogonal x-y-z coordinate system is presumed, this 

overall probability can be generated as the product of the probability that the x-component of the 

dot’s position will fall within the straw, the y-component of the dot’s position will fall within the 

straw, and the z-component of the dot’s position will fall within the straw. If this coordinate 

system is aligned so that one of the axes (e.g., the z axis) aligns with the direction of the straw, 

because one is assuming rectilinear motion, the soda straw can be presumed to be unbending and 

infinite in length, and as such, it will contain all of the z-component probability of the dot’s 

falling within the straw. As such, the z-component probability in this arrangement will be unity 

and will be what is called “marginalized out,” meaning that the overall probability can be fully 

represented by the probability remaining with the x- and y-components. The entire situation can 

thus be reduced from three to two dimensions and analyzed as a phenomenon that occurs on a

plane that is orthogonal to the soda-straw direction, which is the direction of the relative velocity 

vector. This procedure defines the “conjunction plane,” which can be viewed in two equivalent 

representations as discussed by Chan (2008, see Figure 5.1), and as shown in Figure N-4.

Figure N-4 Two Equivalent Representations of the Conjunction Plane

In the first representation, shown in the left panel of Figure N-4, the center of the secondary 

object is placed at the origin, and the local (x, y) coordinate system configured so that the miss 

vector (which extends a distance of rmiss from the secondary to the primary object) lies along the 

horizontal x axis. The “soda straw” is coming out of the page and represented as the hard-bodyradius circle. With this planar reduction, the Pc is now the frequency with which the missdistance vector will fall within the hard-body-radius circle; this is equivalent to the amount of 

joint covariance probability density (illustrated here using a 1 ellipse) falling within that circle. 

Since the projected joint covariance represents a bivariate Gaussian distribution, the amount of 

its probability density falling within the hard-body-radius circle is given by the following twodimensional integral (Foster and Estes, 1992)

Pc =

1

√det(2πC)

∫∫ exp (−

r

TC−1r

2

) dx dy

A

(N-1)
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in which r is the 21 miss vector, C is the 22 covariance matrix, and A is the hard-body-radius

circular area. There are several different approaches to evaluating this integral. Foster and Estes 

(1992) applied a two-dimensional quadrature technique; this works well, and MATLAB®’s13

adaptive quad2d integrator is quite equal to the task, although perhaps not the most 

computationally efficient of all possible choices. Chan (2008) uses equivalent-area transforms to 

produce a single-dimensional integral, which has a series solution. Garcia-Pelayo et al. (2016) 

also derives a multi-term series approximation. However, even though these series 

approximations are relatively computationally efficient, experience indicates that they 

occasionally produce inaccuracies. Elrod (2019) formulates the integral in terms of 

complementary error functions (to improve accuracy for conjunctions with small Pc values) and 

uses Gauss-Chebyshev quadrature with nodal symmetry (which improves the efficiency of the 

numerical integration considerably). The Foster and Elrod approaches (the former being the 

established standard, and the latter being extremely fast, especially with a vectorized MATLAB 

implementation) are included as the Pc2D_Foster and PcElrod functions in the Pc Computation 

Software Development Kit (SDK) in the NASA CARA software repository. (See Section 7, 

Contact Information in this document for the specific URL.)

In the second conjunction plane representation, shown in the right panel of Figure N-4, the 

secondary object location again is placed at the origin, but in this case the local (x, y) coordinate 

system is configured so that the principal axis of the covariance ellipse lies along the horizontal 

axis. The center of the primary object lies at (xmiss, ymiss), and the axes are oriented so that this 

miss position lies within the 1st quadrant, so that xmiss ≥ 0 and ymiss ≥ 0. Using this representation,

the Pc is given by a one-dimensional integral involving error functions (Alfano, 2005a) 

Pc =

1

√8πσx

∫ {erf(y+) − erf(y−)} exp [−

(u + xmiss)

2

2σx

2

] du

R

−R

(N-2)

with R indicating the combined hard-body radius, u = x

′ − xmiss the integration variable, and

y± = (ymiss ± √R2 − u

2)/(√2σy). The integrand factor in the curly brackets represents the 

difference of two error functions, ∆ = −erf(y−). In many software environments (e.g., 

MATLAB), this factor often can be computed significantly more accurately as a difference of 

complementary error functions, i.e., ∆ = erfc(y−) − erfc(y+), especially when calculating very 

small Pc values (Elrod, 2019). See Abramowitz and Stegun (1970) and Press et al. (1992) for 

details on computing erf(-) and erfc(-) functions.

For most conjunctions, Gauss-Chebyshev quadrature provides an efficient and accurate means to 

calculate the one-dimensional integral in equation (N-2), using an approach similar to that 

described by Elrod (2019). However, for conjunctions involving relatively large hard-body radii

(or, equivalently, small covariance ellipse σx dimensions), this method can potentially become

inaccurate. Specifically, Gauss-Chebyshev quadrature becomes increasingly inaccurate as the 

hard-body radius grows beyond the limit Rlim = 4σx − min(R). In such cases, which rarely 

occur in practice, an adaptive numerical integrator can be used to calculate an accurate estimate, 

e.g., MATLAB’s integral function. (The function PcConjPlaneCircle of the NASA CARA SDK 

13 MATLAB is a registered trademark of The MathWorks, Inc.
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Appendix N Pc Calculation Approaches 135

repository implements a vectorized algorithm that automatically determines which of these two 

integration methods should be used to compute Pc values accurately for all input hard-body radii

and covariance values, with a computation speed comparable to that of the PcElrod function for 

most conjunctions. Also, for cases that have hard-body radii well below the limit given above, 

testing indicates that the SDK functions Pc_Foster, PcElrod, and PcConjPlaneCircle all output

nearly identical numerical Pc values, i.e., that typically agree to five digits of precision or more.)

The second conjunction plane representation shown in the right panel of Figure N-4 also 

provides an extremely efficient means to calculate an upper limit estimate for the Pc value. This 

upper bound corresponds to the two-dimensional (2-D) integral over the square that 

circumscribes the hard-body radius circle (as shown in Figure N-4), which has the following 

analytical solution

Pc < Psq =

[erf(X+) − erf(X−)] [erf(Y+) − erf(Y−)]

4

(N-3)

with

X± =

xmiss ± R

√2σx

and Y± =

ymiss ± R

√2σy

(N-4)

Again, in many cases the erf(-) differences in equation (N-3) can be computed more accurately

using erfc(-) differences. Notably, the circumscribing square probability estimate does not 

require any numerical integration at all, but instead only requires the computation of four erf(-) 

or erfc(-) functions, usually making it relatively easy to program into software and significantly

more computationally efficient. These considerations could be important in some circumstances 

(e.g., for computations performed on orbiting satellites), prompting the use of Psq as an

approximation for Pcitself. For instance, CDMs generated by the USSPACECOM ASW

processing system often reports Psq as the estimate of conjunction’s collision probability. (An 

optional, non-default mode of the function PcConjPlaneCircle in the NASA CARA SDK 

repository implements an efficient vectorized algorithm that calculates Psq values).

It is perhaps helpful at this point to review the four assumptions employed by the conjunction 

plane Pc calculation methods given by equations (N-1) through (N-4), because alternative Pc 

estimation techniques will be needed when these assumptions do not inhere:

1. Statistical Independence: The two objects’ uncertainty distributions are statistically 

independent so that the joint covariance can be obtained by simple addition of the two 

covariances. This assumption is largely true but can break down for objects that share global 

atmospheric density forecast error in a manner that influences the conjunction. This issue will 

be discussed as an isolated topic in a subsequent section of this appendix.

2. Rectilinear Motion: The conjunction circumstances are such that it is reasonable to presume 

rectilinear motion and static covariances during the encounter. These conditions inhere for 

most conjunctions between Earth-orbiting satellites. The objects’ relative velocity at TCA is 

in some places used as an indication of the reasonability of these assumptions, but this 
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Appendix N Pc Calculation Approaches 136

parameter alone is not sufficient to identify situations in which the conjunction plane Pc

approximation will miscarry.

3. Gaussian Position Distributions and Negligible Velocity Uncertainties: The position vector 

state errors for each satellite at TCA follow Gaussian distributions, and the velocity vector 

state errors are negligibly small. When combined, these assumptions lead to the conjunction 

plane representations shown in Figure N-4. Conjunctions that do not satisfy these 

assumptions are addressed by alternate analytical and Monte Carlo methods, discussed in the 

sections below.

4. Temporally Isolated Event: The conjunction presents a single, well-defined event so that the 

collision likelihood can be ascertained by examining that single instance. Objects that stay in 

close proximity for extended periods accumulate risk throughout long interactions, rather 

than quickly accumulating risk at or near a well-defined TCA. A different approach is also 

required for their evaluation, which is discussed in the sections below.

As mentioned previously, the issue of statistical independence (i.e., assumption 1 above) will be 

discussed in a subsequent section of this appendix. To address conjunctions that do not satisfy 

any of the other assumptions, two alternative (but more computationally intensive) analytical 

methods are available: the “three-dimensional Nc” method, which research indicates can be 

applied to conjunctions that violate assumptions 2, 3 and/or 4 above, and the “two-dimensional 

Nc” method, applicable to temporally isolated conjunctions that violate assumptions 2 and/or 3.

Notably, the three-dimensional Nc method could, in principal, be applied to all conjunctions to

estimate Pc values. However, this is not justified because most LEO satellite conjunction Pc 

values can be estimated accurately using the much more efficient conjunction plane methods 

described above. Additionally, most of the remaining conjunctions can be estimated accurately 

using the two-dimensional Nc method, which, although much slower than the conjunction plane 

methods, is still significantly faster than the full three-dimensional Nc method. (The function 

PcConjPlaneUsageViolation soon to be posted on the NASA CARA Software Development Kit

(SDK) repository provides an algorithm that determines if a given conjunction violates one or 

more of conjunction plane Pc estimation assumptions, and if so, which of the other available Pc 

estimation methods are appropriate.)

N.3 Three-Dimensional Nc Method Analytic Pc Calculations

The relatively infrequent conjunctions that do not satisfy the conjunction plane method

assumptions discussed in the previous section must be addressed with a different methodology,

and in response to this need, several authors have formulated semi-analytical approaches 

relaxing some or all of these assumptions. Coppola (2012) proposed a method for single 

encounters designed to account for non-linear orbital motion and velocity uncertainties, resulting 

in an approximation for the probability rate, Ṗ

c

(t), calculated using integration over the surface 

of a unit sphere. When combined with a one-dimensional time integration, this yields a “threedimensional Pc” approximation. Chan (2015) contested Coppola’s formulation, arguing that a 

proper approach must employ a set of random variables associated with a time-invariant 

Probability Density Function (PDF). NASA CARA implemented the three-dimensional Pc

method in software (Hall et al. 2017a) and subsequently discovered that, for some conjunctions, 
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it can produce Pc estimates that differ significantly from high-fidelity Monte Carlo Pc

calculations, even though all the required three-dimensional Pc assumptions are satisfied.

Shelton and Junkins (2019) provided a key insight into why the original three-dimensional Pc

approximation fails in certain situations. Their analysis indicates that accurate Pc approximations 

require that the state uncertainty PDFs of the two satellites be estimated accurately in the volume 

of space where they overlap the most. The original Coppola (2012) three-dimensional Pc

formulation did not incorporate this concept, but Hall (2021) reformulated the method to do so 

explicitly. For single encounters, the reformulated approach approximates the curvilinear motion 

of each satellite using a first-order Taylor series expansion, not centered on the mean orbital 

state, but centered instead on a state that coincides with the maximum overlap of the PDFs for

the two satellites. The analysis demonstrates that such “peak overlap” states can be determined 

using an iterative calculation that converges quickly. The formulation derives an expression for 

“Nc” ⎯ the statistically expected number of collisions ⎯ which equals Pc for single, temporally 

isolated conjunctions, but that may exceed Pc for multi-encounter interactions. The resulting 

“three-dimensional Nc” method entails a total of three numerical integrations, one over time and 

two over the surface of a sphere. The outermost, time integration expression has the form

Nc

(τa, τb) = ∫ Ṅ

c

(t) dt

τb

τa

(N-5)

This expression estimates Nc

(τa, τb), the number of collisions statistically expected to occur at 

some time during the risk assessment interval τa ≤ t < τb, which can represent either a short 

duration closely bracketing a single close-approach encounter, or an extended duration spanning 

multiple encounters. The expected collision number is closely related to the collision probability. 

In fact, they are equal for single, isolated encounters between well-tracked satellites. The

collision rate for such a temporally isolated conjunction is expressed as a two-dimensional 

integral over the unit sphere

Ṅ

c

(t) = R

2 ∫ ∫ [νt(r̂) MVN(Rr̂, r̆t

,Ãt)] sin(θ) dθ dφ

π

0

2π

0

(N-6)

In this equation, the radial unit vector is given by r̂ = [cos(φ) sin(θ), sin(φ) sin(θ), cos(θ)]

T

, 

so the surface of the unit sphere is spanned by the azimuthal angle 0 ≤ φ < 2π and the axial 

angle 0 ≤ θ ≤ π. The leading factor of R

2

represents the square of the combined hard-body 

radius, meaning that the expression actually represents an integration over the surface area of the 

collision sphere. As explained in Hall (2021), the integrand function in the square brackets is the 

product of two factors. The first in an average velocity term, νt(r̂), which is a function of time

(as indicated by the t subscript) and calculated using the TCA states and covariances of the 

primary and secondary objects. The second factor, MVN(Rr̂, r̆t,Ãt), represents a multi-variate 

normal (MVN) function which depends on r̂ and R, as well as a 31 relative position/velocity 

state vector, r̆t, and an associated 33 Ãt covariance matrix, both of which are also calculated 

from the TCA states and covariances. Lebedev quadrature (Lebedev and Laikov, 1999) provides 

an efficient method for numerical integration over the unit sphere. (The function Pc3D_Hall of 
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the NASA CARA SDK repository computes conjunction Pc estimates, along with associated Nc 

and Nc rate estimates, using the Hall (2021) three-dimensional Nc method as summarized in 

equations (N-5) and (N-6) above.)

Figure N-5 Pc Rate and Cumulative Pc for a Non-Rectilinear Conjunction

Figure N-5 shows the time-dependent collision rate (left) and the cumulative Pc (right) 

calculated using the three-dimensional Nc method, as applied to an archived CARA conjunction 

that has a high relative velocity (~13 km/s), but that fails to satisfy the rectilinear motion and 

Gaussian PDF assumptions. This specific event does not satisfy these assumptions because it 

involves an object in a highly eccentric orbit with a conjunction occurring in the relatively tightly 

curved part of the trajectory near perigee, a phenomenology discussed by Hall (2018). In this 

case, the three-dimensional Nc method calculates a Pc value which accurately matches the 

Monte Carlo from TCA method Pc estimate, but that is a factor of fifteen larger than the 

erroneous conjunction plane Pc estimate, calculated in this case using the two-dimensional 

Foster and Estes (1992) method. It is of interest that the peak point of risk accumulation occurs 

nine seconds before the TCA, with essentially all the risk accumulated by 8 seconds before TCA. 

Such a result can seem counterintuitive at first, for one would initially expect that the point of 

highest risk would always be at the TCA. However, what is operative is the alignment between 

the geometric miss distance and the covariance. If at TCA very little of the position uncertainty 

lies along the relative miss vector, then that miss vector is a strong statement of the actual miss; 

and if the vector is somewhat larger than the hard-body radius (HBR), then the collision risk at 

that point is quite low. If, however, somewhat earlier or later than TCA the combined covariance 

(which, it must be remembered, is constantly changing position) does more substantially align 

along the miss vector, then more possible instantiations of the true miss are likely to be smaller 

than the HBR (even with the nominal miss vector larger than the expected miss at TCA), so the 

risk at that point is actually higher. In the more extreme cases, such as that shown in the above 

example (and even more strongly in the one below), most of the risk accumulation can be 

relatively far from TCA, meaning that methods that examine the situation only at TCA can 

misrepresent this risk.
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Figure N-6 Pc Rate and Cumulative Pc for a Low Velocity Conjunction

Figure N-6 shows the collision rate (left) and the cumulative Pc (right) for low relative velocity 

conjunction (~3 m/s), that fails to satisfy the rectilinear motion, temporally isolated, and 

Gaussian PDF assumptions. In this case, the three-dimensional Nc algorithm estimates a Pc 

value which matches the Monte Carlo from TCA method Pc estimate, but that is a factor of 330 

larger than the erroneous conjunction plane Pc estimate.

N.4 Two-dimensional Nc Method Analytic Pc Calculations

As formulated in equations (N-5) and (N-6), the three-dimensional Nc method requires the 

computation of a time-series of many unit-sphere integrations, each calculated using Lebedev 

quadrature. However, for temporally isolated conjunctions (i.e., those that are not “extended” or 

“blended” in time as described by Hall 2021), the integration over time can be approximated 

analytically, ultimately yielding a single unit-sphere integral. This relatively efficient “twodimensional Nc” method yields accurate Pc estimates for high velocity, temporally isolated

conjunctions (such as the example shown in Figure N-5). However, it is not applicable to low 

velocity events that are temporally extended or blended (as shown in Figure N-6); these 

conjunctions still require the use of the three-dimensional Nc method or Monte Carlo estimation.

The first step in the “two-dimensional Nc” formulation involves rewriting the MVN function in 

(N-6) in the following form

MVN(Rr̂, r̆t,Ãt) = (2π)

−3/2

e

−QR,t/2

(N-7)

with

QR,t = QR,t(r̂) = (Rr̂ − r̆t

)

T

[Ãt

−1

](Rr̂ − r̆t

) + ln(|Ãt

|) (N-8)

The first term of the QR,t expression corresponds to an effective Mahalanobis distance that 

accounts for curvilinear trajectory effects, a function which typically experiences a minimum in 

time near (but not exactly at) TCA. The second term typically varies slowly in time relative to 

the first. The next step of the derivation entails numerically finding the minimum of the function 
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Q0,t(i.e., the function QR,t evaluated at R = 0, which corresponds to the center of the collision 

sphere) and denotes the time that this minimum occurs as T. In other words, T = argmin(Q0,t).

For high velocity conjunctions, this time usually occurs within a few seconds of the TCA (and 

often much less). The next step is to expand the function QR,tto second order about the time T, 

yielding the simplified approximation

QR,t ≈ QR,T∗ + (

t − T∗

σR,T

)

2

with T∗ = T − Q̇

R,T Q̈ ⁄ R,T

(N-9)

and

QR,T∗ = QR,T −

Q̇

R,T

2

2Q̈

R,T

and σR,T

2 =

2

Q̈

R,T

(N-10)

For this, the required time derivatives Q̇

R,T and Q̈R,T are estimated numerically using finite 

difference equations (Press et al., 1989). Note, for brevity, the functional dependence on r̂ has 

been suppressed for all of the quantities expressed in equations (N-9) and (N-10). Combining 

equations (N-5) through (N-10) allows the time integral to be evaluated analytically, and yields 

the following approximation for a temporally isolated conjunction’s statistically expected 

number of collisions:

Nc ≈

R

2

2π

∫ ∫ [νT σR,T e

−QR,T∗

⁄2

] sin(θ) dθ dφ

π

0

2π

0

(N-11)

The integrand depends on the quantities νT, σR,T, and QR,T∗, each of which is a function of r̂, 

which in turn depends on the angles φ and θ. Equation (N-10) entails two-dimensional 

numerical integration over the unit sphere, calculated using Lebedev quadrature. (The function 

Pc2D_Hall of the NASA CARA SDK repository computes Pc estimates for temporally isolated

conjunctions using the two-dimensional Nc method.)

N.5 Comparison of Pc Estimates for Temporally Isolated Conjunctions

Figure N-7 shows a comparison of collision probabilities for 63,603 temporally isolated 

conjunctions extracted from the NASA CARA database for the period 2017-05-01 and 

2019-08-15 and for events with 2D Pc > 10-7(Hall, 2021). The vertical axes on all three panels 

plot Monte Carlo (MC) estimates for the collision probability⎯specifically, Monte Carlo from

TCA method Pc estimates, which are also referred to in this figure as two-body Monte Carlo 

method Pc estimates (i.e., TBMC-Pc estimates, as described in more detail in section N.13). The

error bars in Figure N-7 show 95% confidence intervals estimated using the Clopper-Pearson 

method (1934); several of the conjunctions had zero hits registered in the Monte Carlo

simulations, which are represented in Figure N-7 using downward-pointing triangles and a 

single-sided error bar. The horizontal axes plot the corresponding semi-analytical 

approximations: two-dimensional Pc on the left graph, three-dimensional Nc in the center, and 

two-dimensional Nc on the right. The colored points on each plot indicate the results of a 
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binomial proportion statistical test that evaluates the agreement between the estimates. 

Specifically, black points in Figure N-7 indicate analytical Pc estimates that agree reasonably 

well with the Monte Carlo estimates as they do not violate a null-hypothesis that the two are 

equal at a p-value  10-3significance level. However, those highlighted in yellow do violate the 

hypothesis at this significance level, and those in red at a more stringent level of p-value  10-6. 

Overall, the two-dimensional conjunction plane Pc comparison plotted in the left graph contains 

254 yellow and 436 red points, which both significantly exceed the number of disagreements 

expected from purely statistical variations, even though together they represent a small fraction 

(~1%) of the original conjunctions. These disagreements represent conjunctions that violate one 

or more of the assumptions required for conjunction plane Pc estimation. The center graph

clearly shows that the three-dimensional Nc method matches the Monte Carlo Pc estimates 

better, producing only 66 yellow and zero red points. Finally, the two-dimensional Nc method

plotted on the right produces very nearly the same results as the three-dimensional Nc method

but requires much less computation time. The three comparisons shown in Figure N-7 indicate

that, for temporally isolated conjunctions, the two- and three-dimensional Nc methods are 

consistent with one another and match Monte Carlo Pc estimates significantly better than the 

conjunction plane Pc estimation method.

Figure N-7 Comparison of Monte Carlo Collision Probabilities with the

Two-Dimensional Pc Method (left), the Three-Dimensional Nc

Method (center), and the Two-Dimensional Nc Method (right) for a Large 

Set of CARA Conjunctions

N.6 Pc Calculations for Multi-encounter Interactions

An additional feature of the two- and three-dimensional Nc methods is their ability to address 

explicitly the amalgamated risk of repeating conjunctions. While most conjunctions are 

temporally isolated, there are two conjunction types that exhibit different behaviors. The first 

type is produced by objects in orbits in synodic alignment that generate a temporal sequence of

conjunctions once every revolution or multiple of a revolution (e.g., two nearly circular orbits at 

different inclinations that produce conjunctions at one or both nodal crossing points). The second 

type involves objects that orbit close to each other for extended periods, generating extended 
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interactions with multiple close approaches (e.g., two satellites in nearly the same orbit, but with 

only a slight difference in inclination and/or eccentricity). In both cases, if each of the multiple 

encounters is considered separately, situations can arise in which each encounter in the series 

falls below a Pc mitigation threshold, but the combined risk of all of the encounters exceeds that 

threshold. The two- and three-dimensional Nc methods account for such multi-encounter 

interactions by providing estimates for the total expected number of collisions, and upper and 

lower bounds for the probability of collision (Hall, 2021). The total statistically expected number 

of collisions for a multi-encounter interaction is given by a summation of Nc values for each 

conjunction in the sequence

Nc

(τa, τb) = ∑Nc,k

K

k=1

(N-12)

with the index k = 1...K indicating the close approaches applicable to the risk assessment 

interval τa ≤ t < τb, and Nc,k representing the associated expected number of collisions for 

each. The upper and lower Pc bounds for the combined interaction are given by

max(Nc,k) ≤ Pc

(τa, τb) ≤ 1 −∏(1 − Nc,k)

K

k=1

(N-13)

which also implies that Pc

(τa, τb) ≤ Nc(τa, τb). Figure N-8 shows an example of a multiencounter interaction, in which a pair of satellites experience four conjunction events over about 

a five-hour period. Each of the individual conjunctions produces a Pc value in the upper yellow 

region (between 10

-5

and 10

-4

), as plotted in the bottom panel. The solid line in the top panel

shows the upper limit of the cumulative Pc for the interaction; notably, after the third 

conjunction, the cumulative Pc exceeds 10

-4 — a value frequently selected as a risk mitigation 

threshold. So, while these events would not necessarily prompt a mitigation action if examined 

individually, when considered collectively they do appear to represent a situation of sufficiently 

high collision likelihood to warrant mitigation. In such a case, it is advisable to run a Monte 

Carlo investigation (discussed in a subsequent section of this appendix) to verify that the upperlimit Pc value generated by the method is in fact representative of the actual cumulative risk. The 

utility of the analytic calculation, however, should be clear: if the upper-bound calculation for 

repeating events is found to be below the mitigation threshold, then there is no need to marshal 

computationally intensive methods (such as Monte Carlo), for it has already been demonstrated

no mitigation action is warranted.
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Figure N-8 Cumulative Three-Dimensional Nc Risk Over 

Four Repeating Conjunctions

N.7 Input Covariance Data Considerations

Most calculations are only as good as the input data that drive them, and Pc calculation is no 

exception. Appendix P discusses orbit determination quality and propagation issues for 

individual objects and addresses the question of the circumstances under which the state estimate 

and covariance might be considered sufficiently poor so as not to constitute a basis for 

conjunction risk mitigation actions. The purpose of this section is to address the routine 

improvement and basic error checking extended to covariances as part of the Pc calculation. 

These activities fall into three basic groups: correction for known problems in propagation, 

covariance formation and stability issues, and correlation between primary and secondary 

covariances. Each of these topics will be treated in turn.

N.7.1 Propagation Error Compensation

Historically, accuracy analysis of state estimate and uncertainty estimates has focused on 

products that emerge directly from the orbit determination fit. These direct orbit-determination

products include best-estimate states and covariances of the satellite at an epoch that usually 
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coincides with the acquisition time of the last tracking metric observation incorporated into the 

analysis. While these direct orbit-determination products are of course foundational, it is 

important to remember that most SSA activities, and conjunction assessment in particular, are 

not usually conducted with these direct products but rather with predictions propagated from the 

orbit-determination epoch solution, often over a non-trivial duration that spans many orbital 

revolutions into the future. The batch orbit-determination analysis method used by the DOD 

produces a formation covariance that represents the expected at-epoch state uncertainty based on 

the number, quantity, and temporal spacing of the incorporated metric observations; when the 

state is propagated forward, a parallel process can also be used to propagate the covariance 

forward in time. The same dynamical models used for the orbit-determination analysis as well as 

the state propagation itself are used to perform this covariance propagation, although in a 

linearized way. This means that the propagated covariance will be sized (mostly) appropriately 

for both the propagation duration and the final prediction point in the orbit.

Despite the use of appropriate models to propagate the covariance forward in time, a number of 

additional sources of error manifest themselves during the propagation interval yet are not part of 

the dynamical model used during the fit; these errors are therefore neither incorporated into the 

orbit-determination-produced covariance nor added as part of the regular propagation process. 

Because of the prevalence of such outside-of-model errors, techniques have been developed to 

account for them, the most familiar of which is the addition of process noise during propagation. 

Originally developed to account for acceleration errors that, due to model inadequacy, were to 

some degree known, this method propagates a noise matrix alongside the propagated covariance 

and combines both matrices as part of the overall process. The result is a covariance that is larger 

than it would have been otherwise to account for these (characterized) errors in the force 

model(s). A second approach, which is the one used by DOD in the propagation of their orbit 

prediction products, applies parameters to the covariance before propagation to guide the 

propagation process in producing a more realistic result. Because this is the approach reflected in 

the CDM covariances that conjunction assessment practitioners receive from the DOD, it will be 

described here in some detail. 

Orbit determination makes a distinction between “solved-for” parameters that are actually 

estimated during an orbit-determination activity, and “consider” parameters that are not “solved 

for” but represent a priori information that is “considered” as part of the orbit-determination

process. In the present case, the use of the term “consider parameter” is somewhat non-nominal 

in that it is referring not to additions or alterations made during the fit but to modifications to the 

fit-produced covariance so that when it is propagated, it may give a more realistic representation 

of the expected state errors. For DOD covariances, two different consider parameters are applied 

to compensate for two distinct expected errors during propagation: atmospheric density forecast 

error and satellite frontal area uncertainty.

Atmospheric drag is a significant force that affects satellite orbits with perigee heights less than 

1000 km, and the calculation of the expected atmospheric drag at any particular moment requires 

an estimate of the neutral atmospheric density that that satellite will encounter at that moment. 

Because the atmospheric models that generate this estimate are driven by space weather indices, 

the ability to predict these indices accurately affects the fidelity of the predicted atmospheric 
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density and thus the atmospheric drag. Unfortunately, it is difficult to predict future space 

weather indices well, primarily because they are affected by activities on the part of the sun’s 

surface that has not yet rotated into view from the Earth. This particular issue was studied with 

the Jacchia-Bowman High Accuracy Satellite Drag Model (HASDM) 2009, which is the 

atmospheric density model used by DOD, by comparing predicted densities (using predicted 

space weather indices) to actual densities and producing polynomial fits of the relative density 

error as a function of satellite perigee height and the Ap (major magnetic storms list) and Dst 

(disturbance storm-time) space weather indices. Figure N-9 shows the behavior of these 

polynomial fits divided into four different classes of Ap/Dst activity; y-axis values are omitted 

here to allow full releasability of the figure:

Figure N-9 Behavior of Relative Density Error by Perigee Height and

Solar Activity

These fits produce a variance term that can be added to the ballistic coefficient variance in the 

covariance: because in the drag equation the ballistic coefficient and the atmospheric density 

estimate are multiplicatively coupled, changing one of these parameters has the same effect as 

changing the other. When the covariance is propagated, this augmented term will appropriately 

expand the other covariance terms.

The amount of drag acceleration a satellite encounters is also governed by the frontal area that 

the satellite presents to the atmosphere; this makes intuitive sense (amount of resistance is a 

function of area presented to the resisting fluid) and is reflected in the ballistic coefficient (B) 

equation

M

A

B = CD

(N-14)

in which CD is the (dimensionless) drag coefficient, which indicates the degree to which the 

satellite surface is susceptible to drag resistance; M is the satellite mass; and A is the satellite 

frontal area. As A increases, B increases as well, increasing the overall drag acceleration value. 
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Stabilized satellites should manifest a stable B term, but rotating satellites, because their frontal 

area term is continuously changing, can exhibit a range of B terms. Three outcomes are possible 

depending on the rapidity of the rotation: the effect can be washed out during the fit (because the 

rotation is so rapid that an average value is quite representative), the effect can be not relevant 

during the fit (because the rotation is so slow that it does not affect near-term look-back and 

look-forward), or the effect can be such that the rotation does affect results fit-to-fit. It is this last 

case for which compensation is helpful. A history of regularized B histories for individual 

satellites is examined and a relative error and variance calculated, and this variance is added to 

the drag variance in the covariance as a corrective term whose influence will be realized in 

propagation.

There is some additional subtlety regarding the exact way these consider parameters are applied. 

A typical propagation consists of two conceptual stages: the first stage is the propagation forward 

from the epoch time of the orbit determination to the present time, which can make use of 

measured and thus highly reliable space weather indices; and the second stage is from the present 

time to the desired final propagation time, which has to use predicted space weather indices and 

the errors that these introduce. The two consider parameters are thus applied at different times. 

Because satellite rotation and its resultant uncertainty will occur for the entire interval from 

epoch time to the propagation end point, that consider parameter is applied at epoch. 

Atmospheric density forecast error, however, is encountered only forward in time from the 

present moment, so it is added only for that portion of the propagation. Figure N-10 outlines the 

two-phase application of these consider parameters:

DCP = Dynamic Consider Parameter

Figure N-10 Two-phase Application of Consider Parameters

If the CDMs generated by the DOD are used for conjunction assessment applications, the good 

news is that all the consider parameter activities described above are already performed—the 

propagated covariances that the CDM contains have had these two consider parameters applied 

during the covariance propagation executed at the DOD work center. If one is working with 

epoch state estimates, which is sometimes necessary when performing Pc calculations with 

Monte Carlo techniques, then manual application of the consider parameters may be necessary. 

This issue is discussed at greater length in the section that addresses Monte Carlo Pc

calculations.
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N.7.2 Defective Covariances

There are several ways in which a covariance contained in a CDM can be defective. 

• Null Covariances. All-zero, or null, covariances are sometimes observed, usually arising 

from a conjunction assessment screening for which the O/O-provided ephemeris does not 

contain covariance data. In such a case, it is possible to compute the Pc either using only 

the one covariance that the CDM message contains or by applying a special technique 

that determines the maximum Pc possible presuming that the null covariance could take 

on any possible value (developed and described in Frisbee 2015). 

• Default Covariances. Default covariances are diagonal covariances that contain a value 

of ten earth radii squared for each of the three position variances. The presence of this 

covariance indicates that a precision, special-perturbation solution for the object was not 

possible; the state estimate provided arose from a general-perturbation solution, and an 

orbit-determination-produced covariance was not available. Such a result is not a 

precision solution and does not constitute a basis for conjunction risk mitigation actions.

• Non-Positive-Semidefinite Covariances. Another defective covariance type found in 

CDMs, now quite rare due to improvements to the DOD operational system, is a 

covariance that fails to be positive semidefinite. A positive semidefinite matrix is one that 

contains no negative eigenvalues. Because the covariance represents a hyperellipsoid of 

actual state error information, it must have a set of eigenvalues all greater than or equal to 

zero for error information to consist of real rather than imaginary quantities. The orbitdetermination mechanism that generates the covariance should always produce at least a 

positive semidefinite matrix, for the linear algebra function involves the product of a 

square matrix and its transpose, and one can prove that this procedure always produces a 

positive semidefinite result. Due to either numerical precision limits or interpolation, the 

provided matrix is sometimes not positive semidefinite. If the 2 × 2 projection of the 

covariance matrix into the conjunction plane is not positive semidefinite, the twodimensional Pc calculation is not possible. If the full 6 × 6 or 8 × 8 matrix is not positive 

semidefinite, then Monte Carlo sampling on the entire matrix is not possible either. 

As such, some attention must be paid to this issue of positive semidefinite matrix conditioning. A 

recent paper on this subject (Hall 2017b) examined the issue in some detail and compared 

different matrix repair algorithms to minimally adjust the covariance to make it positive 

semidefinite compliant; it found that most repair approaches yield equivalent answers in terms of 

the resultant calculated Pc. An “eigenvalue clipping” procedure was developed in which any 

negative eigenvalues (which are almost always small) are set to a small positive or zero value, as 

required. 

The CARA operational implementation of this method proceeds parsimoniously, namely by 

directing such repair only to the level needed to perform a calculation. For example, a covariance 

used for the two-dimensional Pc calculation would neither be tested for positive semidefinite 

compliance in its full 8 x 8 form nor its position-only 3 x 3 form; instead, the 2 x 2 projection of 

the joint covariance into the conjunction plane would be tested and repaired only when necessary 
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to enable the two-dimensional Pc calculation. To do otherwise is to make repairs and potentially 

alter the result when this is not strictly necessary. 

The Pc Computation CARA SDK includes the source code for identifying the need for and 

making the covariance matrix repairs described above; it is available in the NASA CARA 

software repository. (See Section 7, Contact Information in this document for the specific URL.)

N.7.3 Covariance Correlation

For nearly all the broader conjunction assessment conduct during the past decade, practitioners 

operated with the presumption that the primary and secondary objects’ covariances could be 

considered uncorrelated. Not only was this the “right” answer in that it greatly simplified the Pc

computation because the joint covariance could be formed by simple addition of the two 

covariances, but there was also a good intuitive justification for the presumption. Because the 

focus had been on the two objects’ orbit-determination fits, which are based on separate sets of 

observations, there was no expectation that there would exist any significant correlation between 

the two objects’ covariances. The principal source of potentially correlated error was presumed 

to be uncharacterized but correlated errors in space sensor observations used by both primary and 

secondary objects. Because most primaries receive many observations from many different 

sensors, it was seen as unlikely that this particular source would introduce much correlation. 

Correlation between covariances was thus expected to be small, and conjunction assessment

operators proceeded as though it were.

With the initiative several years ago to include outside-of-fit prediction error characterization 

into DOD satellite covariances (see the above section on Propagation Error Compensation), the 

issue of covariance cross-correlation began to be rethought. The principal outside-of-fit 

prediction error is global atmospheric density forecast error due to inadequate space weather 

index prediction. Because this is a global error, it is likely to be shared among large classes of 

objects, some of which might constitute both the primary and secondary objects in a conjunction. 

As discussed previously, this global density forecast error has been parameterized by satellite 

perigee height and predicted geomagnetic index, so the degree of such error, both identified 

separately and injected into each DOD-furnished covariance by means of a consider parameter, 

is known for each satellite. It is possible to determine the degree of shared error from this source 

and account for it when forming the joint covariance.

A study by Casali et al. (2018) provides a full development of this theory and presents results for 

an evaluation set of conjunction data. Essentially, one has to determine the global density 

forecast error relevant to each satellite and the degree to which the associated drag error induced 

by this density forecast error will manifest itself in position error relevant to the particular 

conjunction. The governing equation is the following:

Pm = Ps + Pp - s/g p/g Gs G

T

p - s/g p/g Gp G

T

s (N-15)

in which Pm is the decorrelated joint covariance at TCA, Ps is the secondary covariance at TCA, 

Pp is the primary covariance at TCA, σs/g is the density forecast error germane to the secondary 

satellite, σp/g is the density forecast error germane to the primary satellite, Gs is the sensitivity 

vector mapping drag acceleration error to secondary satellite position error at TCA, and Gp is the 
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sensitivity vector mapping drag acceleration error to primary satellite position error at TCA. One 

could wonder how the conjunction assessment practitioner would come upon all of the needed 

data to effect the proposed compensation. A recent enhancement to the DOD operational system 

has placed all of this information in the CDM itself, allowing the direct calculation of the 

decorrelated joint covariance. The CARA Pc Calculation SDK, available on the NASA CARA 

software repository, contains both a math specification outlining this calculation and source code 

to perform it. (See Section 7, Contact Information in this document for the URL.) Hall (2021) 

describes how the density forecast errors and sensitivity vectors can be used to estimate 

decorrelated joint covariances for the two- and three-dimensional Nc methods.

A heuristic probing of the situation reveals that, conjunction by conjunction, different levels of 

Pc changes are possible due to cross-correlation remediation. Orbits that are insensitive to 

atmospheric drag are little affected by density forecast error and will have Pc estimates that, as 

expected, also change little. Head-on conjunctions are expected to be left mostly unaffected as 

well, for the components of the error that govern the Pc are not subject to density forecast error 

perturbation. Crossing events are perhaps the most susceptible to cross-correlation effects, 

especially if the drag level of both satellites is similar.

The plot in Figure N-11 profiles 250 conjunctions in which the primary and secondary satellites 

are of non-negligible drag (i.e., Energy Dissipation Rate (EDR) values greater than 0.0006 

watts/kg; see Hejduk 2008 for an explanation of energy dissipation rate) and plots the ratio of the 

Pc calculated with the decorrelated joint covariance to that of the Pc calculated with the 

unmodified joint covariance. One can see that for somewhat more than half of the events, the 

ratio hovers near unity, meaning that the conjunction is little affected by the compensation. For 

about one-third of the cases, the decrease in Pc is notable, in many instances more than an order 

of magnitude. For the remaining cases, there is an increase in Pc from a factor of 1.5 to 5. 
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Figure N-11 Profiles of 250 Conjunctions with Primary and Secondary 

Satellites of Non-negligible Drag14

While the Pc value changes by less than a factor of 1.5 for most of the conjunctions, a sufficient 

number are affected more substantially therefore justifying the integration of this additional 

consideration into the Pc computation, especially because it is a straightforward calculation from 

data provided directly in the CDM.

N.8 Monte Carlo Pc Calculation Techniques

Analytic approaches to Pc calculation are more computationally efficient than Monte Carlo 

methods, especially the conjunction plane two-dimensional Pc method. However, as discussed 

previously, analytic methods require certain enabling assumptions that are not necessarily valid 

for all conjunctions. Monte Carlo approaches require fewer enabling assumptions, but they are 

not typically employed as the first method of computation. Instead, Monte Carlo methods are 

usually reserved for cases that are suspected of violating the enabling assumptions of the analytic 

methods. As described by Hall et al. (2018) and Hall (2021), there are two strains of the Monte 

Carlo method that are regularly employed:

• “Monte Carlo from epoch,” in which the orbit-determination-epoch mean states and 

covariances are used to generate sampled states, and potentially long (i.e., multiday) 

high-fidelity propagations are required for each Monte Carlo trial.

• “Monte Carlo from TCA,” in which the mean states and covariances predicted at TCA 

are used to generate sampled states, and only relatively short propagations to each trial’s 

new TCA are required.

Each of these two approaches will be discussed in turn.

N.8.1 Monte Carlo from Epoch

14 From Casali et al. 2018.
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The principal appeal of calculating the Pc using the Monte Carlo from epoch approach is that it 

requires almost no simplifying or restrictive assumptions, making it is as close to a “gold 

standard” for Pc estimation as can be devised. The input information includes the states and 

covariances for the primary and secondary objects at their respective orbit-determination epoch 

times, the combined hard-body radius of the two objects, and an ensemble of environmental 

datasets required for the high-fidelity propagations (such as predicted space weather indices and 

atmospheric density debiasing data; see Hall et al. 2018). The most elaborate instantiation of this

technique uses the full eight-dimensional orbital state vectors (each containing six coordinate or 

element variables, plus drag and solar radiation pressure variables) along with the associated 8x8 

covariance matrices for the primary and secondary satellites. 

For each Monte Carlo trial, a state perturbation is obtained by performing a random draw from 

the distribution using the covariance matrix to generate the associated Gaussian distribution for 

each variable. These perturbations are then used to alter the initial states by adding each to the 

appropriate epoch mean state estimates. To do this for the primary satellite, for example, one 

would generate random perturbations for the eight variables representing the primary satellite’s 

state based on their distribution as defined by the covariance, and then create a new, sampled 

state vector by adding the (signed) perturbations to the mean epoch state vector. This same 

procedure would also be performed for the secondary satellite. This sampling process generates 

epoch states for both the primary and secondary objects that represent statistically reasonable 

alternatives for their actual states. These two sampled epoch states are then propagated forward, 

a TCA identified, and a check performed to determine whether the miss distance at TCA is 

smaller than the hard-body radius; if it is, the trial results in a simulated collision and a “hit” is 

registered; if not, it is considered a “miss.” This sampling/ propagation/ hit-registration 

procedure is then repeated for a large number of Monte Carlo trials, and the final number of hits 

divided by the total number of trials constitutes the Monte Carlo Pc estimate. There are 

algorithms that can be applied to estimate the confidence interval on the Monte Carlo Pc after a 

given number of trials due to event counting uncertainties (e.g., MATLAB’s binofit function). 

This procedure seems straightforward enough, and in many respects it is. But there are subtleties 

that require attention, especially if the technique is deployed for LEO conjunctions:

• For the result to be valid, the same force models and force model settings must be used 

for the Monte Carlo propagations as were used when generating the original orbitdetermination solution. While it often is not difficult to apply the same general force 

model settings, there does need to be overall compatibility between the orbitdetermination engine and the Monte Carlo propagator, such as the same set of 

geopotential Legendre polynomial coefficients (not just the same geopotential order) and, 

most critically for LEO, the same atmospheric density model. While it may be possible to 

deviate somewhat from this level of compatibility and still obtain reasonably accurate 

outcomes, the “gold standard” propriety of the result is lost.

• Correlation between the primary and secondary covariances, as described in the previous 

section, should be considered. This correlation can be modeled during the random draw 

process by forcing correlation in the primary and secondary objects’ drag perturbations.
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• Monte Carlo from epoch often requires extremely long computation run times. The run 

time is a function of the actual Pc, since this will determine how often hits are likely to 

occur and the number of trials required to obtain a result with a desired confidence level. 

Without marshalling extensive high-performance computing, the Pc levels that can be 

explored with this method have to remain relatively large (e.g., 10-5or above). 

Computation times for smaller Pc events can be prohibitively long. For example, 

validating a Pc estimate of ~10

-7

at the 95% confidence level for a conjunction with TCA 

five days from the orbit determination epoch time would require an estimated two years 

of execution time on a 20-CPU, reasonably modern server (Hall et al. 2018). For this 

reason, it is typically necessary to reserve the Monte Carlo from epoch method for larger 

Pc events only, which means that one must trust analytic methods to identify a candidate 

subset of conjunctions for follow-up Monte Carlo analysis.

• High-fidelity orbital state propagations require the most processing during typical Monte 

Carlo from epoch computations, so when applying this approach, there is a temptation to 

“reuse” propagations to gain computational efficiency. Suppose that ten perturbations 

were performed for the primary satellite and ten propagated ephemerides were generated, 

and the same was done for the secondary object as well. Ephemeris #1 for the primary 

could be compared to ephemeris #1 for the secondary to determine whether a hit 

occurred, ephemeris #2 for the primary to ephemeris #2 for the secondary, ephemeris #3 

for the primary to ephemeris #3 for the secondary, etc., and have as a result ten 

comparisons/trials. To go further, one could compare ephemeris #1 for the primary to 

ephemeris #2 for the secondary, ephemeris #1 for the primary to ephemeris #3 for the 

secondary, etc., and realize 100 comparisons/trials from merely 20 total propagations. 

Such a procedure certainty seems advantageous, given that processing time is the limiting 

factor to the deployment of Monte Carlo from epoch, and following such a procedure will 

produce a result that converges on the true Pc. The drawback is that such reuse of 

samples violates the conditions for the proper application of the formulae to calculate Pc 

uncertainty confidence intervals. Monte Carlo results without associated reliable 

confidence intervals are not operationally useful because it is never known how close one 

is to the true Pc value. Schilling et al. (2016) discuss this issue and confirm it to be a 

problem, and they recommend some estimation techniques that allow (large) confidence 

intervals to be constructed around Monte Carlo products that avail themselves of sample 

reuse. The CARA implementation has avoided any such sample reuse to ensure that the 

“gold standard” status of the results not be in question and to produce more narrow 

confidence intervals.

Due to all the above considerations, but especially the run-time requirements, Monte Carlo from 

epoch is usually reserved only for those cases that require it for accurate Pc estimation.

A study effort discussed in greater detail in the next section determined that the Monte Carlo 

from epoch method appears to be needed only when the two objects stay in such close proximity 

that they experience a sequence of multiple, comparable-risk close approaches during a multiday

risk assessment projection interval. For closely spaced co-orbiting objects, these conjunctions 

may also become effectively “blended” in time with one another such that collision probability 
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accumulates appreciably even during the mid-point times between the encounters rather than just 

during short bursts very near the close approaches (Baars et al. 2019). In such cases, two 

impediments arise to estimating accurate Pc values using methods formulated for temporally 

isolated close approaches. First, there is no clear, single TCA at which to evaluate the collision 

likelihood. While one could in fact find the unique point of closest approach between the two 

nominal trajectories for the entire sequence and perform a two-dimensional Pc calculation for 

that encounter, there is no guarantee that another encounter in the sequence may actually possess 

a higher Pc due to different covariance orientations even though it has a larger nominal miss 

distance. Second, calculating a single encounter Pc at each of the close approaches and then 

amalgamating these using the following formula (derived from DeMorgan’s Law of 

Complements)

PTot = 1 − ∏ (1 − Pci)

n

i=1

(N-16)

potentially overestimates the overall collision likelihood because it presumes that the individual 

events in the sequence are statistically independent, but in fact they may not be, especially if 

blended in time. This total probability estimate matches that given in equation (N-13) and 

provides an upper bound for the amalgamated risk over the time interval of interest. For 

maximum efficiency, Monte Carlo from epoch would then be run operationally only in cases in 

which this upper bound is above a mitigation threshold and there is interest in determining 

whether the higher-fidelity Monte Carlo calculation would reduce this value to one much closer 

to or below the threshold. Monte Carlo from epoch can also be run if there is any question about 

the overall rectitude of the Pc calculation. As stated earlier, lower-Pc conjunctions may present 

intractable Monte Carlo execution times, but if one wishes only to ensure that the Monte Carlo 

Pc falls below the mitigation threshold (rather than establish a high-fidelity Pc value), this can 

usually be accomplished with far fewer Monte Carlo trials.

Optimal application of the Monte Carlo from epoch Pc estimation method does not entail Pc

evaluation over a relatively short time interval bracketing a single conjunction’s TCA, but rather 

over a more extended interval that spans several close approach encounters. For example, the 

collision likelihood between two objects would not be evaluated at the nominal TCA for a single 

conjunction, but, perhaps, over a risk assessment interval projecting forward seven days. This 

multiday interval would not only include the original nominal TCA but also a sequence of other 

encounters between the primary and secondary as well. In this case, each Monte Carlo trial 

would be propagated forward seven days and a hit registered at the earliest time that the hardbody radius is violated, if such a time exists (Hall et al. 2018 and Hall 2021). Temporal risk plots 

can be produced using the sequence of hits registered during all the trials, an example of which is 

shown in Figure N-12 (which shows the same conjunction sequence as Figure N-8 from the 

earlier discussion of two- and three-dimensional Nc calculation methods). The pink shaded area

in Figure N-12 shows the Monte Carlo Pc estimation confidence region, and the pink line shows 

the best estimate Monte Carlo result. As can be seen, the black upper line, which is the upper 

bound estimate from the three-dimensional Nc function, is within the confidence interval of the 

Monte Carlo results and thus is a reasonable actual realization of the repeating conjunctions’ 

cumulative risk.
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Figure N-12 Three-Dimensional Nc Temporal Risk Plot with 

Monte Carlo from Epoch Result Overlay (in Pink)

Because it is complicated to set up the execution environment for the Monte Carlo from epoch

calculation, and because “gold standard” results require assembling extensive environmental data 

and software settings identical to the original DOD orbit-determination solutions, it is envisioned 

that the ability to run this strain of Monte Carlo estimation will remain with NASA CARA. 

However, a more computationally efficient mode of Monte Carlo estimation, which is 

serviceable for several different applications and is easier to obtain and employ operationally, is 

described in the next section.

N.8.2 Monte Carlo from TCA

A much more computationally efficient variant on Monte Carlo from epoch, which has been 

used by conjunction assessment practitioners for some time, is Monte Carlo conducted from 

TCA, or two-body Monte Carlo (TBMC)-Pc estimation. As the definition implies, the Monte 

Carlo simulation begins with the primary and secondary objects’ equinoctial element states 

propagated to TCA. Perturbation and sampling of both states is conducted much as described 

earlier for Monte Carlo from epoch, and each sampled primary and secondary state is propagated 

both forward and backward in time to find the pair’s TCA and determine whether the 

corresponding miss distance is smaller than the hard-body radius (backward propagations are 

required to register hits that occur at times before TCA). The simplification arises from the fact 

that, since one is beginning from TCA, the propagations required will be short. This means that 

an efficient two-body motion propagation scheme usually provides an accurate trajectory 
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approximation, and this, combined with the very short propagation times, vastly improves the 

computational efficiency of the calculation—by a factor of 10,000 to 100,000 according to the 

study by Hall et al. (2018). This specific method of Monte Carlo from TCA is also referred to as 

“two-body Monte Carlo” Pc (TBMC-Pc) estimation. To use the TBMC-Pc method, the 

conjunction duration needs to be short so that one may safely presume a single, unblended event 

that does not require the Monte Carlo from epoch method. As a second condition, one must have 

confidence that both objects’ states and covariances propagated to TCA are good representations 

of the states and state uncertainties at that point. Usually, there is reasonable confidence in the 

mean state estimates themselves, but the covariances are a different matter: a number of studies 

(e.g., DeMars et al. 2014) have indicated that propagated covariances represented in Cartesian 

space fail to represent the actual uncertainty distributions, due both to the potential failure of the 

linearized dynamics to remain representative over long propagation intervals and, more 

importantly, a mismatch between elongated in-track uncertainty volumes and the forced 

representation of these uncertainty volumes as Cartesian ellipsoids. The latter problem is 

illustrated in Figure N-13. The actual in-track error volume should follow the curved trajectory 

of the orbit, but the Cartesian covariance is limited to the rectilinear representation shown: as the 

elongation grows in the in-track direction (which occurs for longer propagations), the mismatch 

between the two representations also increases.

Figure N-13 Mismatch between Elongated In-track Covariances and 

Forced Cartesian Ellipsoidal Representation

To address the latter problem, the results from a study conducted by Sabol et al. (2010) are both 

important and extremely helpful. This study addressed directly the question of the optimal choice 

of orbital state representation for covariances, finding that it is not the specific state 

representation in which the propagation is executed but rather the one in which the propagated 

covariance is rendered that ultimately governs the realism of the uncertainty distribution and 

associated error volume. Specifically, if the covariance is rendered and used in a curvilinear state 

representation, such as equinoctial elements, then it tends to represent the error volume much 

more accurately than if it is transformed and used in Cartesian coordinates. The surprising result 

r
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is that a non-representative Cartesian covariance transformed into an equinoctial covariance 

becomes a representative covariance. Furthermore, taking random samples using the equinoctial 

state representation and performing the non-linear conversion of each sample to Cartesian 

coordinates generates a point cloud in the Cartesian frame that also approximates the true error 

volume much more accurately. 

This latter procedure allows the Monte Carlo from TCA method to employ more realistic 

uncertainty volumes, at least with respect to orbital state representation-related mismatches. The 

detailed procedure is the following:

1. Convert both objects’ states and covariances at TCA to equinoctial elements.

2. Generate a set of perturbations for each object based on the equinoctial covariances.

3. Combine these with the mean equinoctial states to generate sampled equinoctial states for 

the primary and secondary.

4. Convert these sampled states from equinoctial elements to Cartesian coordinates using 

the non-linear transformation.

5. Propagate the Cartesian states for both the primary and secondary using two-body 

equations of motion to find the new TCA, which may precede or follow the nominal 

TCA.

6. Determine whether the new miss distance is less than the hard-body radius, and if so, 

register a hit at the time that the hard-body radius sphere is violated.

7. Repeat steps 5-6 until the entire set of Monte Carlo sampling trials has been processed.

8. The Pc is the number of hits divided by the total number of trials, and the confidence 

interval can be calculated from an appropriate formula.

This approach seems reasonable enough; but it would be presumptuous to assert, without further 

study, that it is truly robust, especially since the question of the durability of the linearized 

dynamics typically used to propagate covariances was not directly addressed. As it is, additional 

study efforts have been performed to verify that it is indeed sufficiently representative for 

conjunction assessment applications, and they are described below.

The first of these study efforts was performed as part of the previously cited analysis by Hall et 

al. (2018). A set of 373 high-Pc conjunctions was selected and evaluated with both Monte Carlo 

from epoch and Monte Carlo from TCA, and the comparative results are shown in Figure N-14. 

The top window is a scatter plot of the Pc calculated by Monte Carlo from epoch versus that 

from Monte Carlo from TCA. The intersection of each “plus” sign gives the scatter-plot point, 

and the length of the plus-symbol tails indicates the uncertainty of the calculation. One can see 

that the agreement is strong because all the points are close to the dashed y-x line that would 

indicate perfect equality. The bottom window plots the base-ten logarithm of the ratio of Pc 

values estimated using the Monte Carlo from epoch method to those estimated with the Monte 

Carlo from TCA method. The largest deviations are about 0.2 of an order of magnitude in Pc, 

which is considered to be below operational significance. A separate statistical test for similarity 

of results produced p-values all less than 10-3, indicating that one should reject a hypothesis that 
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these results arise from different distributions. Good agreement is thus observed between the 

abbreviated Monte Carlo from TCA and Monte Carlo from epoch results.

Figure N-14 Comparative Results of 373 High-Pc Conjunctions15

The second study effort involved a comparison between the Monte Carlo from TCA Pc 

estimation method and the two-dimensional Pc method (Hall 2019b), which was later extended 

to compare the from TCA method to two- and three-dimensional Nc methods (Hall 2021). In 

these studies, 63,603 temporally isolated conjunction events with two-dimensional Pc values 

greater than 10-7 were subjected to Pc calculation by the two-dimensional Pc method, as well as 

the two- and three-dimensional Nc methods, and all of these were compared to the Monte Carlo 

from TCA method. The comparative results are shown in Figure N-15 (which refers to Pc values 

estimated using the Monte Carlo from TCA method as TBMC-Pc values). These plots are similar 

to those already shown in Figure N-7, except in this case the colored diamonds represent the 

worst kind of Pc estimation failure, i.e., conjunctions in which the analytical calculations

significantly underestimate the Monte Carlo from TCA method Pc values. The left panel shows 

that, although the two-dimensional Pc method performs reasonably well for the vast majority of 

temporally isolated conjunctions, it underestimates from TCA Pc values by a factor of 1.5 or 

more in 0.258% of the investigated cases. (See the top legend of the left graph.) For those cases 

that showed large disparities, the subset that had true Pc values in the tractable range for Monte 

Carlo from epoch were validated with this methodology; and in each case the Monte Carlo from 

15 From Hall et al. 2018.
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epoch reruns matched the output from the Monte Carlo from TCA. To the degree that nonrepresentative covariances may be responsible for two-dimensional Pc failures (due to coordinate 

frame mismatches), Monte Carlo from TCA certainly appears to be able to recover the true Pc. 

As an aside, some of these differences between the conjunction plane two-dimensional Pc

estimates and the Monte Carlo method estimates are considerable; there are several cases in 

which the two-dimensional Pc estimate understates the Monte Carlo from TCA estimate by more 

than an order of magnitude, as shown in the red in the left panel of Figure N-15. The center and 

left panels of Figure N-15 show that the three- and two-dimensional Nc methods do not similarly 

underestimate the from TCA Pc method values, except in a few statistically insignificant cases.

Figure N-15 Comparative Results of 63,603 Conjunction Events16

Originally, Monte Carlo from TCA was advanced as a robust and computationally tractable way 

to ensure reliable Pc calculations in the face of occasional miscarriage of the two-dimensional Pc

algorithm. However, Figure N-15 demonstrates that the development and testing of the two- and

three-dimensional Nc analytic methods have led NASA CARA to recommend that these methods

supplant routine use of Monte Carlo from TCA. One may still resort to this more 

computationally efficient Monte Carlo method if desired, but testing indicates that the Nc

calculation methods outperform Monte Carlo from TCA (in that it accurately matches Pc 

estimates for isolated conjunctions and also provides a cumulative risk upper bound for repeating 

conjunctions) and is at least an order of magnitude more computationally efficient, especially for 

events with small Pc values. Monte Carlo from TCA is a capability available for download from 

the NASA CARA software repository,

17 and O/Os who are currently using it or a similar 

implementation are not urged to take it out of service, but as a Pc calculation approach, it does 

not seem to offer any enduring advantage over the two- and three-dimensional Nc methods.

Finally, a dedicated study on covariance Gaussianity was recently conducted (Lechtenberg 

2019b). The same set of 44,000 conjunctions used by Hall (2019b) was analyzed for multivariate 

16 From Hall 2019b and Hall 2021.

17 Specifically, the MCWorkbench SDK function estimates TBMC-Pc conjunction values using CDM test files as 

input. See Section 7, Contact Information in this document for the CARA software repository URL.
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normality of the position covariance in Cartesian coordinates. The methodology was to convert 

the covariance to equinoctial elements, generate a set of random position samples from this 

covariance, convert the sample set to Cartesian coordinates, and apply a multivariate normality 

test (here the Henze-Zirkler test) to assess compliance to this distribution. At a 5% significance 

level, only 60% of the cases could be considered to conform to a multivariate Gaussian 

distribution in Cartesian coordinates. In principle, such conjunctions would be considered 

suspect cases whose two-dimensional Pc results would be considered doubtful. As it is, since 

such a large fraction of the investigated cases show good agreement between the Monte Carlo at 

TCA and the two-dimensional Pc, clearly the Gaussianity of the covariances in the Cartesian 

framework does not matter appreciably for the Pc calculation. This result corroborates that of an 

earlier study by Ghrist and Plakalovic (2012), which reported similar findings.

How can this be, given that the covariance is integral to the two-dimensional Pc calculation? It is 

important to remember that the analyses above are restricted to high-Pc events. For the 

probability of collision to be high, significant overlap needs to exist between the primary and 

secondary object covariances; this means that the central parts of the covariances, which are 

where most of the probability density lies, have to overlap substantially. Such a requirement 

makes the behavior of the tails of the covariance much less important, and it is in the tails that 

non-Gaussian behavior is most strongly manifested. Even though a good number of conjunctions 

fail tests for covariance Gaussianity in Cartesian coordinates, for high-Pc events, this result does 

not appear to affect the rectitude of the calculated Pc. A difference probably is observable for 

lower-Pc conjunctions, but because these conjunctions are not operationally significant, it is not 

operationally important to identify or characterize this phenomenon. 

There is the lingering question of the eventual failure of the linearized dynamics in propagating 

covariances since DOD covariances are propagated through a pre- and post-multiplication by a 

linearized state transition matrix. It is agreed that, given sufficiently long propagations, such an 

eventuality should arise. However, the propagation duration required for this problem to manifest 

itself substantially is believed to be much longer than encountered for most conjunctions—on the 

order of weeks. This is why more attention is paid to this phenomenon in other areas of SSA 

such as uncorrelated track processing for which propagations of 30 days or more may be 

required, whereas it is rare for propagations longer than ten days to take place in conjunction

assessment. Of course, fresh tracking data are always appreciated as they shorten the propagation 

interval and lend additional confidence to the solution.

N.9 Choosing an Appropriate Hard-Body Radius

As discussed in the first section of this appendix, the hard-body radius represents the combined 

size of the primary and secondary objects; the word “radius” is used because this combined size 

is typically envisioned as a sphere, and the radius of a sphere is a convenient linear 

representation of its size. The hard-body radius is needed for the Pc calculation because it 

represents the circle/sphere within which a simultaneous penetration by both the primary and 

secondary objects’ trajectories will constitute a presumed collision. It is not just a required input 

to the Pc calculation, however, it is also one of the governing parameters of the calculation: the 

Pc value represents an integral over the area of the hard-body radius circle (or surface area of the 

hard-body radius sphere) and thus in many circumstances, varies roughly in proportion to the 
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square of the hard-body radius, so an increase of the hard-body radius by a factor of three 

increases the calculated Pc by a factor of nine, or nearly one order of magnitude. Because of this 

sensitivity, it is important not to overstate the hard-body radius simply for “conservatism”

because the effect on the calculated Pc can be considerable. The best overall strategy for 

applying conservatism, should one wish that, is to apply it at the end of the process by lowering 

the Pc threshold at which mitigation actions should occur. Injecting conservatism into different 

places throughout the Pc calculation makes it difficult to determine how much conservatism has 

actually been introduced, whereas addressing this desire through a modification of the Pc

threshold for mitigation allows it to be understood precisely. 

Mashiku and Hejduk (2019) recently completed a study of different hard-body radius calculation 

and setting strategies, and a streamlined summary of the possibilities examined is provided 

below:

1. Large a priori value. For some years it was standard practice simply to choose a hardbody radius value that was notably larger than the expected actual size of the combined 

primary and secondary object; 20 meters is a value that was typically used. Perhaps in 

the early days of conjunction assessment, this was an acceptable initial screening 

strategy to identify potential serious events, and the hard-body radius would then be 

reduced when analysis began in earnest. As the space catalog has grown in size, and 

especially with the recent growth through the deployment of the Space Fence radar, this 

particular strategy merely creates additional false alarms that needlessly burden the 

process. Nearly all O/Os have moved away from this hard-body radius strategy.

2. Circumscribing sphere. The use of a circumscribing sphere to set the primary object’s 

hard-body radius is perhaps the most commonly used present operational technique, 

which admits of two typical variants: placing the sphere’s center at the center of mass of 

the primary satellite and defining the radius by the length from this center to the 

satellite’s most distant extremity; or allowing the center point to float freely and then 

defining the smallest circumscribing sphere. The overall sphere size then has to be 

increased by the expected size of the secondary object using either an averaged value or 

an estimate for the particular secondary encountered. This size could be obtained either 

from known or published dimensions (for intact spacecraft or rocket bodies) or estimated

from remote sensing data, such as radar cross-section or photometric brightness

measurements. In the latter case, the estimated hard-body radius size of the secondary 

may also have an associated uncertainty estimate, which can also be incorporated into 

the Pc estimation process (as discussed in more detail below).

3. Maximum projected area into any plane. Since the circumscribing sphere described 

above most often ends up being projected into the conjunction plane, it is instructive to 

examine in more detail the implications of such a projection. Clearly the sphere itself 

will project as a circle, but the projection of the three-dimensional spacecraft inside will 

necessarily be smaller in area than the projected circle, and for some spacecraft shapes 

and orientations, it will be substantially smaller in area. In this latter case, the substantial 

“white space” within the projected circular area not occupied by the primary could 

justifiably be excluded in the Pc estimation process, especially for the most common 
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debris-encounter scenario when the incoming secondary object is much smaller than the 

primary asset. A straightforward way to address this issue that does require knowledge 

of the satellite’s actual orientation in relation to the conjunction plane is simply to 

determine in advance the maximum area that the satellite can possibly project into any 

plane (based on a three-dimensional CAD18 model of the satellite) and use a hard-body

radius circle of that equivalent area (which of course must then be enlarged to include 

the estimated size of the secondary) for Pc estimation. It is true that this is a conservative 

formulation in that it uses the maximum possible projected area, but this is often 

substantially smaller than the area of the projected circumscribing sphere. One could 

argue that uncertainty is introduced by using the equivalent circular area rather than a 

contour integral to perform the integration over the actual projected shape, but individual 

exploratory examples show that this difference is usually negligibly small, and in any 

case, the most conservative projection approach should compensate for any differences 

in the shape chosen to represent the hard-body radius area for the Pc calculation.

4. Projection into actual conjunction plane. The most accurate, and at the same time the 

most difficult, approach is to perform a projection of the primary satellite’s shape into 

the actual conjunction plane. Specifically, this requires a three-dimensional CAD model 

of the satellite plus knowledge of its inertial attitude and the orientation of any major 

articulating components at TCA along with a calculation to project the resulting shape 

into the conjunction plane. Once this projection is obtained, its boundaries have to be 

augmented to account for the expected size of the secondary, and the integration of the 

joint covariance probability density can take place over this figure via contour 

integration or over a more convenient shape of equivalent area. Chan (2019) recently 

proposed a method to decompose complex shapes into individual triangles and use an 

equivalent-area method to evaluate the Pc for each triangle; the composite Pc is simply 

the sum of the Pc values for these individual trials of decomposition.

Each successive approach among the four presented brings greater precision to the hard-body

radius determination but at the same time, additional complexity. A reasonable via media would 

appear to be approach 3) above, which keeps the hard-body radius value grounded in reality and 

free from excessive conservatism but avoids the difficulties of gathering and maintaining shape 

and attitude data to enable a detailed projection calculation for each conjunction.

To facilitate Pc estimation, CARA has undertaken an effort to estimate hard-body radii of 

unknown orbiting objects based on radar cross section (RCS) measurements obtained by the 

Space Fence radar system (Baars and Hall 2022; Hall and Baars 2022). Even after accounting for 

radar calibration irregularities and occasional outlier data points, such RCS measurements have 

considerable point-to-point scatter, and the process of converting the RCS data into hard-body 

radius estimates introduces considerable additional uncertainty. The resulting hard-body radius 

uncertainty PDFs are non-Gaussian, although they can be roughly approximated using a lognormal distribution. Notably, RCS-based hard-body radius estimates are typically uncertain by 

factors of two to three, so it is essential that Pc estimates account for these uncertainties. For an 

18 Computer-aided Design
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unknown secondary involved in a conjunction, the RCS-based uncertainty PDF can be used to 

calculate a mean hard-body radius estimate, R̅

2, and an associated variance, σR2

2

. As mentioned 

previously, for many conjunctions, the estimated Pc value varies roughly in proportion to the 

square of the hard-body radius. In these cases, the appropriate hard-body radius to use for Pc 

estimation is given by the effective combined hard-body radius

Reff = √(R1 + R̅

2)

2 + σR2

2

(N-17)

with R1 representing the primary object’s hard-body radius, usually established using methods 2 

or 3 listed above, as discussed previously. (The current recommendation for the less often used

method 4 is to increase the projected shape of the primary object outwardly on the conjunction 

plane by the length R̅

2 + 3σR2

to produce a conservative Pc estimate, although CARA continues 

to research a more accurate approach in these cases.) So for most cases, CARA recommends 

calculating Pc values using the combined hard-body radius given in equation (N-17) for all 

conjunctions involving secondary objects with uncertain sizes, partly because of the formula’s 

relative simplicity, but primarily because using the effective radius approach reproduces

remarkably well the more accurate RCS-based Pc estimates calculated using Monte Carlo 

analyses. (See Hall and Baars 2022 for details.)

Currently, Space Fence RCS measurements sufficient for size estimation are available for over 

90% of CARA conjunctions involving unknown secondary objects (Baars and Hall 2022). 

Analysis indicates that about 98% of such conjunctions involve secondary objects with mean 

hard-body radius estimates less than 35 cm, and only about 0.3% have R̅

2 > 1.5 m. For known 

objects (e.g., active or retired payloads, rocket-bodies), this approach tabulates the known hardbody radii with zero uncertainty, along with a reference for the source of the size information. 

For unknown objects with sufficient RCS data (which includes a large fraction of tracked LEO 

orbital debris objects), this approach tabulates the mean estimated hard-body radius and the 1-

sigma uncertainty, which can be used in equation (N-17). For reference, this approach also 

tabulates the median hard body radius values, as well as the associated 95% and 99% confidence 

intervals, as estimated from the actual RCS-based uncertainty PDF. For unknown objects with 

insufficient RCS data, one can assign a reasonably conservative default size estimate of 1.5 m.
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Appendix O. Collision Consequence

O.1 Introduction

It is common in conjunction assessment circles to speak of “collision risk metrics” such as the 

Probability of Collision (Pc), but in fact, calling such parameters risk metrics is a misnomer. As 

was first laid out formally in the literature by Kaplan and Garrick (1981) and has been adapted 

and reinforced by NASA’s own project risk assessment paradigms, risk is actually the 

combination of the likelihood of a detrimental event and the consequence if such an event should 

come to pass. Conjunction risk assessment metrics such as the Pc are simply measures of 

collision likelihood, which is only part of the overall risk assessment. Because conjunction 

assessment practice arose originally from individual missions whose focus was to protect their 

own spacecraft, it seemed unnecessary to add any considerations beyond collision likelihood. 

The loss of the mission’s spacecraft was considered a catastrophic event to be avoided at all 

costs, so all that needed to be evaluated was the likelihood of a collision, which if it took place 

was presumed to be fatal to the satellite’s operation and the mission.

When the conjunction assessment risk analysis for groups of satellites or an entire agency or 

nation is considered, however, the problem broadens. There is certainly the desire to see 

individual missions protected from catastrophic termination. The particular urgency of protecting 

any given spacecraft from premature end-of-mission life is a product of a number of factors such 

as the degree to which mission objectives have been met, the age of the satellite, and the 

functional redundancy within a constellation. Because the individual mission has the best sense 

of these considerations, they are in the best position to assess the consequences of potential 

spacecraft loss. However, there is a second parallel consideration, which is the preservation of 

orbital corridors from debris pollution to ensure their utility for future missions, both by the 

United States and all space-faring nations. The NASA Orbital Debris Program Office (ODPO) 

has for some years been the NASA project chartered with this concern. They have outlined 

spacecraft design and disposal recommendations to mitigate orbital debris production, but there 

has not yet been an effort to establish clear requirements for debris minimization through 

on-orbit conjunction assessment activities during mission lifetimes. One of the purposes of the 

present document is to lay out best practices for conjunction assessment operations that promote 

debris minimization. To reduce the production of debris, one must not only consider the 

likelihood of any given collision between a NASA primary satellite and other space objects but 

also evaluate the amount of debris that such a conjunction, should it result in a collision, may 

engender.

O.2 Debris Production Determination Methodology

It is very much the case that different types of satellite collisions can produce substantially 

different amounts of debris. The ODPO has studied this phenomenon in some depth through 

staged collisions of satellites with simulated debris objects in vacuum chambers and established 

relationships among conjunction parameters and the number and size of the resultant debris 

objects (Johnson et al. 2001). The basic distinction is between catastrophic collisions, in which 

both the primary and secondary object are fully fragmented and thus generate large amounts of 
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debris, and non-catastrophic collisions in which the smaller/lighter satellite is fully fragmented 

but the larger/heavier satellite only cratered, generating much smaller amounts of debris. The 

catastrophic/non-catastrophic distinction is governed by the following relationship, based on the 

relative kinetic energy of the encounter:

ε =

min (M1, M2)

max (M1, M2)

(

Vrel

2

2

) (O-1)

in which Vrel is the relative velocity between the two satellites, M1 is the mass of the primary

satellite, and M2 is the mass of the secondary satellite. When the relative kinetic energy exceeds 

40,000 Joules per kilogram, ε∗, the collision is expected to be catastrophic and produce much 

larger amounts of debris. The ODPO has further developed a relationship that estimates the 

number of debris pieces greater than a specified size that the collision will generate:

FEV(M1, M2

) = {

0.1(Vrel min(M1, M2

))

0.75Lc−1.71 if ε ≤ ε∗ (noncatastrophic)

0.1(M1 + M2

)

0.75Lc−1.71 if ε > ε∗

(catastrophic)

(O-2)

in which Lc is the characteristic length (size) above which one wishes to determine the number of 

debris pieces. According to Lechtenberg and Hejduk (2019) and Lechtenberg (2019a), 

“trackable” fragments are those with characteristic lengths exceeding a cutoff of Lc = 0.05 m. If 

the collision is catastrophic, the number of fragments is determined by the sum of the two 

satellites’ masses; if it is non-catastrophic, the equation uses the product of the mass of the 

lighter satellite and the conjunction’s relative velocity.

These relationships conform to first-order intuition regarding expected relative levels of debris 

production. Any schoolboy who has played with dirt clods can testify that a greater relative 

velocity between two conjuncting dirt clods will produce greater fragmentation. Furthermore, if 

the masses of the heavier and lighter object differ substantially, which probably also means that 

their relative sizes differ as well, one can imagine the (much) smaller object simply passing 

through (cratering) the larger one and, while itself fragmenting, leaving the larger object 

essentially intact. This full versus partial fragmentation division introduces a discontinuity in the 

debris production relationship (as a function of relative mass and relative velocity), and the entire 

dynamic, illustrated by Figure O-1, shows the extremely broad range of debris production 

outcomes—from very few debris pieces to thousands—all of which represent real possibilities 

for satellite conjunctions because the full range of secondary object mass values and relative 

velocities shown in the figure are frequently encountered in practice.

To assess fragmentation risks a collision presents to the orbital environment, Hall and Baars 

(2022) introduced a “fragmentation probability” metric that measures a conjunction’s probability 

of producing more than a threshold number of trackable fragments, F, given by:

P̅

F = E[PF

(R1, R2, M1, M2)] ≈ E[Pc(R1 + R2) × U(FEV(M1, M2) − F)] (O-3)

where R1 and R2 are the primary and secondary object’s hard-body radii (HBR), respectively, 

U(−) is the unit step function, and E[−] is the expectation value operator, which indicates the 

expected results by averaging over all relevant random variables.
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Figure O-1 Range of Debris Production Possibilities19

Since the debris production potential can vary so greatly among different conjunctions, it makes 

sense that conjunction remediation requirements should take cognizance of this parameter, 

presuming of course that it can be estimated from available conjunction information. The 

conjunction relative velocity is easy to calculate and is in fact provided directly as part of the 

CDM, and the HBR and mass of the primary object are known by the satellite O/O. The HBR 

and mass of the secondary object, however, are more elusive; in the great majority of 

conjunctions, this object is a debris object for which there is no a priori information. One must 

therefore look to estimation processes to estimate this object’s HBR and mass.

In formulating a HBR and mass estimation methodology, an approach is desired that is informed 

by and accounts for associated uncertainties in the estimate. If conjunction mitigation 

requirements are to be somewhat relaxed for low-debris-potential conjunctions, it is important to 

err on the side of debris quantity overestimation to guarantee that all situations in which this 

relaxed threshold may be applied are truly warranted. In nearly all practical cases, larger 

secondary object HBR and mass values will result in larger produced debris counts. A 

conservative approach requires ensuring, to a desired degree, that the estimation process 

overestimate rather than underestimate the HBR and mass of the secondary object. Such an 

orientation can be tuned and verified by attempting to estimate the HBR and mass of small 

objects with known HBR and mass values such as microsats.

19 From Hejduk et al. 2019.
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O.3 Estimating the Sizes of Unknown Objects

Stokely et al (2006) describe the NASA size estimation model (SEM), which provides a semiempirical method to convert radar cross-section (RCS) measurements for an unknown satellite 

into a statistical ensemble of estimates for the “characteristic length” of the object. Notably, this 

characteristic length is not equivalent to the hard-body radius, but instead represents the average 

of the largest dimensions of an object measured along three orthogonal axes, which corresponds 

to the diameter for spherical objects. Applying the SEM to the n

th RCS measurement available 

for the j

th satellite yields:

Dj,n = {

λj,n√4z/π z > 5

λj,n √4z/(9π

5)

6

z < 0.03

λj,n gSEM(z) otherwise

(O-4)

with Dj,n denoting the characteristic length (m) corresponding to the RCS measurement, λj,n the 

radar wavelength (m), and z = Yj,n/λj,n

2

, with Yj,n representing the measured RCS value (m2). 

Stokley et al (2006) provide an interpolation table for the function gSEM(z). Notably, the NASA 

SEM provides no direct means to estimate the error or uncertainty of RCS-based characteristic 

length estimates. This can be especially problematic if only one representative (e.g., median) 

RCS value is available per satellite. As described in Hall and Baars (2022), numerous RCS 

measurements are used per satellite over extended time periods (e.g., ~1,000 RCS measurements 

acquired over ~2 years) to analyze the resulting characteristic length distributions to estimate 

both the unknown hard-body radii and the associated uncertainties.

To start the HBR estimation process, Space Fence RCS data are collected for the two years prior 

to the calibration epoch date. The analysis is restricted to objects with twenty or more well 

calibrated and quality-curated Space Fence system RCS measurements, as described in detail by 

Baars and Hall (2022). Next, the NASA SEM is used to estimate RCS-based characteristic length 

estimates for each satellite, which typically have considerable point-to-point variability or 

scatter. Sources of this scatter include the object’s aspect-dependent radar reflection properties 

and projected area (which vary in time due to rotation and changing observational geometry), as 

well as RCS measurement noise (which is often relatively minor). Empirical cumulative 

distribution functions (CDFs) and probability density functions (PDFs) are generated from these 

data.

Using the empirical PDF approximation, the mean characteristic length for the j

th satellite is:

D̅j ≈

1

Nj

RCS ∑ Dj,n

Nj

RCS

n=1

(O-5)

The corresponding variance is:

σDj

2 ≈

1

Nj

RCS ∑(Dj,n − D̅j)

2

Nj

RCS

n=1

(O-6)
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with Nj

RCS indicating the number of RCS measurements for the j

th satellite. Since the variable 

radar reflection properties of a satellite causes some of the variation of the Dj,n values, the 

empirical PDF approximation tends to overestimate the variance of the object’s actual 

characteristic size distribution.

If the SEM were free of any estimation inaccuracies and the RCS measurements were free of any 

measurement noise, then the relationship between the circumscribing HBR and the characteristic 

length for idealized spherical objects would be relatively simple: Rj = Dj/2. To quantify the bias 

and uncertainty for noisy measurements of actual non-spherical objects, a calibration factor is 

introduced into this relationship, expressed in either linear or logarithmic form as follows:

Rj = Ωj(Dj/2) = e

ωj(Dj/2) (O-7)

The formulation assumes that the calibration factors Ωj and ωj = loge(Ωj) = ln(Ωj) are time 

invariant, but that they vary from satellite to satellite.

Hall and Baars (2022) uses a set of relatively small calibration satellites that all have convex 

cuboid shapes. Specifically, the calibration analysis employs sizes obtained from the Database 

and Information System Characterising Objects in Space (DISCOS), which tabulates the 

bounding dimensions and general shape descriptions of a large number of known satellites.20 The 

calibration analysis is restricted to satellites labeled as “box” shaped in the DISCOS database, 

and that have no tabulated additional panels or attachments. The circumscribing HBR for a boxshaped satellite with sides of length Lj

, width Wj and height Hj, is given by:

Rj

K =

1

2

√Lj

2 + Wj2 + Hj2

(O-8)

The calibration analysis is also restricted to DISCOS satellites with Rj

K ≤ 0.35 m, which are 

comparably small to the typical unknown debris objects involved in CARA conjunctions.

Space Fence observations collected in the two years preceding a calibration epoch date provide 

usable RCS measurements of box-shaped satellites tabulated in the DISCOS database.21 Each of 

these provides an independent (albeit noisy) measurement of the logarithmic calibration factor:

ωj = ln (2Rj

K

/D̅j) (O-9)

Sivia and Skilling (2006) present a Bayesian analysis approach that can be used to estimate the 

mean logarithmic calibration factor from the set {ωj,j = 1 ... J}, with J equal to the number of 

selected calibration satellites from the DISCOS database which also have Space Fence RCS data. 

The method assumes that satellite-to-satellite variations in the ωj values are Gaussiandistributed, and applies an uninformed-prior Bayesian analysis method to derive the maximum 

posterior estimates for the mean calibration factor and variance:

20 From Flohrer et al (2013) and Mclean et al (2017).

21 https://discosweb.esoc.esa.int/
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ω̅ =

1

J

∑ωj

J

j=1

and σω

2 =

1

J − 1

∑[ωj − ω̅]

2

J

j=1

(O-10)

As an example, for the calibration epoch date of 2022-01-15, sufficient RCS data are available 

for J = 586 of the DISCOS box-shaped satellites. The calibration analysis yields ω̅ = 0.319 and 

σω = 0.507. The estimate for σω indicates significant satellite-to-satellite variation in the 

calibration factors.

Figure O-2 CDF of the Ratio of Calibrated HBR Values to Known HBR 

Values for 586 Satellites22

Figure O-2 compares the empirical CDF of the ratio of calibrated RCS-based HBR values to the 

known values for the 586 satellites. The CDF indicates that, among this population, calibration 

uncertainties limit the 95% confidence accuracy range of the HBR estimation process to within a 

factor of 2.4 for potential underestimations, and to within a factor of 3.1 for potential 

overestimations.

O.4 Estimating the Masses of Unknown Objects

Several approaches may be used to estimate the mass of an unknown object, the first involves the 

use of the orbit determination-based ballistic coefficient (BC) estimate while the second uses the 

orbit determination-based solar radiation pressure coefficient (SRPC) estimate. For satellites that 

experience measurable atmospheric drag orbital perturbations, the BC estimation method is 

preferred. However, for satellites with a perigee height above 450 km in altitude, the SRPC mass 

estimates are somewhat more accurate.

O.4.1. RCS + Ballistic Coefficient Method

Combining RCS-based size estimates and orbit determination -based BC estimates provides a 

means to estimate the masses of LEO satellites that experience measurable atmospheric drag. 

22 From Hall and Baars (2022)
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This “RCS+BC” mass estimation method approximates the characteristic mass of a LEO satellite 

using an expression formulated previously23:

MD,j = AjBjCD,j ≈ (πDj

2

/4)BjCD,j (O-11)

In this expression, MD,jindicates the mass that characterizes the atmospheric drag experienced 

by the j

th satellite, which is proportional to the product of the projected area, Aj

, the inverse 

ballistic coefficient, Bj, and the drag coefficient, CD,j. The analysis uses RCS-based 

characteristic projected areas to estimate satellite cross sectional areas projected normal to the 

local atmospheric flow, Aj ≈ (πDj

2

/4), which is a rough approximation, especially for highly 

elongated or flattened objects. As before, a positive scalar calibration factor, Ψj, is introduced to 

equation O-11 to quantify the bias and uncertainty of the RCS+BC mass estimation process:

Mj ≈ ΨjMD,j = e

ψj[(πDj2

/4)BjCD,j] (O-12)

with Mjindicating the calibrated mass of the satellite, Ψjthe linear calibration factor, and ψjthe 

logarithmic calibration factor. Again, the analysis assumes these calibration factors are time 

invariant, but do vary from satellite to satellite. Applying equation O-12 to the j

th calibration 

satellite yields:

Mj

K = eψjE[Mj

] ≈ e

ψj[A̅

jB̅jC̅D,j

] (O-13)

This approximation neglects correlations between the quantities Dj, Bj, and CD,j. In order to use 

equation O-13, the mean projected area, inverse ballistic coefficient, and drag coefficient will 

need to be calculated for each satellite.

The mean projected area is approximated from the mean characteristic length and associated 

variance:

A̅

j = E[Aj

] ≈ π (D̅

j

2 + σDj

2

) /4 (O-14)

The formulation approximates the inverse ballistic coefficient PDF, by first empirically 

estimating the ballistic coefficient mean and variance parameters, and then assuming a lognormal 

distribution of the form:

ρ(Bj) ≈

N (ln(Bj) , b̅

j

, σbj

2

)

Bj

(O-15)

with σbj

2 = ln (1 + σBj

2

/B̅

j

2

) and b̅

j = ln(B̅j) − σbj

2

/2. (Note: Sampling this PDF, as will later be 

required for Monte Carlo estimations, cannot produce negative Bj values, which are physically 

unrealistic for satellites that experience measurable levels of atmospheric drag. This unrealism is 

why this analysis does not assume a PDF of the form N (Bj, B̅

j

, σBj

2

), which can potentially 

produce negative sampled values.) The mean and variance of the inverse ballistic coefficient, B̅

j

23 From Lechtenberg 2019a.
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and σBj

2

, respectively, are estimated empirically by combining a set of orbit determination 

solutions accumulated over the six months prior to the calibration epoch date. Specifically, the 

analysis uses a series of orbit determination solutions separated by one week or more in time that 

each represent an orbit determination solution for the j

th satellite. The corresponding ballistic 

coefficients, {(βj,m, Δβj,m), m = 1 ... Nj

VCM}, typically number NjVCM ≈ 25 for most satellites. 

The ballistic coefficients, βj,m, and associated 1-sigma orbit determination estimation 

uncertainties, Δβj,m, are then combined using a weighted averaging scheme. The first step in the 

process is to calculate the inverse ballistic coefficient and uncertainty for the m

th Vector 

Covariance Message (VCM) available for the j

th satellite:

Βj,m = 1/βj,m and ΔΒj,m = Δβj,m/βj,m

2

(O-16)

The next step calculates the weighted average:

B̅

j =

1

Wj

∑ Wj,mBj,m

Nj

VCM

m=1

(O-17)

with Wj,m = (ΔΒj,m)

−2

and Wj = ∑m Wj,m. The analysis estimates the variance using a hybrid 

scheme as follows:

σΒj

2 = max(Wj

−1

, Vj) (O-18)

with

Vj = Wj

−1

[

Nj

VCM

Nj

VCM − 1

∑ Wj,m(Βj,m − Β̅j)

2

Nj

VCM

m=1

]

1/2

(O-19)

This scheme conservatively uses the larger of the variances estimated using two methods: the 

first assumes statistical independence of the Βj,m values, yielding variance equal to Wj

−1

; the 

second accounts for the observed scatter of the Βj,m values, yielding the empirically estimated 

variance equal to Vj. In the rare cases when only one orbit determination solution is available for 

an object, the analysis uses σBj

2 = Wj

−1 = (ΔΒj,m)

2

for the variance.

Finally, the analysis approximates the PDF for the satellite drag coefficients CD,j using a uniform 

distribution spanning a fixed, bounded range:

ρ(CD,j) ≈ {

(CD,max − CD,min)

−1

if CD,min ≤ CD,j ≤ CD,max

0 otherwise

(O-20)
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This study uses the bounds CD,min = 2.1 and CD,max = 2.9 for all objects, based on the range of 

drag coefficients presented in previous analyses.24 The uniform PDF yields a mean of C̅

D,j =

(CD,max + CD,min)/2 = 2.5, and variance σCD,j

2 = (CD,max − CD,min)

2

/12 = 0.053 (i.e. σCD,j =

0.23).

The mass calibration process uses box-shaped DISCOS satellites, as described previously for the 

HBR calibration process. Each calibration satellite that has sufficient RCS data and VCM BC 

estimates provides an independent (albeit noisy) measurement of the logarithmic calibration 

factor, ψj = ln [Mj

K

/(A̅

jB̅jC̅D,j) ], yielding combined estimates of:

ψ̅ =

1

J

∑ψj

J

j=1

and σψ

2 =

1

J − 1

∑[ψj − ψ̅]

2

J

j=1

(O-21)

derived by applying the same Bayesian method used for the HBR calibration process.

For the calibration epoch date of 2022-01-15, sufficient RCS data and VCM BC estimates are 

available for J = 554 of the DISCOS box-shaped satellites. The calibration analysis yields ψ̅ =

−0.159 and σψ = 0.959. The estimated σψ value indicates significant satellite-to-satellite 

variation among the calibration satellites.

Figure O-3 CDF of the Ratio of Calibrated RCS+BC Mass Estimates to 

Known Masses for 554 Satellites25

Figure O-3 compares the empirical CDF of the ratio of calibrated mass estimates to the known 

values for the 554 satellites. The CDF indicates that, among this population, calibration 

uncertainties limit the 95% confidence accuracy range of the RCS+BC mass estimation process 

to within a factor of 4.1 for potential mass underestimations, and to within a factor of 10.4 for 

potential mass overestimations.

24 From Lechtenberg and Hejduk (2019) and Lechtenberg (2019a).

25 From Hall and Baars (2022)
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Appendix O. Collision Consequence 172

O.4.2. RCS + Solar Radiation Pressure Coefficient Method

Combining RCS-based size estimates and orbit determination-based solar radiation pressure 

coefficient estimates provides a means to estimate the masses of satellites that experience 

measurable solar radiation pressure (SRP) perturbations. This “RCS+SRPC” mass estimation 

analysis approximates the characteristic mass of a LEO satellite using an expression similar in 

form to that used for RCS+BC based mass estimation given by equation O-11:

MR,j ≈ (πDj

2

/4)GjCR,j

(O-22)

In this expression, MR,jindicates the mass that characterizes SRP perturbations experienced by 

the j

th satellite, which is proportional to the product of three quantities: the area projected 

towards the incident sunlight (again approximated using πDj

2

/4), the inverse solar radiation 

pressure coefficient, Gj, and the reflectivity coefficient, CR,j. See Vallado (2001) for more details 

on orbital SRP perturbations. As before, this study introduces a positive scalar calibration factor, 

Θj, into equation O-22 to quantify the bias and uncertainty of the RCS+SRPC mass estimation 

process:

Mj ≈ ΘjMR,j = e

θj[(πDj

2

/4)GjCR,j] (O-23)

with Mjindicating the calibrated mass of the satellite, Θjthe linear calibration factor, and θjthe 

logarithmic calibration factor. The process of estimating the calibration factors for the 

RCS+SRPC mass estimation process uses the same exact analysis steps as outlined in the 

previous section for the RCS+BC mass estimation process but substitutes the orbit 

determination-based inverse solar radiation pressure coefficient, Gj, for the inverse ballistic 

coefficient, Bj, and also substitutes the reflectivity coefficient, CR,j, for the drag coefficient, CD,j. 

The analysis assumes a uniform PDF with bounds CR,min = 1 and CR,max = 1.4 for all satellites, 

which yields a mean of C̅

R,j = 1.2, and variance σCR,j

2 = 0.013 (i.e., σCR,j = 0.12). The lower 

bound of CR,min = 1 corresponds to that expected for dark bodies (i.e., that have negligible 

overall reflectance) of any shape. The upper bound of CR,max = 1.4 represents the theoretical 

value for a Lambertian sphere with 90% reflectance,26 and is assumed to provide a reasonable 

upper limit for unknown secondary objects.

The analysis restricts RCS+SRPC mass estimation to satellites with perigee altitudes above 450 

km altitude to ensure that imperfectly modeled atmospheric drag perturbations do not bias the 

solar radiation pressure coefficients estimated in the orbit determination analysis, which has been 

observed to occur for LEO satellites at lower altitudes. For the calibration epoch date of 2022-

01-15, sufficient RCS data and VCM SRPC estimates are available for J = 303 of the DISCOS 

cuboid satellites with perigees above 450 km altitude. The calibration analysis yields θ̅= 0.173

and σθ = 0.884.

26 From Li et al (2018).
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Appendix O. Collision Consequence 173

Figure O-4 CDF of the Ratio of Calibrated RCS+SRPC Mass Estimates to 

Known Masses for 303 Satellites27

Figure O-4 compares the empirical CDF of the ratio of calibrated mass estimates to the known 

values for the 303 satellites. The CDF indicates that, among this population, calibration 

uncertainties limit the 95% confidence accuracy range of the RCS+SRPC mass estimation 

process to within a factor of 3.8 for potential mass underestimations, and to within a factor of 8.4 

for potential mass overestimations. This means that, for satellites with perigee altitudes above 

450 km, the RCS+SRPC method provides somewhat more accurate mass estimates than the 

RCS+BC estimation method, although both methods provide rough mass estimates overall.

O.5. The Probability of Exceeding a Threshold Number of Trackable 

Fragments

Recall equation O-3 that defines a fragmentation probability metric, which is calculated using an 

expectation value to determine the probability that a conjunction will generate more than a 

threshold number of trackable fragments. For known-on-unknown conjunctions, calculating this 

expectation value represents integrating over a set of five random variables that account for the 

size and mass estimation uncertainties of the secondary object. Specifically, for the RCS+BC 

mass estimation method, these five random variables are {D2, ω2, ψ2, B2, CD,2}; for RCS+SRPC 

mass estimation they are {D2, ω2, θ2, G2, CR,2}. Correspondingly, unknown-on-unknown 

collisions require integrations over ten random variables associated with both objects. In other 

words, estimating the statistically expected fragmentation probability, P̅

F, entails evaluating 

either a 5-D or 10-D integral. The integrand function of these multi-dimensional integrals 

contains the product of the conjunction’s collision probability, Pc

(R1 + R2), and the binary 

probability that the number of fragments, FEV(M1, M2

), exceeds the threshold value, F. Both of 

these functions are non-linear, and the latter possesses discontinuities. The Monte Carlo method 

provides and efficient and straightforward means of computing such multi-dimensional integrals.

27 From Hall and Baars (2022)
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Appendix O. Collision Consequence 174

Focusing on the known-on-unknown collision case for the RCS+BC mass estimation method, the 

five random variables are computed as follows:

1. D2 is modeled as a normally distributed variable using the mean and variance defined in 

equations O-5 and O-6.

2. ω2 is modeled as a normally distributed variable using the mean and variance defined in 

equation O-10.

3. ψ2 is modeled as a normally distributed variable using the mean and variance defined in 

equation O-21.

4. B2 is modeled as a normally distributed variable in logarithmic space using the mean and 

variance defined directly below equation O-15.

5. CD,2 is modeled as a uniformly distributed variable with CD,min = 2.1 and CD,max = 2.9.

The RCS+SRPC mass estimation method uses the same computations for D2 and ω2. For the 

remaining variables, ψ2 is replaced with θ2, B2 is replaced with G2, and CD,2 is replaced with 

CR,2 (along with the associated CR,min and CR,max values).

In the Monte Carlo method these random variables are used to generate a set of R2 and M2

values for a number of Monte Carlo trials, NMC. The fragmentation probability is then estimated 

as:

P̅

F ≈

1

NMC

∑[Pc(R1 + R2,n) × U(FEV(M1, M2,n) − F)]

NMC

n=1

(O-24)

For F = 0, it is straightforward to show that P̅

F = P̅c

. More generally, a conjunction’s 

fragmentation probability cannot exceed the collision probability, P̅

F ≤ P̅c

. For groups like 

CARA that use the collision probability to assess close approach risks, this inequality property 

makes P̅

F a convenient choice to assess environmental risks, for two reasons. First, if the 

screening process indicates that P̅

c

is less than a negligibly small green-level cutoff (i.e., 10−10), 

then P̅

F also must be less than that cutoff. Second, the inequality implies that all conjunctions 

that represent red-level environmental risks (i.e., those with P̅

F ≥ 10−4

) are naturally contained 

within the set of conjunctions identified as red-level risks (i.e., those with P̅

c ≥ 10−4

).

To demonstrate how collision and fragmentation probabilities can be used together, a threshold 

of F = 103 was used to assess an unacceptably high level of risk to the orbital environment. 

Figure O-5 compares fragmentation and collision probabilities for known-on-unknown CARA 

conjunctions, calculated using this fragment production threshold. Among the conjunctions 

analyzed, 1,734 represent red-level close approach risks with P̅

c ≥ 10−4

. Among these, 122 (or 

7%) also have P̅

F ≥ 10−4

, so they represent red-level environmental risks as well. Figure O-5 

plots these dual high-risk conjunctions as red stars, illustrating how collision and fragmentation 

probabilities can be used together to identify the subset of events with the highest spacecraft and 

environmental risks. Pink diamonds and triangles represent conjunctions with red-level close 

approach risks, but lower environmental risks.
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Appendix O. Collision Consequence 175

Figure O-5 Collision and Fragmentation Probabilities for Known-onUnknown Conjunctions28

As discussed above, a fragment production threshold of F = 103indicates that 7% of the 

analyzed known-on-unknown conjunctions with P̅

c ≥ 10−4

also have P̅

F ≥ 10−4

. This analysis 

uses F = 103as a threshold number of trackable fragments because such a collision would 

potentially represent a major source of LEO debris generation, comparable to the IridiumCosmos collision in 2009 which produced about 1,200 trackable fragments that remained in 

Earth orbit for longer than one year. Other production thresholds provide different assessments 

of environmental risk in a non-linear fashion. For instance, about 20% of the studied 

conjunctions have P̅

F ≥ 10−4

for the somewhat more moderate threshold of F = 102. So,

considering the range of 102 ≤ F ≤ 103indicates that 5% to 20% of the high mission risk 

conjunctions also could be assessed to pose an elevated risk to the orbital environment.

It must be emphasized that no O/O would be asked to take advantage of the low-debrisproducing-event possibility for relaxed mitigation requirements. Whether to focus on the 

protection of their own payload or merely to take a more conservative posture generally, 

missions certainly may embrace the 10−4 Pc threshold for all conjunctions. From an orbit regime 

protection point of view, however, it would not be unreasonable to relax this threshold mildly for 

situations that are non-catastrophic and only expected to create a small amount of debris, 

especially in the presence of other relevant considerations, such as the inability to identify a truly 

adequate mitigation action that did not impose non-trivial mission compromise. The use of 

fragmentation propensity may also be desirable for triage situations in which a mission is 

experiencing more serious conjunctions than it is possible to remediate. In such cases, one could 

direct mitigation focus to those conjunctions that hold the greatest debris production potential. 

28 From Hall and Baars (2022)
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Appendix P. Event Actionability 176

Appendix P. Event Actionability

P.1 Introduction

Although widely used, the term “conjunction event actionability” is a somewhat unfortunate 

term because it implies a broader scope than it merits. Its precise meaning is the assessment of 

the propagated state and state uncertainty information for the two satellites in conjunction (but 

with the focus usually on the secondary object) to determine whether these data constitute a 

reasonable basis for conjunction risk assessment and mitigation actions. It does not include the 

further step of deciding, in the presence of a high-risk situation, whether the mitigation actions 

are excessively invasive or detrimental to the mission’s objectives to warrant their being set aside 

despite the collision risk; that is, whether an O/O would be justified in refraining from taking 

“action” to mitigate the conjunction and lessen the collision risk because of the mission impact 

of the mitigation action. This latter consideration is real and constitutes part of the risk 

assessment process, but one arrives at this decision point only after determining that the orbital 

data feeding the analysis are durable and thus are enabling credible collision risk calculations.

The propriety of considering the quality of the event’s input orbital data is obvious because an 

O/O will certainly wish to certify that the collision risk is truly high and that a proposed 

mitigation action will remediate the collision risk before considering its actual execution. The 

desire for a conservative risk approach does not make the problem simpler. If the input 

astrodynamics data are questionable, it is also questionable whether any proposed mitigation 

action will actually improve the situation because such an action could in fact make the situation 

worse. So it is not appropriate simply to say that situations of questionable data quality should, 

out of conservatism, be afforded such actions if the calculated risk parameters exceed the 

threshold for mitigation actions. Rather, it is necessary to establish a method for identifying those 

cases in which the input data may be sufficiently poor to make meaningful risk assessment 

impossible.

It is important to recognize that the question to be addressed here is whether the orbital data 

properly represent the two objects’ states and uncertainties and not whether the associated 

uncertainties are large or “too large.” If one embraces Pc as the principal (but not necessarily the 

sole) collision likelihood assessment metric, excessively large covariances have the effect of 

depressing the Pc value and thus giving a (much) lower statement of risk. This particular 

phenomenon, called the “dilution region” situation, is a known peculiarity of Pc and is discussed 

at some length in Appendix M, but there is general agreement that high Pc values do represent 

situations of high collision likelihood. In such situations, the fact that covariances may seem

excessively large should not constitute an impediment to event actionability. If, despite a 

somewhat tracking-data-impoverished situation (hence the large covariance), a worrisome Pc is 

still produced, a fortiori the situation should be treated as serious and worthy of mitigation.

This area of conjunction risk assessment—the determination of event actionability—possesses 

the least precision in terms of clear, documentable standards. The certification of orbitdetermination updates as valid and reasonable and propagation intervals and methods as 

sufficiently representative is, in the end, rendered not through conformity to strict, fully
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Appendix P. Event Actionability 177

articulated rules but rather through the judgment of expert orbital analysts who have personally 

performed thousands of orbit-determination updates and propagations. Astrodynamics is often at 

least as much an art as a science, and batch orbit-determination update particularly so. To be 

sure, most of the cases that are actually encountered in conjunction assessment practice can be 

judged to be valid and acceptable through rule conformity alone, and there are certain cases that 

are so poor that there is little difficulty in recognizing their invalidity immediately. But there is 

also a relatively small input data group that cannot be directly assigned to either of these 

resolutions, and it is here that expert opinion is required. 

There are two separate aspects of the astrodynamics input data to consider: the states and 

covariances for the primary and secondary objects at epoch as outputs of the orbit-determination

process, and the states and covariances propagated forward to TCA. These two aspects will be 

treated separately below, with the concluding section outlining how considerations from each are 

combined into a judgment of actionability/non-actionability for a particular event. Some of the 

threshold values for the actual parameters used in the tests to be described below are placed in an 

annex to this appendix, both for ease of reading and to allow easier document update should 

these values be modified. Finally, while it is the case that in principle a judgment of the 

suitability of the primary object’s state and covariance is required as part of the overall 

actionability assessment, in practice it is almost always the secondary object’s data quality that is 

an issue. To simplify the treatment, the following discussion will frequently frame the discussion 

in terms of a single object that can be presumed to be the secondary.

P.2 Evaluation of the Propriety of the Orbit-Determination Fit

It should be obvious that a quality orbit-determination fit for the object is a foundational element 

in any use of its state and uncertainty data. If the fit itself is questionable, it is difficult to have 

confidence in any astrodynamics products propagated forward from it. Because the

USSPACECOM catalog is at present usually the sole supplier for all data on the secondary 

object (especially in the case of debris objects with a small radar cross section value) and also 

provides solutions for the primary object, the focus has to be placed on the orbit-determination fit 

mechanism used for this catalog, which is not a sequential estimator but a minimum-variance 

batch process. This means that in addition to the force model settings for the dynamical models, 

the time-span of the tracking data for the fit, data density, tracking data sensor composition, and 

retention of the sensor data used in each batch update have to be considered. If a different data 

provider for orbital information about the secondary object were to be used, a set of orbitdetermination quality criteria tailored to that particular provider’s orbit-determination

methodology and engine would need to be developed and consulted. The remainder of this 

section can be seen as a proposed template for how that development and consultation might 

proceed.

If it were possible to generate hard-and-fast rules for determining the control settings and data 

handling for these batch updates, the assessment of fit acceptability would be much more 

straightforward. Despite decades of attempts, astrodynamics specialists for DOD have concluded 

that such a rule set is simply not possible, especially when densely-packed debris clouds are 

considered. The only way truly to evaluate the propriety of an orbit-determination fit is a manual 
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Appendix P. Event Actionability 178

review by an expert. This individual has access to information of the full suite of input sensor 

raw and “management” data including:

• Tables of residuals,

• Residual plots in a variety of different constructions and the ability to edit out individual 

observables,

• Before-and-after values of key orbital elements in the context of long-term plots to 

evaluate trends, and 

• The ability to attempt multiple corrections with different force-model settings and data 

contents to evaluate the results comparatively and choose the best outcome.

Such evaluations, most of them visual, simply cannot be replaced by rules themselves.

However, what is possible is to provide a set of guidelines that, if violated, would typically 

prompt a manual review by an expert. Within a NASA or USSPACECOM context, an expert 

could be summoned and, with access to the data products enumerated in the above paragraph, 

could render an expert opinion on the propriety of the orbit determination. Outside of these 

agencies, such data access is not available. Nonetheless, the rule set can be useful; for example,

orbit-determination results that do conform to all of the general rules can, with a high degree of 

confidence, be accepted as a basis for conjunction risk assessment. 

The following subparagraphs describe the particular orbit-determination input summaries, 

settings, and quality factors evaluated by the rule set, and the annex to this appendix gives 

threshold values that allow for the evaluation of an orbit determination’s conformity to these 

rules. All the information needed to evaluate a particular orbit determination is present in the 

CDM.

P.3 Force Model Settings and Non-Conservative Force Model 

Parameter Values

Any space catalog has at its core a set of astrodynamics dynamical models that are used to 

predict the trajectories of space objects, and the orbit-determination process determines 

parameter values to use within these models to predict future positions of a particular satellite. 

Different physical phenomena and their effects on satellites are modeled, and for some of these 

models, varying levels of fidelity can be selected. The following paragraphs list each of the 

selectable force models that can be applied, identify the selection criteria, and give some 

indication of parameters and parameter values that might lead one to question the propriety of an 

orbit determination.

1. Geopotential. Two-body motion, the simplest of possible orbit solutions, is the 

foundation of the astrodynamics model set. The first major improvement in precision is 

the recognition that the Earth is not a uniform and uniformly dense sphere but varies from 

this idealization in many ways. A spherical harmonic representation of the actual 

geopotential is used to represent the Earth’s bulge at the equator and other density nonuniformities; the spherical harmonic order is specified as part of the correction. The 

minimum required geopotential order (in terms of zonals and tesserals) for an acceptable 
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Appendix P. Event Actionability 179

fit is determined by considering characteristics of the satellite’s orbit, and any orbitdetermination update that uses a geopotential order lower (smaller) than this specified 

value is flagged for manual review. The actual minimum geopotential order thresholds as 

a function of orbital parameters are given in the annex to this appendix.

2. Lunar-Solar Perturbations. While the Earth is obviously the most significant central 

attracting body for a satellite, the sun and moon are large enough to visit a non-negligible 

effect on a satellite’s orbit. For precision solutions, this modeling (called “third-body 

effects”) should always be engaged.

3. Solid Earth Tides. The gravitational force of the moon deforms the quasi-spherical 

Earth, and this deformity changes the geopotential and satellite orbits. Often, the effect is 

small and unlikely to alter conjunction assessment results. Because it is not 

computationally difficult to characterize, it is standard practice to include this modeling 

input in precision solutions. In the main, however, it is unlikely that the failure to include 

this perturbation would make the resultant orbit determination questionable from a 

conjunction assessment perspective although it could alter the results observably.

4. Atmospheric Drag. The major non-conservative force affecting many LEO orbits is 

atmospheric drag. The modeling of drag acceleration is a function of the satellite’s 

velocity relative to the atmosphere, the atmospheric density, and the satellite’s ballistic 

coefficient, which itself is a combination of the coefficient of drag, the satellite’s frontal 

area, and its mass. Because for most satellites, especially debris objects, neither the drag 

coefficient nor the frontal area nor the mass is known, the entire ballistic coefficient is 

treated as a single solved-for parameter as part of the orbit determination. Certain LEO 

orbits should include atmospheric drag modeling and solutions for the ballistic 

coefficient, and for those that do, there are ranges of reasonable solutions for this solvedfor parameter. The annex to this appendix delineates the LEO orbits that require a drag 

solution and the ranges of acceptable ballistic coefficient values.

5. Solar Radiation Pressure. While electromagnetic radiation has no mass, it does impart 

momentum, and the momentum carried by the sun’s energy and incident upon the 

satellite has a discernable effect on the resultant orbit. The USSPACECOM dynamical 

model set employs a standard solar radiation pressure model (SRP), which is a function 

of a solar radiation pressure coefficient (SRPC) (analogous to the ballistic coefficient) 

and a scalar and vector distance to the sun. Certain orbits should have the solar radiation 

pressure model enabled, and for these there are acceptable ranges of values for the solar 

radiation pressure coefficient. The relevant orbits for solar radiation pressure 

compensation and the associated ranges of values for the coefficient are given in the 

annex to this appendix.

P.4 Orbit Determination Fit Span (or Length of Update Interval)

Sequential estimators process each measurement individually, usually as each is received; batch 

estimators collect a “batch” of measurements and process them as a group. When using batch 

estimation, it is necessary to identify the particular group of measurement data to be fit, which 

usually means determining the period back in time from the present for retrieval of data to use in 
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an update. While this activity may at first not seem important, in fact it can greatly affect the 

quality of the resultant orbit determination. If the data period is too long, the prediction error 

from the orbit-determination fit state is increased; if the data period is too short, a robust drag or 

solar radiation pressure solution is not possible; and if there are too few measurements contained 

within the span, the solution is not reliably representative.

To set the data interval and density correctly, the USSPACECOM batch update process employs 

a complicated algorithm called the Dynamic Length of Update Interval (LUPI) Assignment 

(DLA) to examine the measurement data history for each fit and assign the proper LUPI to strike 

an acceptable balance between maximizing prediction accuracy and ensuring a reasonable 

solution for the non-conservative force parameters (drag and solar radiation pressure). The 

algorithm operates by beginning with the maximum acceptable LUPI for a particular orbit and 

attempting to minimize it while preserving sufficient observational data to endure a quality 

update, and if the maximum LUPI itself does not encompass enough tracking data, the algorithm 

will expand past this theoretical maximum value to attempt to bring more data into the 

correction. The goal of this approach is to provide quality updates most of the time and 

serviceable updates all the time, with “serviceable” defined here as sufficient to allow sensor 

reacquisition of the satellite. Updates that are merely serviceable are, however, not in themselves 

of sufficient quality for conjunction risk assessment. Also worrisome are LUPI lengths shorter 

than the default minimum, which occur when large amounts of measurement data are eliminated 

from a satellite’s history (due, for example, to a satellite maneuver after which the old 

observational data have to be thrown away because they no longer represent the satellite’s 

current trajectory). While a subject matter expert could, with broader data access, perhaps certify 

some of these results as acceptable for conjunction risk assessment, as a general rule, orbit 

determinations with LUPI lengths that are either longer than the theoretical maximum or shorter 

than the theoretical minimum cannot produce reliable state updates and reliable covariances and 

thus cannot serve as a basis for conjunction risk assessment. 

A table of these maximum and minimum lengths is given in the annex to this appendix.

P.5 Residual Acceptance

The batch solution generates an optimal solution by minimizing the sum-of-squares residual of 

the data chosen for the fit; therefore, large residuals against individual observables affect the 

fitting process substantially. Because it is not uncommon to receive “bad” measurement data 

from sensors, a stratagem has been implemented to limit the overall effect of potentially errant 

data: between iterations of the non-linear regressive solver, the measurement residuals against 

the provisional solution are examined, and data points that manifest excessively large residuals 

are eliminated. This allows the fit to proceed without being influenced disproportionately by only 

a few measurements.

The elimination of measurement data in a data-fitting context merely because they appear to 

encumber a more satisfactory fit is always somewhat disconcerting as most numerical analysts 

discourage the elimination of any given datum without some a priori reason to suspect that it 

may be errant. However, incidences of satellite cross-tagging (in which the assignment of data to 

the correct satellite miscarries by the data being assigned to some other, usually nearby satellite) 
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are frequent enough that some provision has to be made for eliminating sensor observations that 

simply do not seem consistent with the rest of a satellite’s measurement data. There are also 

situations in which data mismatches are overtly recognized, such as after a satellite maneuver,

because the trajectory has changed impulsively and observational data before the maneuver do 

not represent the current trajectory and have to be eliminated intentionally.

If too much of the measurement information is eliminated, the concern is that the fit may not be 

properly representative. Therefore, when the percent of the residuals eliminated exceeds a certain 

value, the fit merits manual review. A table of these values is given in the annex to this appendix.

P.6 Weighted Root-Mean-Square of Residuals

It is common when performing an iterative batch fit to use the root-mean-square of the residuals 

as an indication of fit quality, tracking this value to ensure that the fit is improving with each 

iteration. For an unweighted root-mean-square, the ideal value would be zero as it would indicate 

that the model fits the data exactly without any residual error. For the USSPACECOM 

minimum-variance batch solver, a weighted root-mean-square is used (WRMS), in which the 

square of each residual is divided by the variance of the a priori expected error for that 

observable type (e.g., range to target, azimuth angle, elevation angle) from that particular sensor 

as established by a sensor calibration process separate from the orbit-determination activity. If 

the residual errors and actual sensor errors are Gaussian, then the average of these ratios should 

equal unity (as will its square root). The weighted root-mean-square is a better measurement of 

fit error because the best reasonable expected outcome is that the error of the fit will be of 

essentially the same magnitude as the inherent error in the observations.

If the fit’s weighted root-mean-square is too large, then the fit is not particularly convincing, and 

manual review would generally be counselled. A weighted root-mean-square value less than 

unity, while not necessarily bad, nonetheless would also warrant a manual review: while a fit of a 

higher quality than the inherent error in the observations is possible, it is usually a result of too 

few data in the orbit determination and therefore should be investigated. Thresholds for

excessively high weighted root-mean-square are set by object type and given in the annex to this 

appendix.

P.7 Default Covariance

The DOD precision orbit-determination solution produces an estimation error covariance as a 

regular product. There are situations, however, in which the automatic precision orbitdetermination solution cannot be made to converge, and in such cases, the system executes a 

general perturbations analytic orbit-determination solution, employing the same theory used to 

produce TLEs. This process as presently designed produces a state (although an inaccurate one 

with 1-2 km of expected error in LEO) but no covariance, and this is indicated by providing a 

diagonal covariance for which the diagonal elements for the position portion are each ten Earth 

radii.

General perturbation solutions are not sufficiently accurate to serve as a basis for conjunction

mitigation actions, so if one of these default covariances is encountered, the state data that 

accompany it are not suitable for conjunction risk assessment.
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P.8 Review Process

As stated above, if the full orbit-determination data are present and a subject matter expert is 

available to render an expert opinion, situations in which the general rules given above are 

violated can be investigated and an adjudication obtained. If this level of access is not available, 

the above rules can serve as a one-sided test; namely, if the current orbit determination conforms 

to all of the rules, then it can be presumed that the orbit determination is durable and can serve as 

a basis for conjunction risk assessment and, if necessary, mitigation action planning.

P.9 Evaluation of Propagation from Epoch to TCA

Most conjunction risk assessment approaches make assessments using the states and covariances 

of the primary and secondary objects propagated to TCA, so in addition to considering the 

propriety of the orbit-determination fits themselves, one also has to consider whether any issues 

with the propagation itself might make the TCA products unsuitable for conducting risk 

assessment. Issues related to propagation are often called out as potentially problematic, and a 

treatment of each of these is given in this section. But the overall conclusion is that the 

USSPACECOM approach to producing astrodynamics products at TCA is robust and contains 

mechanisms to address the major sources of expected propagation error, and these can be 

augmented with additional processes within risk assessment. As such, if an orbit determination

sustains the criteria for an acceptable fit, it can be presumed that this fit propagated to TCA 

renders a state and covariance acceptable for conjunction risk assessment, except in a few narrow 

instances called out below.

P.9.1 Propagated Covariance is Defective

In some situations, the propagated covariance can be defective to the degree that it cannot be 

used as presented for conjunction risk assessment. 

1. Null Covariances. The first is a null covariance in which all the entries are zeroes. This 

is the equivalent of not having a covariance at all, and when described in the previous 

section that addressed orbit-determination fit results, it was pointed out that situations 

with such a covariance cannot be used for conjunction risk assessment. If there is no 

covariance at epoch, there cannot be a propagated covariance at TCA either, so such a 

situation can be considered to be inactionable. It is possible to use maximalist techniques 

such as those developed by Alfano (2005b) and by Frisbee (2015) to proceed in situations 

in which only one of the two objects has a covariance, but these techniques are 

exceedingly conservative and therefore not recommended as a routinely used proxy for 

collision likelihood. 

2. Default Covariances. The second is a default covariance in which the presence of 

diagonal elements of ten Earth radii indicates a general perturbation solution that 

produced no covariance. While in principle this covariance can be propagated to TCA, it 

will essentially be an “infinite” covariance at TCA—just as it was at epoch—and 

therefore force any calculated Pc to zero (and sometimes introduce convergence 

problems in Pc calculation routines). Situations such as this can be judged to be nonactionable (because the covariance for one of the objects cannot be established) or 
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Appendix P. Event Actionability 183

produce in every case a Pc of zero (because this is what very large covariances do).

Embracing either possibility leads to the same conclusion of not requiring a mitigation 

action. 

3. Non-Positive-Semidefinite Covariances. The third is for the TCA covariance to become 

non-positive-semidefinite. This issue is addressed at greater length elsewhere (Hall et al.

2017b), and the takeaway from that discussion is that the problem arises due to truncation 

and interpolation errors (not fundamental problems with the orbit determination) and can 

be straightforwardly repaired. The article recommends certain repair techniques, and the 

source code for them is provided on the NASA CARA software repository. (See Section 

7, Contact Information in this document for the specific URL.) A modification to the 

USSPACECOM operational system has been implemented that should essentially 

eliminate non-positive-semidefinite situations. 

Of the mainstream direct defects in TCA covariances, null and default covariances do produce 

situations that result in inactionability; non-positive-semidefinite covariances do not.

P.9.2 Excessive Propagation Interval to Retain Gaussian Covariance 

Behavior

The astrodynamics discipline has had to address the question of Gaussian uncertainty volumes 

and the difficulties introduced by the Cartesian framework’s inability fully to represent 

curvilinearly produced results. As discussed at greater length in Appendix N, while this debate 

continues in the critical literature, the conjunction assessment enterprise has been able largely to 

set it aside by recognizing that the issue is not really relevant to high-Pc events because of the 

amount of overlap of the “main” portions of the covariance necessary to produce a high Pc. 

Furthermore, the issue can be remediated easily by performing Monte Carlo from TCA with the 

random sampling conducted from the equinoctial representation of the covariance. While much 

has been made in the literature of the problem of non-Gaussian covariances for conjunction 

assessment, based on NASA CARA’s analysis, this problem is not crippling for the categories of 

events that actually matter to conjunction risk assessment, and in any case, it can be addressed 

with a particular Pc calculation technique that is both straightforward and tractable.

P.9.3 Excessive Propagation Interval Due to a Lack of Tracking Data

The USSPACECOM orbit-determination process places the epoch time of its orbit-determination

fits at the time of the last observation. Since this is the time at which the fitted results are 

modeled, any propagation into the future takes place from that time. Because this orbit 

determination is used as the most current update until more tracking data are received and a new 

update executed, to propagate the state and covariance to TCA usually involves two stages: to 

propagate forward from the epoch time to the current time, and then to propagate from the 

current time forward to TCA. If no new tracking data are received for some time, then a quite 

long propagation of the original orbit-determination state may be required. For example, if the 

object has not been tracked for five days and TCA is three days from the present time, a total of 

eight days’ propagation is required to produce the state and covariance at TCA.
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It is best if tracking data are received frequently because this produces better data density for the 

fit and reduces the overall amount of propagation time. There is nothing about long propagation 

times per se that indicts the utility of the resultant products; as the propagation proceeds, the 

uncertainties in the propagated covariance grow appropriately to represent the expected 

uncertainties of the states at the propagation termination, which is here TCA. Additionally, 

adjustments to the covariance to account for atmospheric density forecast error and satellite 

frontal area uncertainty are included and contribute to the propagated covariance’s growth 

(discussed in Appendix N). Finally, a large covariance matrix will in most cases depress the 

calculated Pc value, naturally correcting for a situation in which the state uncertainties are so 

large that it may not be comfortable to use them as a basis of action. Given this dynamic, the lack 

of recent tracking data invalidates neither the original fit (presuming there was sufficient tracking 

in the fit-span to produce an acceptable fit) nor the propagation to TCA. 

Nonetheless, a rule of thumb that has been used over the last few decades for orbit-determination

batch updates is that the propagation interval should not be longer than the fit-span/LUPI. It is 

generally considered dangerous to try to propagate longer than the span of measurement data that 

directed the orbit-determination update. While there are undoubtedly situations in which 

propagations of this type could still be representative, it is believed that the reasonable span of 

the orbit determination has been exceeded in such a case, and it is thus reasonable to refrain from 

any mitigation action for conjunctions for which either object’s orbit determination at TCA was 

generated with so extended a propagation interval.

P.9.4 Excessive Atmospheric Density Error Due to Solar Storms

As explained in Appendix N, for some years, the USSPACECOM orbit-determination process 

has adjusted the covariance in the CDM for anticipated atmospheric density forecast error 

through the application of a consider parameter. The Jacchia-Bowman-HASDM 2009 (JBH09)

atmospheric density model used by USSPACECOM contains special functionality to reduce 

propagation error in the presence of Coronal Mass Ejections (CMEs), a commonly encountered 

type of solar storm. A special model given the name “Anemomilos” attempts to predict the size, 

time of arrival, and geoeffectiveness of CMEs, and the atmospheric density is modified 

appropriately during the prediction interval to reflect the storm’s predicted arrival and effects. 

(Tobiska et al. 2013) Paired with the appropriate consider parameter value, which will 

compensate for the expected uncertainty in this type of modeling, the predicted product should in 

principle account for atmospheric density mismodeling. The fact that the solar environment is 

perturbed should not, therefore, result in an a priori conclusion that the predictions of an event’s 

severity are errant and that a claim of event inactionability is appropriate. Having said that, it is 

also the case that the performance of the Anemomilos model during the most recent solar cycle 

(solar cycle 25) has been disappointing: normed on data from earlier solar cycles, the model is 

not producing representative results presently. A number of different mitigation activities are 

presently being considered, including simply turning off this particular modeling feature. 

Unfortunately, it is not possible during regular operations to determine the degree to which 

Anemomilos is affecting prediction outcomes, although this model will engage only when the 

predicted Disturbance Storm Time (Dst) parameter value is smaller than -75nanoTeslas, so one 

can consult space weather predictions to determine whether there is any possibility of the 
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Appendix P. Event Actionability 185

model’s being employed. This general issue is addressed at greater length in the walk-through of 

a sample event in Appendix Q.

Some additional insight into such situations can be gained by constructing what are called Space 

Weather Trade Space (SWTS) plots that explore how the collision likelihood of a particular 

event would change if the atmospheric density were mismodeled. Because atmospheric density 

and ballistic coefficient are multiplicatively coupled in the atmospheric drag acceleration 

equation, changing one of these parameters has the same effect as changing the other. It is thus 

possible to vary the primary and secondary objects’ drag parameters to understand the effect of 

drag modeling on the event’s conjunction likelihood.

The plots are constructed by varying the nominal ballistic coefficient by half an order of 

magnitude in each direction with the x-axis giving the primary object ballistic coefficient 

variation, the y-axis that for the secondary object, and the color indicating the resultant Pc value.

However, these details are not so important because it is the overall morphology of the figure 

that is meaningful. In Figure P-1, despite large variations in the ballistic coefficient (as a proxy 

for atmospheric density), the Pc changes little. This event is not sensitive to space weather 

mismodeling, and thus actionability is not strongly affected by solar storm developments and 

potential mismodeling. 

Figure P-1 SWTS Plot for Invariant Situation29

In Figure P-2, the current Pc, as represented by the center point of the figure, lies on a “ridge” of 

high Pc values; any atmospheric drag mismodeling that moves the situation off the center point 

29 From Hejduk et al. 2017.
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Appendix P. Event Actionability 186

will result in a lower rather than higher Pc. So, if the current Pc is below the threshold that would 

require a mitigation action, the event should still be safe even in the presence of model error.

Figure P-2 SWTS Plot for “Ridge” Situation30

Finally, in situations in which the Pc is not on a ridge and where non-trivial variation is 

observed, then model error could either increase or decrease the Pc, as shown in Figure P-3. In 

such cases, one is left without the reassurance of either of the two previous examples. However, 

given that the estimation process attempts to take account of drag uncertainty through modeling 

even of solar storms, the CDM result is presumed to represent the best estimate possible and, in 

the absence of other indicting data, is expected to be reliable and actionable.

30 From Hejduk et al. 2017.

Log10 Scale Factor for Primary B Coeff. Log10 Scale Factor for Secondary B Coeff.

Log10(Pc) as Function of Altered Primary / Secondary Drag

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0
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Figure P-3 SWTS Plot for Variation Situation31

P.10 Summary

As the previous discussion indicates, the orbit determination and propagation process nearly 

always produces data that can be considered actionable. There are certain indications that an 

orbit-determination fit may potentially fall short, and an even smaller number that would counsel 

the dismissal of an orbit determination as the basis for conjunction risk assessment. It is similarly 

infrequent that the propagation results to TCA can be questioned, and these situations can 

usually be addressed in other ways (e.g., the repair of a non-positive-definite covariance). In both 

situations, there are additional one-sided tests that, if passed, can reassure the user about the 

propriety of the data and its ability to subtend conjunction risk assessment.

31 From Hejduk et al. 2017.
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P.11 Annex

This annex provides specific thresholds for the orbit-determination quality checks. 

Table P-1 Geopotential, Atmospheric Drag, and Solar Radiation Pressure

Table P-2 Ballistic Coefficient and Solar Radiation Pressure Coefficient 

Reasonability

Geopotential Solve for

Perigee Zonal and Solve for Solar Rad.

Height (km) Eccentricity Object Type Tesseral Drag? Pressure?

0 < p < 500 < 0.25 Payload 36 Y N

Rocket Body / Platform 36 Y N

Debris/Unknown 36 Y N

500 < p < 900 < 0.25 Payload 36 Y Y

Rocket Body / Platform 36 Y Y

Debris/Unknown 36 Y Y

900 < p < 2000 < 0.25 Payload 24 Y Y

Rocket Body / Platform 24 Y Y

Debris/Unknown 24 Y Y

0 < p < 500 > 0.25 Payload 36 Y N

Rocket Body / Platform 36 Y N

Debris/Unknown 36 Y N

500 < p < 1000 > 0.25 Payload 24 Y Y

Rocket Body / Platform 24 Y Y

Debris/Unknown 24 Y Y

1000 < p < 2000 > 0.25 Payload 18 N Y

Rocket Body / Platform 18 N Y

Debris/Unknown 18 N Y

2000 < p < 10000 any Payload 12 N Y

Rocket Body / Platform 12 N Y

Debris/Unknown 12 N Y

p > 2000 any Payload 8 N Y

Rocket Body / Platform 8 N Y

Debris/Unknown 8 N Y

Energy

Dissipation

Rate (w/kg) Object Type Min Max Min Max

< 0.0006 Payload 0.001 0.1 0.001 0.1

Rocket Body / Platform 0.001 0.2 0.001 0.2

Debris/Unknown 0.001 1 0.001 1

> 0.0006 Payload 0.001 0.1 0.001 0.1

Rocket Body / Platform 0.001 0.2 0.001 0.2

Debris/Unknown 0.001 1 0.001 1

Coefficient Pressure Coefficient

Ballistic Solar Radiation
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Table P-3 LUPI Minimum and Maximum Values

Figure P-4 LUPI Upper Bound for Certain EDR Values

• Residual Acceptance. Fewer than 80% residual acceptance would generally prompt 

manual review of an orbit determination.

• Weighted Orbital-Determination Residual Root-Mean-Square. Weighted root-meansquare values exceeding the following thresholds are considered excessive:

Payload: 1.5

Rocket Body / Platform: 2.0

Debris/Unknown: 5.0

No thresholds for sub-unity weighted root-mean-square levels have yet been established.

EDR EDR

Min Max e Lower Bound Upper Bound

0 0 any 14 See graph

0+ 0.0006 < 0.25 3.5 18

> 0.25 14 See graph

0.0006 0.001 any 1.5 17

0.001 0.0015 any 1.5 15

0.0015 0.002 any 1.5 14

0.002 0.003 any 1.5 12

0.003 0.006 any 1.25 11

0.006 0.009 any 1.25 10

0.009 0.015 any 1.25 8

0.015 0.05 any 1.25 8

0.05 0.05+ any 1.25 7

Length of Update Interval (days)
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Appendix Q. Notional Display Flow for Conjunction Event Processing 190

Appendix Q. Notional Display Flow for Conjunction Event 

Processing

Q.1 Introduction

While appendices E through P in this Handbook address many of the technical aspects of the 

conjunction event processing discipline, this appendix illustrates how the individual pieces come 

together to perform on-orbit conjunction risk assessment. The operational orbital safety process 

is illustrated through a series of graphical displays that conjunction risk assessors use to 

determine whether a mitigation action is warranted for a particular conjunction and, if it is, what 

sorts of such actions might be effective in adequately reducing the collision risk. 

The graphical displays in this appendix are a subset of those used by the NASA CARA group to 

perform risk assessment in protection of NASA’s fleet of non-human space flight satellites, and 

the examples presented are for a recent actual event that resulted in the planning and execution of 

a mitigation action. To facilitate public release of the information, neither spacecraft is 

specifically identified, and the orbital data have been slightly altered.

NASA executes conjunction assessment screenings of its assets against the DOD space catalog 

once every eight hours, and for the orbit regime that contains the particular protected asset in use 

in this example, a screening volume of 0.5 km x 17 km x 20 km was used. This particular 

conjunction appeared at the 6.5 days-to-TCA point, which means that it was essentially 

identified as early as possible (using 7-day predicted ephemerides for the primary object). 

Because the initial Pc was greater than 1E-07, this event was in “yellow” status from the very 

beginning, meaning that the collision likelihood was high enough to merit close attention as the 

event developed. As such, the conjunction risk assessment process was engaged from the 

beginning. 

The displays in this appendix follow this event from initial detection to the mitigation action 

commitment point, which for this event was one day prior to the time of the closest approach. 

Commentary is provided for each display, and since there is always more that can be said about 

each display, the commentary is reasonably abbreviated and focused on the most salient points of 

each presentation.

Q.2 Primary and Secondary Object Background Information

In making a risk assessment determination, it is important to have information about the orbits 

and maintenance history of the primary and secondary objects as background. Different orbits 

have different properties and expected stability, and maintenance histories and parameters testify 

to the quality of the orbit determination available to analyze this event. It is helpful to display 

these data in consolidated form so that the parameters of interest can be viewed and apprehended 

quickly.
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Q.2.1 Primary Object Information

Table Q-1 provides the orbital and orbit determination estimation information for this 

conjunction’s primary object.

Table Q-1 Primary Satellite Vital Statistics

In most cases, the primary object is much better maintained than the secondary object, meaning 

that the primary object’s orbit determination information is generally good and therefore not 

determinative in assessing the event’s overall data quality. Furthermore, if the object is screened 

using the owner/operator (O/O) ephemeris, there will typically not be any available orbit 

determination estimation information at all. But it is helpful to examine whatever information is 

available for the primary object to make sure the situation is well understood. 

One observes that the primary is in a nearly circular, sun-synchronous LEO orbit with an average 

altitude of about 700km. The energy dissipation rate (EDR) value indicates that, while drag has 

an effect, it is relatively mild. The altitude is such that both drag and solar radiation pressure 

(SRP) should be modeled, and the two resultant solved-for values are reasonable. (Consult 

Appendix P for acceptable ranges of values for parameters such as this.) The weighted root mean 

square (WRMS) value here is low enough not to raise any objection. The tracking density is 

reasonably large, and tracking data has been included in the orbital solution that was collected 

within the last day, so propagation to TCA will not have to extend very far into the future. 

Overall, this primary satellite is well maintained and not propagated excessively, so there is 

nothing to indicate any problems with the fit or propagation.

Q.2.2 Secondary Object Information

Basic orbital and orbit determination estimation information for the secondary object is shown in 

Table Q-2. 

Orbital Parameter Value

Period (min) 97.6

Perigee Height km) 681.3

Apogee Height (km) 721.7

Inclination degrees) 98.2

EDR (W/kg) 2.77e-04

RCS Large

(>1m^2)

Orbital Information at TCA

Parameter Value

Avg. Tracks Per Day 5.7

Num. Obs. In Span 237

Time of Last Observation <24 hours

WRMS 1.55

Ballistic Coefficient (m^2/kg) 0.027

SRP Coefficient (m^2/kg) 0.005

Estimation Specifics
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Table Q-2 Secondary Satellite Vital Statistics

The orbit of the secondary object is not substantially different from that of the primary, although 

the inclination is somewhat lower. However, due presumably to a different area-to-mass ratio, 

the drag influence is much higher for the secondary object: the high EDR value indicates a 

significant drag effect, and this is confirmed by the large solved-for ballistic coefficient. The 

orbit altitude indicates that SRP should be solved for as well, and it is: the large value here also 

indicates a high area-to-mass ratio. The tracking levels for the secondary object are poor: 0.5 

tracks/day is an order of magnitude smaller than the tracking density for the primary. 

Examining the Conjunction Data Message (CDM) (not shown here) reveals that the 15

observations (obs) used in the latest orbit determination update for this object span a 9.5-day 

period. Thus, while the overall tracking situation is not the best, the length of the update interval 

(LUPI) is only half the maximum value and therefore tolerable. (Consult Appendix P for 

information about the LUPI parameter.) The fact that all the tracking comes from a single sensor 

is undesirable, but it is a circumstance that is observed occasionally with small debris objects, 

which this is given its radar cross section (RCS) value. The WRMS is high but below the quality 

threshold of 5 for a debris object. Data in the CDM also indicates that the propagation time to 

TCA is not all that long (a few days) and certainly much shorter than the length of the update 

interval. 

Overall, while the maintenance history and propagation situation for this object is not the best, it 

is good enough to serve as a basis for risk assessment, presuming that other issues (e.g., space 

weather) do not ultimately jeopardize the credibility of the propagation.
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Q.3 Primary and Secondary Object Trajectories

The ground trace plot shown in Figure Q-1 depicts the two satellite trajectories in relation to each 

other and identifies the geographical position of their point of closest approach.

Figure Q-1 Ground Trace Plot

In the above encounter, the closest-approach point—over Antarctica—is far away from the field 

of regard of any of the SSN ground sensors, meaning that this part of both satellites’ trajectories 

will not be modeled as well as if the ground sensor were directly under the point of closest 

approach. The relative velocity value indicated in Figure Q-1, almost 14 km/sec, is both very fast 

and typical for LEO conjunctions; it is certainly large enough to allow hyperkinetic assumptions 

about the conjunction to inhere and thus to allow the use of simplified approaches to calculating 

the probability of collision, such as the 2D Pc. 

The approach angle may also be of some interest. A zero-degree approach angle describes a 

situation in which one object “chases” another, usually presenting lower-velocity encounters; a 

180-degree approach angle constitutes a “head-on” collision. In both such instances, in-track 

error plays a smaller role in the conjunction dynamics because it controls the timing of any 

collision more than whether a collision would in fact take place. (This is of course only partially 

true because in-track error is usually correlated with radial error and thus will engender a radial 

component.) Values in between these extremes describe the typically encountered oblique 

situation, which is the case in this particular event being evaluated.

Protected 

Object

Secondary 

Object
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Q.4 Conjunction Plane Information

The Figure Q-2 visual, called a Conjunction Plane Plot, communicates certain information about 

the event. In interpreting this representation, it may be helpful to review the development of the 

2D Pc calculation methodology outlined in Appendix N. 

Figure Q-2 Conjunction Plane Plot

The relative miss vector lies along the x-axis, with one end at the origin and the other terminating 

at the blue dot. This blue “dot” is in fact a circle with a radius equaling the hard-body radius

(HBR) that represents the combined sizes of the primary and secondary objects. The ellipses 

represent the combined uncertainty of the primary and secondary objects’ positions, here 

resolved from an ellipsoid to an ellipse in the plane in which a collision, should it occur, would 

take place. 

For low-likelihood conjunctions, the blue dot is far outside of the three-sigma ellipse, and 

frequently, the ellipse itself is collapsed onto the x-axis, indicating that the in-track error is 

dominating the conjunction. In the case being discussed, the situation is different: the blue dot is 

within the one-sigma error ellipse, and the ellipse itself has visible definition, indicating that the 

uncertainties in this situation are more varied.

Q.5 Collision Probability Evolution

The Figure Q-3 graphic gives a time history of the probability of collision (Pc) during this 

event’s development.
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Figure Q-3 Probability of Collision Time-History Plot

While it is true that in most cases operational practice is grounded correctly on the Pc at the 

“mitigation action commitment point” (namely, that temporal point before TCA at which a 

decision must be rendered regarding whether a mitigation action will take place), the behavior of 

the Pc over the event’s history does help to indicate whether the event’s risk assessment data are 

stable enough to allow a durable risk assessment decision to be made. 

Figure Q-3 shows the Pc time history:

• For the primary and secondary objects’ states and covariances based on the skin-tracking 

results (indicated as “ASW” in the legend), and 

• For the primary object’s state and covariance derived from a submitted owner/operator 

ephemeris (indicated as “O/O” in the legend). 

An additional feature of Figure Q-3 is that the graphic markers (square or circle) are filled in for 

the particular updates that received new tracking.

Figure Q-3 makes clear that the secondary object is not particularly well tracked; most of the 

updates, noted by the open markers, are based only on the update of the space weather

coefficients and do not constitute a new state estimate resulting from fresh tracking. However, 

the significant state update that does contain new tracking (just a little less than two days to 

TCA) is barely under the mitigation threshold (red line), and after additional space weather 
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updates, the last such update before the mitigation action commitment point (one day) exceeds 

the red threshold. While there is a large variation observed in the Pc history, it is not so extreme 

as to indicate to an analyst that the situation is so unstable that a mitigation action cannot be 

planned or counselled wisely. As such, based (provisionally) on Figure Q-3, it would be 

recommended for this O/O to take a mitigation action.

Q.6 Miss Distance Evolution

While the Pc is the collision likelihood metric of choice, it is helpful to examine the miss 

distance history as well to see if it is manifesting a dramatically different pattern from the Pc 

history.

Figure Q-4 Total Miss Distance Plot

Miss distance is one of the principal inputs to the Pc, but the combined covariance and HBR are 

also important. There are cases in which the miss distance behaves in a manner that would seem 

to reduce collision risk but the covariance evolution is such that the collision likelihood remains 

high; in such situations, further investigation is prudent.

When comparing Figure Q-4 to the Pc history, one observes a situation in which the miss 

distance evolution is not in obvious lock-step with the Pc evolution, which is not an unusual 

outcome given what appears to be happening with the covariance evolution at the same time. But 

one also observes a situation for which the miss distance has moved to a very low value in the 
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last update. Even though this is not brought about via a tracking update but just space weather 

model updates, it is small enough to have driven the Pc above the mitigation threshold. While in 

principle it could change at the next update and push the Pc below the threshold, the situation is 

not so contradictory that one would assert that it has no predictive force. 

As such, the miss distance behavior does not work against a conclusion that collision mitigation 

is appropriate. 

Q.6.1 Miss Distance Component Behavior

In Figure Q-5, the individual miss distance components are examined, which is a more 

meaningful display of the time history of this particular datum.

Figure Q-5 Componentized Miss Distance Plot

Figure Q-5 also gives a time-history of miss distance behavior, but it separates the miss distance, 

helpfully, into three components centered on the primary object: 

• The radial miss (in the direction toward the center of the Earth), 

• The in-track miss (perpendicular to the radial miss in the plane of the orbit), and 

• The cross-track miss (the direction perpendicular to this plane). 
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The blue circles represent the signed miss distance in the particular component of interest (and if 

filled in, tracking was received as part of the state estimate update that produced that miss 

distance), and the red squares represent the one-sigma uncertainty for that miss component. 

Ideal behavior is a set of blue circles that essentially stay at the same value update to update, 

while the red squares shrink closer to that value as the propagation length is decreased from 

7 days to ~1 day. 

The in-track results above (middle graph) essentially exhibit this behavior: the in-track miss does 

not fluctuate wildly (although the y-axis scale should be kept in mind), and the uncertainties 

shrink nicely as the event develops. 

The situation is somewhat less well-behaved for the cross-track graph (far right), but in the main,

the actual miss does converge to a value while the uncertainties shrink. 

The radial component, however, does not behave so nicely; and since this miss component is the 

most determinative for the Pc, it needs to be watched carefully. 

• First, one should notice how much smaller the radial miss values are compared to the 

other two components. It is because of this small radial miss that this event is a high-risk 

event in the first place. 

• Second, its evolution would have to be characterized as at least somewhat unstable: it 

changes sign and does not uniformly focus on a single value over time. However, such 

behavior is not truly unusual for the radial component. 

• Third, when fresh tracking is finally obtained, the miss distance does jump and changes 

sign, but it jumps to a worrisome value (nearly zero) and does not stray far from that 

value as the event pushes forward to the mitigation action commitment point. 

The fact that this key component of the high-risk designation stays reasonably stable coming into 

the mitigation action commitment point gives additional confidence that the reasonably high Pc 

value should be taken seriously.

Q.6.2 Normalized Component Miss Distance Value Comparison

Figure Q-6 is a different way to render the development of the componentized miss distance as 

the event builds to TCA. Rather than actual component miss distance values, Figure Q-6

represents normalized values: the change in componentized miss distance divided by the 

expected error in that component from the previous update. In essence, Figure Q-6 reflects how 

well or poorly each update behaves with regard to its expected error. 

Ideal performance would be for updates to sit very close to the zero line: there would be strong 

agreement update to update, and any actual difference between predictions would be small 

compared to the prediction error or, to be more precise, ~68% of such ratios would fall within 

the +1 to -1 regions. 
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Figure Q-6 State Comparison Consistency Plot

The behavior shown in Figure Q-6 is quite desirable. Most values are very near the zero-line, and 

the few that are not do not deviate much beyond the one-sigma region. One can encounter 

situations in which gyrations beyond the three-sigma region occur throughout; in comparison to 

that, the above is very well behaved. It is also not unusual to see notable changes introduced as 

the result of additional tracking; the value for the radial component right after the two-days-toTCA vertical line (red filled dot) is an example of this. 

Overall, this is a reasonably well-behaved event whose final result can be trusted to yield an 

actionable result.

Q.7 Space Weather Considerations

The space weather situation is important to consider when ascertaining whether the orbital 

dynamics are expected to be sufficiently stable that the data examined at the mitigation action 

commitment point are expected to inhere until TCA.

Q.7.1 Solar Storms

The main area of interest in Figure Q-7 is the expectation of effects from solar storms such as 

coronal mass ejections (CMEs), and these are best predicted by examining the disturbance storm 

time (Dst) parameter prediction.
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(Image from http://sol.spacenvironment.net/~sam_ops/current_data/Dst_streamB_forecast.jpg)

Figure Q-7 Solar Storm Prediction

The upper part of Figure Q-7 gives both a history and prediction of this parameter: the historical 

data are in black, the one-hour Anemomilos (the model used by the DOD to predict this 

parameter) given in blue, and the longer-term Anemomilos forecasts given in purple; the current 

time is indicated by the vertical dotted line. 

Dips in Dst are the behavior of significance with a threshold of -75 nanoTeslas being the

threshold used by CARA to indicate a disturbed situation. In Figure Q-7, one can observe a dip 

below this value, then a “recovery” increase, then some residual dipping before steadying off and 

heading to the zero value. The prediction shows a linear increase to the zero value, which 

indicates a stable situation.

The takeaway from Figure Q-7 is that, while the space weather situation was somewhat 

perturbed in the event’s recent history, at the current time (indicated by the vertical dotted line),

it appears to have largely stabilized, and the future situation looks to be only more stable. 

Therefore, one can be reasonably comfortable acting on the present data at the maneuver 

commitment point since space weather is not likely to cause unexpected changes in drag 

predictions through the time of closest approach.
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Q.7.2 Space Weather Modeling

Figure Q-8 communicates the expected effect on the probability of collision if the space weather 

situation has been mismodeled in the predicted object trajectories.

Figure Q-8 Space Weather Trade-Space Plot

Note that Figure Q-7 and the outcome of this particular event outline a situation in which Figure 

Q-8 probably would not be used operationally, but in a discussion of this type, it seems 

appropriate to include the information nonetheless.

To determine whether space weather has been mismodeled, one first recognizes that, in the drag 

equation, the atmospheric density estimate and the ballistic coefficient are multiplicatively 

coupled; this means that the effect of changing one of these parameters can be emulated by 

changing the other. To produce Figure Q-8, the ballistic coefficients for the primary and 

secondary objects were increased and decreased incrementally by up to half an order of 

magnitude in each direction (e.g., the “Primary Drag Scale Factor” on the x-axis spans from -0.5 

to 0.5 in log space). This produces the same effect on predicted position if the atmospheric 

density were mismodeled by that amount. The colors on the intensity plot are the base-ten 

logarithm of the Pc.

What is important in the presentation, however, is not the actual Pc values but the morphology of

the plot. If the midpoint (which represents the current actual solution) is on a “ridge,” as in 

Figure Q-8, any mismodeling of the atmospheric density will result in a lower Pc value. Thus, if 

the current Pc is below one’s threshold for action, one can embrace a decision to dismiss the 
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Appendix Q. Notional Display Flow for Conjunction Event Processing 202

conjunction; i.e., if the current Pc value is below the threshold, and any mismodeling is expected 

only to lower the Pc from that value, then the event can be considered safe. 

A presentation that is essentially one-color results in a similar conclusion because in such a case,

the presentation is indicating that the event is simply not sensitive to atmospheric density 

mismodeling. If, however, the midpoint dot is on a “slope” (e.g., if it were on one of the light 

blue lines in Figure Q-8), then mismodeling could potentially either increase or decrease the Pc.

Thus, in such a case, the event is sensitive to atmospheric density mismodeling, and changes may 

be observed in future orbit determination updates in either direction that could affect the decision 

to maneuver. If the event is close to the red threshold, CARA would typically recommend 

maneuvering despite the space weather uncertainty for conservatism.

Q.8 Mitigation Maneuver Planning

To assist O/Os in planning mitigation actions, a “Maneuver Trade-Space” plot similar to Figure 

Q-9 is produced.

Figure Q-9 Maneuver Trade-Space Plot

A potential mitigation burn, taken from a variety of different burn sizes at a variety of different 

execution times, is placed into the primary object’s ephemeris, the altered ephemeris is 

propagated forward, new Pcs for both the main conjunction under consideration and any other 

conjunctions that arise from this altered trajectory are calculated, and the Pc that is an 

amalgamation of these individual Pc values is calculated. This calculation is run over and over, 

working through the entire range of burn intensities and burn times, and from the results, an 
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Appendix Q. Notional Display Flow for Conjunction Event Processing 203

intensity plot like Figure Q-9 is constructed. The colors indicated on the second y-axis at right 

indicate the Pc (1E-X, where X is the value on the axis) that will be achieved if a burn of the 

magnitude chosen on the x axis and the phasing time chosen on the right axis is executed. 

Choosing a maneuver time and magnitude that result in a Pc of 1E-07 (dark blue) would be 

considered to fully mitigate the conjunction risk.

A number of interesting conclusions can be drawn from a Maneuver Trade-Space plot. If it is the 

case that the O/O wishes to mitigate the risk down to the CARA-recommended level of 3E-06, 

then a maneuver should be chosen that lies along the dashed white line above. The longer one 

waits to perform the maneuver, the larger the maneuver will need to be; the maneuver possibility 

shown in the bottom right of the graph is twice as large as the one shown at the top right, so 

maneuvering early allows a smaller maneuver to fully mitigate the conjunction. However, it is 

also often the case that waiting an additional half-day will allow more tracking data to be 

collected that will shrink the covariance and potentially push the Pc below the red threshold, 

meaning no maneuver would be necessary at all. This tension ultimately must be resolved by the 

O/O: does the O/O want to commit early and lock in a smaller maneuver, or does the O/O want 

to wait to act until the maneuver commitment point, hoping that the need for the maneuver will 

evaporate completely? The risk of waiting is that a large maneuver would be required to mitigate 

the conjunction, or that it may not be possible to fully mitigate the risk given the size maneuver 

that the spacecraft has the capability to perform.

Note that Figure Q-9 does not dictate any specific action to the O/O; instead, it provides general 

guidance for the sizes and timing of maneuvers that that meet chosen mitigation requirements. 

Based on these data, the O/O selects a promising maneuver (or set of maneuvers), builds them 

into predicted ephemerides, and submits them to the conjunction assessment screening authority 

for screening. This latter action is necessary because it is the only way to give assurance of both 

the safety of the proposed is necessary because it is the only way to give assurance of both the 

safety of the proposed maneuver (or set of maneuvers) relative to other on-orbit objects and the 

actual amount of risk reduction that the maneuver (or set of maneuvers) can be expected to yield.

In this example, the collision likelihood is above the CARA mitigation threshold (1E-04) at the 

maneuver commitment point used by the O/O for this spacecraft, and mitigation actions that 

appropriately reduce the risk are available and not large enough to negatively affect the satellite’s 

main mission appreciably. Therefore, the O/O made the straightforward decision to perform a 

mitigation action.
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Appendix R. List of Works Cited

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NPR 8079.1, NASA Spacecraft Conjunction Analysis and Collision Avoidance for Space 

Environment Protection.

NPR 8715.6, NASA Procedural Requirements for Limiting Orbital Debris and Evaluating the 

Meteoroid and Orbital Debris Environments.

NASA Standard 8719-14B, Process for Limiting Orbital Debris, which defines how NASA 

implements the U.S. Government Orbital Debris Mitigation Standard Practices.

NASA Technical Publication NASA/TP–20220014814, “Astrodynamics Convention and 

Modeling Reference for Lunar, Cislunar, and Libration Point Orbits.” Version 1.1, 1 December 

2022. David Folta, Natasha Bosanac, Ian Elliott, Laurie Mann, Rebecca Mesarch, and Jose 

Rosales. https://ntrs.nasa.gov/citations/20220014814.

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