January 2012 

NASA/TM-2012-217328 

NESC-RP-09-00605 

 

Development of Autonomous Aerobraking 

(Phase 1) 

Daniel G. Murri/NESC 

Langley Research Center, Hampton, Virginia 

Richard W. Powell 

Analytical Mechanics Associates, Inc., Hampton, Virginia 

Jill L. Prince 

Langley Research Center, Hampton, Virginia 
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January 2012 

NASA/TM-2012-217328 

NESC-RP-09-00605 

 

Development of Autonomous Aerobraking 

(Phase 1) 

Daniel G. Murri/NESC 

Langley Research Center, Hampton, Virginia 

Richard W. Powell 

Analytical Mechanics Associates, Inc., Hampton, Virginia 

Jill L. Prince 

Langley Research Center, Hampton, Virginia 
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Hanover, MD 21076-1320 

443-757-5802 

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NESC Request No.: 09-00605 (Phase 1) 

Development of Autonomous Aerobraking 

(Phase 1) 

December 15, 2011
NASA Engineering and Safety Center 

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NESC Request No.: 09-00605 (Phase 1) 

Report Approval and Revision History 

NOTE: This document was approved at the December 15, 2011, NRB. This document was 

submitted to the NESC Director on January 10, 2012, for configuration control. 

Approved: Original Signature on File 1/11/12

NESC Director Date

Version Description of Revision Office of Primary 

Responsibility

Effective Date

1.0 Initial Release Mr. Daniel G. Murri, 

NASA Technical Fellow 

for Flight Mechanics, 

LaRC

12/15/11
NASA Engineering and Safety Center 

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Table of Contents 

Technical Assessment Report (Phase 1) 

1.0 Notification and Authorization ............................................................................................ 7

2.0 Signature Page ..................................................................................................................... 8

3.0 Team List............................................................................................................................. 9

4.0 Executive Summary ........................................................................................................... 11

5.0 Assessment Plan ................................................................................................................. 13

6.0 Problem Description and Proposed Solution ...................................................................... 14

6.1 Conventional AB ........................................................................................................................... 14

6.2 Benefits of AA ............................................................................................................................... 15

6.3 AA Approach ................................................................................................................................. 15

7.0 Data Analysis ..................................................................................................................... 17

7.1 Reference and “Truth” Simulations ............................................................................................... 17

7.1.1 POST2 ............................................................................................................................. 20

7.1.2 AAHFS ............................................................................................................................. 21

7.2 AB Mission Design Methodologies ............................................................................................... 21

7.3 AB Models ..................................................................................................................................... 23

7.3.1 “Truth” Models ................................................................................................................. 23

7.3.2 Onboard AA Models ......................................................................................................... 28

7.4 AADS Model Integration ............................................................................................................... 31

7.5 AA Simulation Results .................................................................................................................. 32

7.5.1 AADS Performance: POST2 Analysis ............................................................................. 32

7.5.2 AAHFS ............................................................................................................................. 62

7.5.3 Future Work ...................................................................................................................... 88

8.0 Findings, Observations, and NESC Recommendations ...................................................... 90

8.1 Findings ......................................................................................................................................... 90

8.2 Observations .................................................................................................................................. 91

8.3 NESC Recommendations............................................................................................................... 91

9.0 Alternate Viewpoints ......................................................................................................... 93

10.0 Other Deliverables ............................................................................................................. 93

11.0 Lessons Learned ................................................................................................................ 93

12.0 Definition of Terms ............................................................................................................ 93

13.0 Acronyms List ................................................................................................................... 94

14.0 References ......................................................................................................................... 96

15.0 Appendices ........................................................................................................................ 97
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List of Figures 

Figure 6.0-1. A Spacecraft using Apoapsis Maneuvers to Control Periapsis Altitude during AB ......... 14

Figure 7.3-1. MRO Spacecraft used for AA Study Simulation .............................................................. 24

Figure 7.3-2. Mars-GRAM 2010 Density Perturbations ........................................................................ 26

Figure 7.3-3. Venus-GRAM Density Perturbations ............................................................................... 27

Figure 7.3-4. Titan-GRAM Density Perturbations ................................................................................. 27

Figure 7.5-1a. AADS Ephemeris Estimator Performance at Mars with Perturbed Atmosphere 

(and 7-day Updates): Current Periapsis Time ................................................................... 34

Figure 7.5-1b. AADS Ephemeris Estimator Performance at Mars with Perturbed Atmosphere 

(and 7-day Updates): Current Periapsis Altitude .............................................................. 35

Figure 7.5-2a. AADS Atmosphere Estimator Performance at Mars (with 7-day Updates): Predicted 

Periapsis Atmospheric Density ......................................................................................... 36

Figure 7.5-2b. AADS Atmosphere Estimator Performance at Mars (with 7-day Updates): Predicted 

Periapsis Atmospheric Scale Height ................................................................................. 37

Figure 7.5-3a. AADS Mission Operations Corridor Performance at Mars with a Perturbed Atmosphere 

and 3-day Updates ............................................................................................................ 38

Figure 7.5-3b. AADS Mission Operations Corridor Performance at Mars with a Perturbed Atmosphere 

and 5-day Updates ............................................................................................................ 39

Figure 7.5-3c. AADS Mission Operations Corridor Performance at Mars with a Perturbed Atmosphere 

and 7-day Updates ............................................................................................................ 40

Figure 7.5-3d. AADS Mission Operations Corridor Performance at Mars with a Perturbed Atmosphere 

and 14-day Updates .......................................................................................................... 41

Figure 7.5-4. AADS Mission Operations Corridor Performance at Mars with a Nominal Atmosphere 

(and 7-day Updates) .......................................................................................................... 43

Figure 7.5-5a. AADS with Perturbed Atmosphere (and 7-day Updates) Comparison with Reference 

Simulation at Mars: Orbit Period “GlideSlope” ............................................................... 44

Figure 7.5-5b. AADS with Perturbed Atmosphere (and 7-day Updates) Comparison with Reference 

Simulation at Mars: Commanded Maneuver ∆v ............................................................... 45

Figure 7.5-5c. AADS with Perturbed Atmosphere (and 7-day Updates) Comparison with Reference 

Simulation at Mars: Periapsis Altitude ............................................................................. 46

Figure 7.5-5d. AADS with Perturbed Atmosphere (and 7-day Updates) Comparison with Reference 

Simulation at Mars: Periapsis Areocentric Latitude ......................................................... 47

Figure 7.5-6a. AADS Constrained Mission Operations Corridor Performance at Mars with a 

Perturbed Atmosphere (and 7-day Updates) for a Tight Corridor Centered on the 

Nominal Corridor Lower Limit ........................................................................................ 49

Figure 7.5-6b. AADS Constrained Mission Operations Corridor Performance at Mars with a 

Perturbed Atmosphere (and 7-day Updates) for a Tight Corridor Centered on the 

Nominal Corridor Upper Limit ......................................................................................... 50

Figure 7.5-7. AADS Mission Aggressive Operations Corridor Performance at Mars with a Perturbed 

Atmosphere (and 7-day Updates) ..................................................................................... 52

Figure 7.5-8. AADS Glide Slope Delay and Recovery Scenario at Mars with a Perturbed Atmosphere 

(and 7-day Updates) .......................................................................................................... 54

Figure 7.5-9a. AADS Mission Operations Corridor Performance for the Nominal Corridor .................. 55

Figure 7.5-9b. AADS Mission Operations Corridor Performance for the Glide Slop Delay and 

Recovery Corridor ............................................................................................................ 56
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Figure 7.5-10. AADS Mission Operations Corridor Performance at Venus with a Perturbed 

Atmosphere (and 7-day Updates) and a Fixed Corridor Target ........................................ 58

Figure 7.5-11. AADS Mission Operations Corridor Performance at Venus with a Perturbed 

Atmosphere (and 7-day Updates) and a Varying Corridor Target .................................... 59

Figure 7.5-12. AADS Mission Operations Corridor Performance at Titan with a Perturbed 

Atmosphere (and 7-day Updates) ..................................................................................... 61

Figure 7.5-13. AAHFS 6-DOF Block Diagram ........................................................................................ 63

Figure 7.5-14. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Nominal 

Atmosphere and 7-day Updates ........................................................................................ 66

Figure 7.5-15. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Nominal 

Atmosphere and 7-day Updates ........................................................................................ 67

Figure 7.5-16. AAHFS Simulation – Glide Slope Performance at Mars with a Nominal Atmosphere 

and 7-day Updates ............................................................................................................ 68

Figure 7.5-17. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Nominal 

Atmosphere and 14-day Updates ...................................................................................... 69

Figure 7.5-18. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Nominal 

Atmosphere and 14-day Updates ...................................................................................... 70

Figure 7.5-19. AAHFS Simulation – Glide Slope Performance at Mars with a Nominal Atmosphere 

and 14-day Updates .......................................................................................................... 71

Figure 7.5-20. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Perturbed 

Atmosphere and 7-day Updates ........................................................................................ 72

Figure 7.5-21. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Perturbed 

Atmosphere and 7-day Updates ........................................................................................ 73

Figure 7.5-22. AAHFS Simulation – Glide Slope Performance at Mars with a Perturbed Atmosphere 

and 7-day Updates ............................................................................................................ 74

Figure 7.5-23. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Perturbed 

Atmosphere and 14-day Updates ...................................................................................... 75

Figure 7.5-24. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Perturbed 

Atmosphere and 14-day Updates ...................................................................................... 76

Figure 7.5-25. AAHFS Simulation – Glide Slope Performance at Mars with a Perturbed Atmosphere 

and 14-day Updates .......................................................................................................... 77

Figure 7.5-26. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Perturbed 

Atmosphere, 7-day Updates, and a Reduced Heat Rate Corridor ..................................... 78

Figure 7.5-27. AAHFS Simulation – Glide Slope Performance at Mars with a Perturbed Atmosphere, 

7-Day Ground Updates, and a Reduced Heat Rate Corridor ............................................ 79

Figure 7.5-28. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Perturbed 

Atmosphere, 7-day Updates, and an Elevated Heat Rate Corridor ................................... 80

Figure 7.5-29. AAHFS Simulation – Glide Slope Performance at Mars with a Perturbed Atmosphere, 

7-Day Ground Updates, and an Elevated Heat Rate Corridor .......................................... 81

Figure 7.5-30. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Perturbed 

Atmosphere, Accelerometer Errors, and 7-day Updates ................................................... 82

Figure 7.5-31. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Perturbed 

Atmosphere, Accelerometer Errors, and 7-day Updates ................................................... 83

Figure 7.5-32. AAHFS Simulation – Glide Slope Performance at Mars with a Perturbed Atmosphere, 

Accelerometer Errors, and 7-day Updates ........................................................................ 84
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Figure 7.5-33. AAHFS Simulation – AADS Heat Rate Performance Histograms for all AAHFS 

Cases ................................................................................................................................. 86

Figure 7.5-34. AAHFS Simulation – Aerodynamic Stability during Drag Passes ................................... 88

List of Tables 

Table 7.1-1. Models Contained in “Truth” Simulations and AADS ........................................................ 19

Table 7.3-1. MRO Mass Properties .......................................................................................................... 24

Table 7.5-1. Summary of AADS Heat Rate Estimate Performance Variability for Various Ground 

Update Frequencies .............................................................................................................. 42

Table 7.5-2. Summary of AADS Performance with a Perturbed Atmosphere (and 7-day Updates) 

Compared to Reference Simulation at Mars ........................................................................ 48

Table 7.5-3. Summary of AADS Performance at Mars with a nominal Atmosphere for Runs using the 

Nominal Operational Corridor, a corridor Constrained to the Nominal Corridor Upper 

Limit, and One to the Nominal Corridor Lower Limit......................................................... 50

Table 7.5-4. Comparison of AADS Performance at Mars with a Perturbed Atmosphere (and 7-day 

Updates) for the Nominal and Aggressive Operational Corridors ....................................... 53

Table 7.5-5. Summary of AADS Performance with Perturbed Atmosphere (and 7-day Updates) 

Compared to Reference Simulation at Venus ...................................................................... 60

Table 7.5-6. Summary of AADS Performance with Perturbed Atmosphere (and 7-day Updates) 

Compared to Reference Simulation at Titan ........................................................................ 61

Table 7.5-7. AAHFS Simulation – Accelerometer Error Sources per Accelerometer ............................. 82

Table 7.5-8. AAHFS Simulation – AADS Performance at Mars ............................................................. 85

Appendices (Phase 1) 

Appendix A. Autonomous Aerobraking Planetary Constants and Models Version 0.07 

(Supplement to Section 7.2) ........................................................................................ 98

Appendix B. Mission Design Appendix (Supplement to Section 7.2) ............................................... 130

Appendix C. Aerodynamics and Aerothermodynamics Computational Methods 

(Supplement to Section 7.3.1.2) ................................................................................. 140

Appendix D. Thermal Modeling (Supplement to Section 7.3.2.4) .................................................... 150

Appendix E. Mars-GRAM 2010 (Supplement to Section 7.3.1.3) .................................................... 168

Appendix F. Onboard Atmospheric Modeling and Prediction for AA Missions 

(Supplement to Section 7.3.2.1) ................................................................................. 177

Appendix G. Ephemeris Estimator User’s Guide (Supplement to Section 7.3.2.2) ............................. 216

Appendix H. AADS (Supplement to Section 7.5.1) ......................................................................... 250

Appendix I. AAHFS (Supplement to Section 7.5.2) ....................................................................... 255

Appendix J. AA Interface Control Document ................................................................................ 263
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Technical Assessment Report (Phase 1) 

1.0 Notification and Authorization 

The NASA Engineering and Safety Center (NESC) received a request from Mr. Daniel Murri 

(NASA Technical Fellow for Flight Mechanics) to develop an autonomous aerobraking (AA) 

capability. The NESC received this request on December 15, 2009. An initial evaluation for all 

phases of this assessment was approved to proceed at the February 4, 2010, NESC Review 

Board. The assessment plan for Phase 1 was approved by the NRB on April 1, 2010. 

The stakeholders for this assessment (all phases) are the NESC (including the technical 

disciplines of Flight Mechanics; Aerosciences; Passive Thermal; Guidance, Navigation, and 

Control (GN&C); Software; Loads and Dynamics; and Human Factors) and future NASA 

programs and projects that may utilize aerobraking (AB). 
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2.0 Signature Page

Submitted by: 

Team Signature Page on File – 1/23/12 

Mr. Daniel G. Murri Date Mr. Richard W. Powell Date

Ms. Jill L. Prince Date

Signatories declare the findings and observations compiled in the report are factually based from 

data extracted from Program/Project documents, contractor reports, and open literature, and/or 

generated from independently conducted tests, analysis, and inspections. 
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3.0 Team List 

Name Discipline Organization

Core Team

Dan Murri NESC Lead, NASA Technical Fellow for Flight Mechanics LaRC

Richard Powell Assessment Lead AMA

Jill Prince Technical Team Lead LaRC

Hollis Ambrose APL Simulation APL

Angela Bowes LaRC Simulation LaRC

David Carelli APL Simulation APL

Alicia Cianciolo LaRC Simulation LaRC

John Dec Thermal LaRC

Hilary Justh Atmospheric Modeler MSFC

Jere Justus Atmospheric Modeler, Flight Mechanics TDT MSFC/MITS

James Kaidy APL Simulation APL

Derek Liechty Aerodynamics/Aerothermal Environments LaRC

Forrest Lumpkin Aerodynamics/Aerothermal Environments JSC

Robert Maddock LaRC Simulation LaRC

Dan O’Shaughnessy APL Simulation Lead APL

Chris Pastore Software Support LaRC/AMA

Holly Ramey Atmospheric Modeler Jacobs

David Skinner Ephemeris Estimator KinetX

Benedicte Stewart Aerodynamics/Aerothermal Environments JSC/Jacobs

Tom Strikwerda APL Project Manager APL

Mark Thornblom Thermal LaRC

Robert Tolson Atmospheric Modeler NCSU/NIA

Bobby Williams Ephemeris Estimator KinetX

Laura Leybold MTSO Program Analyst LaRC

Consultants

Neil Dennehy NASA Technical Fellow for GN&C GSFC

Starr Ginn Loads and Dynamics TDT DFRC

Cynthia Null NASA Technical Fellow for Human Factors ARC

Vicki Regenie Systems Engineering DFRC
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Name Discipline Organization

Peer Reviewers

Mike Aguilar NASA Technical Fellow for Software GSFC

Prasun Desai Flight Mechanics TDT LaRC

Dan Lyons JPL Aerobraking SME JPL

Cynthia Null NASA Technical Fellow for Human Factors ARC

Steve Rickman NASA Technical Fellow for Passive Thermal JSC

Dave Schuster NASA Technical Fellow for Aerosciences LaRC

Scott Striepe NASA Aerobraking SME LaRC

Tung-Han You JPL Aerobraking SME JPL

Administrative Support

Terri Derby Project Coordinator LaRC/ATK

Donna Gilchrist Planning and Control Analyst LaRC/ATK

Carolyn Snare Technical Writer LaRC/ATK
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4.0 Executive Summary 

NASA uses aerobraking (AB) to reduce the fuel required to deliver a spacecraft into its desired 

final orbit around a target planet or moon with a significant atmosphere. Instead of using the 

propulsion system to decelerate the spacecraft, AB utilizes aerodynamic drag. While flying 

through the upper atmosphere of the planet or moon multiple times, the spacecraft maintains a 

periapsis control corridor such that dynamic pressure and thermal loads on the spacecraft remain 

within designed parameters. AB has been used four times by NASA: once at Venus and three 

times at Mars. 

Although AB reduces the propellant required to reach the final orbit, the reduction comes at the 

expense of time (typically 3–6 months), continuous Deep Space Network (DSN) coverage, and a 

large ground staff. The DSN and ground staff are required to design the maneuvers that the 

spacecraft executes during AB to keep the spacecraft safe and provide the desired final orbit. 

The combination of duration, staff, and continuous DSN coverage results in a high cost AB 

operational phase. 

As AB has evolved, the operations have matured to the point where many of the operational 

decisions being made by the ground staff can now be made autonomously onboard the 

spacecraft. With the development of autonomous aerobraking (AA), much of the daily ground

operations could be minimized thereby reducing the AB phase costs. In addition, by relegating 

the decision making to the spacecraft, which eliminates the dependence on staff work schedules 

(e.g., spacecraft can only perform maneuvers during prime shift and must minimize maneuvers 

during weekends and holidays), AA can reduce risk by allowing the maneuver to be conducted at 

the optimal apoapsis opportunity and executed even if DSN or other currently required ground 

elements are unavailable. Another advantage of AA is that it could provide the ability to handle 

multiple AB assets at the same time that would otherwise not be economically feasible using the 

traditional ground-based operational approach. 

Phase 1 of this study investigated the technical capability of transferring the processes of AB 

maneuver decision making (currently performed on the ground through the DSN and an 

extensive workforce) to an efficient flight software algorithm onboard the spacecraft. To 

accomplish this, highly accurate aerodynamic and thermal models for a representative spacecraft 

were developed for both the onboard algorithm known as Autonomous Aerobraking 

Development Software (AADS) and a ground-based “truth” simulation developed for testing 

purposes. Autonomous Ephemeris, Atmosphere, and Maneuver Estimators were developed and 

incorporated into AADS. Previous AB mission experience indicates that an increase in the error 

of the predicted time of periapsis passage requires frequent (daily) ephemeris updates from the 

ground using DSN. One goal of the AA study is to develop an Ephemeris Estimator that can 

provide state estimates within acceptable tolerances for more than a week before requiring a 

ground update, thus eliminating the need for continuous DSN coverage. 
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For Phase 1, AADS was tested in simulated AB missions at three destinations, each requiring a 

unique AB corridor type. At Mars, the corridor was based on aerodynamic heating rate. Due to 

its proximity to the Sun, the AB mission at Venus utilized a solar-panel temperature corridor. 

Finally, an altitude corridor was used at Titan. Nominal and off-nominal AB scenarios were 

simulated and compared with the reference simulation.

Products of Phase 1 included several models and algorithms that were integrated within AADS. 

An Ephemeris Estimator was developed that used an efficient, easily implemented Runge-Kutta 

integration scheme, a high order gravity field model, third body gravitational effects, and 

provided the required accuracy for 7 days. An atmospheric estimator was demonstrated that 

used traditional atmospheric estimation algorithms that provided periapsis density and density 

scale height estimates that were adequate for corridor maintenance maneuver calculations. A 

thermal response algorithm was generated that predicted the maximum temperature of the 

spacecraft given the periapsis density from the Atmosphere Estimator. The entire system was 

embedded into two high fidelity simulations that used detailed models of flight subsystems and 

have vast heritage as simulation tools. 

Results of the Phase 1 simulation analysis show that it is feasible for AADS to provide AA 

control of a spacecraft with ephemeris updates less than once per week at all three sampled 

destinations. These results have been demonstrated in the presence of atmospheric perturbations 

and sensor (e.g., inertial measurement unit (IMU)) measurement errors. Longer intervals 

between ground updates may be possible, as a 14-day ground update interval with atmospheric 

perturbations at Mars, Venus, and Titan has been demonstrated. This 7-day update cycle meets 

the goal set for AADS and could significantly reduce the DSN and ground staffing requirements. 

Future work has been identified and will include enhancements to AADS, improved capabilities 

of the simulation tools, and additional stress testing of AADS in both high fidelity simulations. 
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5.0 Assessment Plan 

The complete development of the AA capability occurs in four phases. This report summarizes 

the activities of Phase 1, which included software development sufficient to demonstrate the 

viability of the proposed AA approach, detailed below. 

 Atmospheric, aerodynamic, and thermal models for a representative AA spacecraft, based 

on Mars Reconnaissance Orbiter (MRO). 

 The AADS package, which includes ephemeris and Atmosphere Estimator s, and a 

corridor control maneuver calculator. 

 Two simulation environments for testing the AADS.

o A 3-degree of freedom (DOF), stand-alone Program to Optimize Simulated 

Trajectories II (POST2)-based AB simulation used to rapidly develop and mature 

the AADS software. 

o A 6-DOF, high-fidelity MErcury Surface, Space ENvironment, GEochemistry 

and Ranging (MESSENGER)-based simulation that more closely represents the 

flight operating environment and sensor characteristics (e.g., IMUs and star 

trackers). 

Both simulation environments were used for proof-of-concept testing and preliminary studies of 

the AADS algorithms and the AA approach in general. 

Until this assessment, the method of ephemeris estimation utilized data provided by continuous 

DSN coverage and ground-based software to provide frequent updates to the stored onboard 

ephemeris. Phase 1 included simulation testing of AA at Mars, Venus, and Titan.

Phase 2 will explore more sophisticated schemes for the ephemeris and atmosphere estimation as 

a means of improving AADS robustness and performance. Improved modeling and error 

checking will be implemented and additional off-nominal stress testing of AADS will be 

performed. 

Phase 3 will incorporate all of the AA software onto a flight-like processor to study the 

implications of operating the AADS in a real-time environment. This phase will quantify the 

computational resources required to support AADS in a flight mission. 

In Phase 4, the AA software will be installed onto a spacecraft that will use AB, and then AA 

will operate during flight in a shadow-mode, where all the steps for AA are performed but the 

commands are not executed. The onboard-determined commands will be validated against AB 

decisions made by the ground staff. 
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6.0 Problem Description and Proposed Solution 

6.1 Conventional AB 

NASA uses AB to reduce the fuel required to deliver a spacecraft into its desired final orbit 

around a target planet or moon with an appreciable atmosphere. Rather than using the 

propulsion system to decelerate the spacecraft after the initial orbit insertion, AB utilizes 

aerodynamic drag induced by repeated passes through the atmosphere. Small propulsive 

maneuvers at apoapsis are used to control the altitude at periapsis to maintain the spacecraft 

within its designed corridor (see Figure 6.0-1). The periapsis control corridor may be defined by 

a range of dynamic pressure, a heat rate indicator, atmospheric density, or periapsis altitude, but 

typically the corridor is constrained by the thermal limit of a spacecraft component. Using a 

multiple-pass approach enables the spacecraft’s loads to remain within designed limits while 

gradually reducing the apoapsis to achieve the appropriate final orbit. 

Figure 6.0-1. A Spacecraft using Apoapsis Maneuvers to Control Periapsis Altitude during AB 

NASA has used AB 4 times. The first flight demonstration of the technique was the Magellan 

spacecraft at Venus where AB was completed at the end of the primary mission. AB 

successfully reduced the spacecraft’s orbital period from just over 3 hours to just under 2 hours 

in 70 days and led to the use of AB as a mission-enabling capability for three Mars spacecraft: 

Mars Global Surveyor (MGS), Mars Odyssey, and MRO. 
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6.2 Benefits of AA 

Although AB reduces the propellant required to reach the final orbit and as a result, reduces 

launch mass, this reduction comes at the expense of time, continuous DSN coverage, and a large 

ground staff required for AB operations. For example, Mars Odyssey operations required the 

expertise of trajectory analysts, thermal modelers, aerodynamicists, atmospheric scientists, and 

systems engineers in multiple locations, to analyze the necessity of an apoapsis maneuver for the 

following day. This is in addition to the numerous engineers required to build and upload the 

spacecraft sequence. The process took nearly 12 hours on each day of the 77-day AB phase. 

Similar analysis was completed every day of the 149-day MRO AB phase, albeit with a reduced 

staff due to the large thermal margin on the spacecraft. The combined cost of DSN and 

workforce results in an expensive operational phase. 

The development of AA would enable much of the daily ground operations to be moved to the 

spacecraft, thus reducing the cost of the AB phase by several million dollars [ref. 1] for a single 

mission. 

AA is also an enabling technology for future multiple-vehicle missions. Not only will small 

communications and science spacecraft benefit from the cost savings of AA, but it should be 

considered essential to establishing the infrastructure required both prior to and during human 

missions to Mars. AA enables a cost-effective way to establish sufficient and redundant satellite 

communication, weather monitoring, and global positioning systems at Mars. AA enables costeffective means for stereo and three-dimensional (3-D) observations at any body in the solar 

system with an atmosphere. In addition, AA is capable of handling multiple orbiting and AB

assets simultaneously, a task which would not be economically feasible using a traditional 

ground-based operational approach. 

6.3 AA Approach 

The concept of AA has been studied over the past decade [refs. 2–6]. Steps toward AA were 

taken when the periapsis timing estimator tested during the Mars Odyssey (2001) AB phase was 

implemented on MRO (2006). However, further development to include the maneuver execution 

capability is required to significantly reduce ground operational costs and is the subject of this 

NESC AA development activity. 

To enable a fully AA system, the spacecraft must calculate and predict its own ephemeris. All 

drag pass activities are referenced to a periapsis time and all periapsis altitude correction burns 

are performed at apoapsis. As a result, successful AB requires accurate knowledge of these 

orbital extrema. Using the subsequent orbit’s predicted periapsis, the spacecraft estimates the 

next predicted periapsis density using an onboard atmospheric model. If predicted density 

causes the corridor control value (e.g., dynamic pressure, heat rate, temperature) to fall outside 

the specified range, then an onboard algorithm would determine the maneuver direction, 

magnitude, and epoch that will be required to move the orbital periapsis back into the corridor. 
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The spacecraft then autonomously executes the required maneuvers. Moving the daily maneuver 

assessment to the spacecraft saves significant cost in staff and DSN usage. 

Additionally, because the spacecraft maneuver decision is no longer tied to the work schedule of 

ground personnel (e.g., previously, maneuvers were ideally performed during staff’s prime shift 

and avoided during weekends and holidays), AA reduces risk, as the maneuver could be 

conducted at the optimal apoapsis and executed even if DSN or other currently required ground 

elements were unavailable. Ground-based weekly activities such as updates to the corridor, 

model parameters, and/or overall mission strategy would continue to be performed from Earth. 

In addition, some one-way communication via DSN may be expected with the use of AA to 

monitor the health and safety of the spacecraft. This health monitoring of the spacecraft would 

be relatively infrequent and does not impede the anticipated cost savings of AA. 

The Phase 1 AA study investigated the technical capability of transferring the processes of AB 

maneuver decision making (currently performed on the ground through the DSN and an 

extensive workforce) to an efficient flight software algorithm onboard the spacecraft; to do so 

requires highly accurate models and test simulations. 

Therefore, aerodynamic and thermal models of the representative MRO spacecraft were 

developed; they are described in Sections 7.3.1.2 and 7.3.2.4 respectively (with more detailed 

descriptions in Appendices C and D). Baseline reference simulations were created at the three 

destinations: Mars, Venus, and Titan. Reference simulations are those trajectory simulations 

that are typically performed during the design phase of the mission and serve as the nominal 

trajectory to which the operational AB trajectory is compared. This reference simulation 

provides the “glideslope” or metric to which AB status is measured. In designing the AA 

capability, an additional “truth” simulation was developed. This “truth” simulation is the 

operational AB trajectory that has full knowledge of the atmosphere, planet, vehicle 

aerodynamics, etc. As there is little “truth” Mars, Venus, or Titan data available, “truth” in AA 

is still modeled data (e.g., Mars-Global Reference Atmospheric Model (Mars-GRAM), VenusGRAM, Titan-GRAM, etc.). Both the reference simulation and the “truth” simulation were 

developed using two independent tools: POST2 at Langley Research Center (LaRC) and a 

MESSENGER-based simulation at the Johns Hopkins University (JHU/Applied Physics 

Laboratory (APL), the Autonomous Aerobraking High Fidelity Simulation (AAHFS). The 

POST2 and AAHFS results are described in Section 7.5 with more information in Appendices H 

and I. Mission design techniques in constructing the reference simulation are described in 

Section 7.2 and Appendix B. 

Finally, the AADS module is a software package onboard the simulated spacecraft with access to 

the spacecraft IMU data and uplinked parameters but no knowledge of the spacecraft 

environment. (Phase 2 will address incorporating thermocouple temperature data from the 

spacecraft to AADS to more accurately predict spacecraft temperature.) The AADS requires 

accurate onboard models to estimate 1) the atmosphere conditions at periapsis (i.e., maximum 
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expected density and corresponding atmospheric scale height), 2) the spacecraft ephemeris, and 

3) a thermal model estimating the maximum expected temperature of the spacecraft (for use at 

Venus only). Using these models, AADS determines whether or not a maneuver is required, and 

if necessary, the magnitude of that maneuver and its location within the orbit, which are sent to 

the spacecraft. The maneuver logic is an adaptation of the mission design analysis developed at 

LaRC for the Mars Odyssey AB mission and refined for MRO mission design and operations. 

The key AADS models, the Atmosphere Estimator and Ephemeris Estimator, are described in 

Section 7.3.2.1 (with detail in Appendix F) and Section 7.3.2.2 (Ephemeris Estimator User Guide 

is in Appendix G). AADS system integration is described in Section 7.4. 

The overall system goal for the AADS is to demonstrate that the appropriate maneuvers’ 

magnitudes and directions are calculated and execution times are sufficient to maintain a desired 

flight corridor for up to 1 week compared to the “truth” simulation. 

For Phase 1, AADS was tested using simulated AB missions at three destinations, each requiring 

a unique AB corridor type. At Mars, the corridor was based on heat rate indicator 

(1/2 * atmospheric density*velocity^3). Due to the proximity to the Sun, the AB mission at 

Venus utilized a solar-panel temperature corridor. Finally an altitude corridor was used for AA 

analysis at Titan. Nominal and off-nominal AB scenarios were simulated and compared with the 

“truth” simulation. Overall AB mission metrics were compared to the reference simulations. 

Follow-on phases are planned that will improve accuracy of models developed in Phase 1; 

execute rigorous testing of AADS within the mission design simulation used at LaRC, POST2, 

as well as the APL MESSENGER-based AAHFS; port AADS to a hardware-in-the-loop testbed; 

and ultimately demonstrate the operability of AA in flight. 

7.0 Data Analysis 

The following sections contain details of the models used and the analysis performed for AA 

development. Reference simulations were developed that incorporate the “truth” models. The 

reference simulations provide the overall AB statistics that AADS will attempt to match. 

Additionally, a “truth” simulation, based on the reference simulation, is used operationally. The 

AADS data is compared to this “truth” simulation at each orbit periapsis. This comparison 

provides the confidence in the capability of AA and is provided below. 

7.1 Reference and “Truth” Simulations

Reference simulations were performed at Mars, Venus, and Titan. These reference simulations 

are the basis of the “truth” simulation used as a comparison of the accuracy of AADS. Both the 

reference simulation and the “truth” simulation include full knowledge of the environment, 

including atmospheric, planetary, and spacecraft properties. The reference simulation utilizes 

full knowledge of these properties along with a maneuver strategy (to make a maneuver every 

day or every 3 days, etc.) to obtain the most accurate estimate of realistic AB mission 
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progression, including glideslope, mission duration, number of maneuvers, amount of fuel 

required, etc. The “truth” simulation also utilizes full knowledge of the aforementioned 

properties, but rather than an internal maneuver strategy, it calls the AADS after each drag pass 

and uses the maneuver provided by AADS at each necessary apoapsis. 

Using AADS, maneuver decisions are made in the “truth” simulation based only on knowledge 

passed to the algorithm by the spacecraft (e.g., parameters uploaded to the spacecraft including 

initial state and ephemeris and onboard data from the IMU (e.g., acceleration data). The models 

within AADS predict the atmosphere based on IMU data and make estimates about the 

subsequent periapsis conditions to estimate whether a maneuver is needed. In the event that one 

is needed, the magnitude and time at which the maneuver should occur is sent to the spacecraft. 

The logic within AADS is described in detail in Section 7.4. 

”Truth” simulations using both POST2 and AAHFS were developed to analyze AADS 

performance. The “truth” simulations are described in detail within this document. For 

reference a table of models contained in both “truth” simulations and in AADS is shown in 

Table 7.1-1. 
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Table 7.1-1. Models Contained in “Truth” Simulations and AADS. Green boxes indicate that those 

models in the same row are identical. A yellow box within the row indicates an identified difference 

in the model or data used. Red boxes indicate that the model in question is not applicable. 

Model POST2 "Truth" AAHFS "Truth" AADS

Gravity

Mars and Venus 

gravity fields are 

truncated to 21x21

Mars and Venus gravity 

fields are truncated to 

21x21

(UT Methodology is used 

for computing 

accelerations due to 

gravity)

Mars and Venus gravity 

fields are truncated to 

21x21

Atmosphere

GRAM models 

directly integrated 

with simulation 

software

GRAM models directly 

integrated with 

simulation software

Atmosphere Estimator 

uses acceleration data to 

estimate density and scale 

height based on a 

simplified (exponential) 

atmosphere

Planetary 

Ephemerides Details in Appendix A Details in Appendix A Details in Appendix A

Planetary Shapes, 

Constants, and 

Orientations

Details in Appendix A Details in Appendix A Details in Appendix A

Solar Radiation 

Pressure

Based on simplified 

spacecraft geometry 

and attitude

High-fidelity model based 

on spacecraft geometry 

and true (6DOF) attitude

(not used for Phase 1 

analyses)

Based on simplified 

spacecraft geometry and 

attitude

Aerodynamics Details in Appendix C Details in Appendix C

Atmosphere Estimator 

utilizes same aerodynamic 

coefficient tables but with 

modified/simplified 

equations

Thermal 

Response Surface

Utilized for 

monitoring purposes 

only

To be implemented in 

Phase 2

Developed for Mars and 

Venus applications

Spacecraft Shape 

& Mass 

Properties

Details in Appendix A Details in Appendix A Details in Appendix A
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Model POST2 "Truth" AAHFS "Truth" AADS

Sensors To be implemented in 

Phase 2

IMU

Star Tracker Not applicable

Actuators To be implemented in 

Phase 2

Thrusters

Reactions Wheels Not applicable

Guidance and 

Control

To be implemented in 

Phase 2

Attitude /Rate Estimation

Wheel Control

Thruster Control

Not applicable

Maneuver 

Execution

Square Pulse Finite 

Burn

Full thrust profile based 

on spacecraft thruster 

model

Not applicable

7.1.1 POST2 

The POST2 is a generalized point-mass, rigid-body, discrete-parameter targeting and 

optimization trajectory simulation program based on the POST software initially developed in 

the 1970s by LaRC in partnership with the Martin Marietta Company to support Space Shuttle 

development. Throughout the years, POST was continually upgraded and modified by LaRC 

and Lockheed Martin (LM) to support a large variety of aerospace vehicle development and 

mission flight operations through trajectory simulation, flight dynamics analyses, vehicle system 

development and evaluation, and integrated system performance assessments. 

POST2 provides state-of-the-art simulation software of endo- and exo-atmospheric flight about a 

central body to support launch, orbital, and entry vehicle design, development, testing, 

assessment, and flight operations for either a single vehicle or multiple vehicles working 

independently or in tandem (e.g., orbital rendezvous or intercept). POST2 has been instrumental 

in planetary entry, descent, and landing design, as well as development, evaluation, and 

operations for robotic and human systems. It has been used for the AB mission design and 

operations for Mars Odyssey and MRO.1

Though POST2 can be run in both a 3-DOF and 6-DOF mode, all of the AA Phase 1 work 

utilized the POST2 3-DOF capability to capitalize on the existing heritage AB trajectory 

software. In the heritage reference simulation, POST2 was tailored by including the specific 

planet, gravity, atmosphere, spacecraft, aerodynamic, and third body perturbation models and 

 

1

Striepe, S.A. et al., “Program To Optimize Simulated Trajectories (POST II): Volume 2, Utilization Manual,” Martin Marietta 

Corporation, 2004 and Brauer, G. L. et al., “Program To Optimize Simulated Trajectories (POST): Volume 1, Formulation 

Manual,” Martin Marietta Corporation, 1990.
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incorporated logic required for corridors and maneuver strategies required for AB mission 

design. 

7.1.2 AAHFS 

The AAHFS is a 6-DOF simulation based on the flight software and truth models previously 

developed for the JHU/APL-designed MESSENGER spacecraft, currently orbiting Mercury 

[ref. 7]. Although this is the first time the simulation has been used for AB, the capability 

demonstration has been developed in the MATLAB/Simulink/Real Time Workshop (RTW) 

environment. It is comprised of the existing MESSENGER algorithms and software, to which 

the AB flight system and truth model test bed algorithms have been added. This approach 

permits rapid study of the AADS and, in the end, generates a high degree of confidence in the 

technology as a precursor to implementation in a flight program. Another important benefit to 

developing the software in this way is that the end product is suitable for use in a flight 

processor, as this study uses the same development environment/process as the MESSENGER 

flight software. 

Like POST2, the AAHFS has included all of the planet and vehicle-specific models used in the 

POST2 for simulation comparisons. 

7.2 AB Mission Design Methodologies 

As mentioned previously, AB reference simulations utilize full knowledge of environmental 

properties, along with a flight corridor and maneuver strategy, to obtain an accurate model of 

realistic AB mission. Both the POST2-based reference and “truth” simulations were used as a 

basis of comparison and assessment of AA performance using AADS. The reference trajectory 

was designed to achieve the final desired orbit conditions using AB while maintaining the 

mission operational constraints and the margin required for the spacecraft design limits [ref. 8]. 

Desired final orbit conditions can include altitude, inclination, argument of periapsis, and 

longitude of the ascending node required to attain a specific local mean solar time (LMST) 

orientation, or combinations of these parameters. However, for this phase of the study all 

simulations ended on a specified apoapsis altitude. 

Mission operational constraints and margin are designed to protect the spacecraft throughout the 

AB mission and depend on the physical properties of the spacecraft as well as required final orbit 

conditions. The operational constraints may consist of spacecraft thermal and structural limits 

(e.g., freestream heating rate, solar array temperature, dynamic pressure, power, attitude, and 

capability to handle atmospheric density fluctuations) and orbit lifetime requirements, maneuver 

frequency restrictions, maneuver magnitude limitations, and required propellant remaining post 

AB to achieve mission objectives. For the study at Mars, the constraints were set similar to those 

utilized in the MRO AB mission. For the Venus simulation, where temperature of the spacecraft 

dominates, a temperature range that generated approximately the same AB duration as the Mars 

mission was selected. It is somewhat arbitrary because it is recognized that the MRO spacecraft 

is not designed for AB at Venus. Finally, no AB mission has been attempted at Titan, therefore 
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without specific mission constraints, the decision was made to start AB in an 8-hour orbit period 

and make the AB duration last at least 2 months utilizing an altitude corridor. 

The reference simulations for this study begin after walk-in (a series of orbits intended to 

incrementally lower the spacecraft periapsis into the sensible atmosphere) and last until the final 

specified orbit conditions are achieved. A corridor, based on a specific operational constraint as 

described previously for each destination, is designed to keep the spacecraft within the 

appropriate design margins. Maneuvers are performed at apoapsis that raise or lower periapsis to 

maintain the spacecraft within the pre-determined corridor. The upper limit of the corridor is 

determined by the required operational constraint margin to ensure spacecraft safety, and 

therefore defines the maximum AB rate (i.e., shortest duration) that can be achieved within that 

constraint margin. For the corridor constraints selected at Mars and Venus, the lower the 

spacecraft is in the corridor, the higher altitude the atmospheric passes, the lower the ΔV from 

aerodynamic drag, resulting in overall increased AB mission duration. The lower corridor limit 

may be set to reduce the frequency of maneuvers required to stay in the corridor and/or to 

maintain the maneuver magnitudes greater than some minimum threshold. A particular lower 

corridor limit may also be set to ensure the AB rate is such that the desired final orbit conditions 

can be reached by a certain time. For instance, in the case where there is a desired final orbit 

LMST, the initial orbit node must have enough time to precess with respect to the Sun to produce 

the desired LMST. The amount of time required for the precession varies as a function of the 

initial orbit conditions, current orbit conditions, central body, gravity, atmospheric environment, 

and other forces such as third body perturbations and solar radiation pressure. AB either too 

quickly or too slowly could cause the final desired orbit apoapsis altitude to be reached at a 

different LMST than required. In the case where a periapsis altitude corridor is used at Titan, the 

roles of the upper and lower corridor constraints are reversed (i.e., lower corridor limit defines 

the maximum AB rate rather than the upper corridor limit since the lower the spacecraft is in the 

corridor means the atmospheric passes are lower and deeper within the atmosphere.) 

The corridor limits can change as a function of time since the specific conditions that the 

spacecraft experiences across the duration of AB are largely a function of orbit geometry. A 

maneuver target, specified as a percentage of the corridor width, is set and can vary with time or 

orbit geometry as well. The minimum amount of time allowed between maneuvers is also set. 

Whether or not a maneuver is performed when it is “allowed” is based on predicting ahead by 

the minimum time between maneuvers plus one additional day at Mars and Venus, or for Titan, 

by predicting ahead two orbits. If a corridor violation occurs at any time during the predicted 

time period, then a maneuver will be performed at the next allowable apoapsis. 

Operationally, the reference trajectory is used to establish the spacecraft flight design corridor 

each week and can be adjusted if necessary during the flight to accommodate observed 

atmosphere fluctuations. The daily operations are used to determine any required periapsis 

adjust maneuvers to maintain the spacecraft within the design corridor. 
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Appendix B contains a description of the reference simulation analyses at Mars, Venus, and 

Titan including all assumptions. 

7.3 AB Models 

Two types of models were developed in Phase 1 to represent an AB spacecraft in the reference 

and “truth” simulations (“truth” models) and within AADS (onboard AA models). “Truth” 

models were incorporated into the reference and “truth” simulations to create a flight 

environment for comparison. It is understood that they are models and not flight data, but for 

lack of enough available flight data (specifically for Venus and Titan) and because historically 

these models have provided a reasonable estimate for flight data, these models are considered 

truth for AA development purposes and “truth” remains in quotation marks. The “truth” models 

include a standard planet gravity model, an atmosphere model, and models of the spacecraft and 

its aerodynamic and aerothermodynamic properties. These are described in Section 7.3.1. In 

Section 7.3.2, the onboard AA models are discussed: the Ephemeris, Atmosphere, and 

Maneuver Estimators and thermal model (for Venus only). 

7.3.1 “Truth” Models

7.3.1.1 Spacecraft Model 

The MRO spacecraft shape and ballistic coefficient were chosen for the AA study (see 

Figure 7.3-1 and Table 7.3-1). Utilizing the MRO spacecraft provided a readily available 

spacecraft model as well as an aerodatabase and thermal model developed for MRO's use during 

AB operations. The aerodatabase and thermal model have been flown operationally and have 

already been correlated with flight data at Mars; thus, they can easily be integrated into the Mars 

AA technology development and verified. Additionally, these models provide good starting 

positions for adapting the aerodatabases and thermal models for use at Venus and Titan. 

However, there is a disadvantage to using the MRO spacecraft shape and ballistic coefficient: 

because the MRO spacecraft was designed for AB specifically at Mars, it does not handle the 

corridor conditions at Venus and Titan as well as a spacecraft that is designed exclusively for use 

at those locations. Details of the spacecraft model can be found in the Autonomous Aerobraking 

Planetary and Constants Document (AA PCMD) located in Appendix A. 
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Figure 7.3-1. MRO Spacecraft used for AA Study Simulation 

Table 7.3-1. MRO Mass Properties 

7.3.1.2 Aerodynamics and Aerothermodynamics 

The direct simulation Monte Carlo (DSMC) method of Bird [ref. 9] was used in the computation 

of the aerodynamic and aeroheating databases for the AA simulation study. This method has 
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become the standard for simulating low-density gas dynamics. Traditional computational fluid 

dynamics (CFD) methods are incapable of modeling flows experienced during AB, because 

assumptions made in developing the differential equations on which they are based break down 

under rarefied conditions. In contrast to continuum CFD methods, the DSMC method performs 

a direct physical simulation of the gas at the molecular level. In the DSMC simulation, 

molecules are tracked in space and time, accounting for both gas-surface interactions and 

intermolecular collisions. The DSMC Analysis Code (DAC) software [refs. 9-13] represents 

NASA’s state-of-the-art implementation of the DSMC method for analyzing rarefied flows. 

The aerodynamic and aeroheating databases are developed by simulating steady-state flows at 

various altitudes (density ranges) and orientations along the expected trajectories for each 

atmosphere under consideration. Once completed, the databases are used by the reference 

simulation and thermal modeling to determine the aerodynamic forces and heating on the vehicle 

throughout atmospheric flight. In the current study, no new modeling was required to be 

developed beyond the standard DSMC practices. (Refer to Appendix C for a complete 

discussion on physical models used, flow conditions, and assumptions made.) 

7.3.1.3 “Truth” Atmosphere

The Mars-GRAM is an engineering model of the Mars atmosphere used in the AA reference 

simulations. Mars-GRAM is based on the Ames Research Center (ARC) Global Circulation 

Model. The model includes spatial (altitude, latitude, and longitude), seasonal, and diurnal 

variations along with perturbation (tides, gravity waves, etc.) variations. The model also 

assimilates data from instruments on recent Mars missions and measurements from past Mars 

AB missions to generate a realistic representation of the atmospheric conditions. For example, 

the model has extensive heritage with Mars mission design and mission operations and has been 

used in much of the mission design simulation work associated with Mars. A detailed 

description of Mars-GRAM 2010 is given in Appendix E. 

Previous versions of Mars-GRAM were less accurate when used for sensitivity studies for 

off-nominal conditions. As part of the AA Phase 1 work, analysis was performed to find 

possible solutions to the differences seen in the sensitivity studies. Mars-GRAM was evaluated at 

locations and times of Thermal Emission Spectrometer (TES) limb observations, and adjustment 

factors (ratio of observed TES density to Mars-GRAM density) were determined. Details of the 

adjustment factor requirements and the development of these factors are given in Appendix E. 

The addition of the adjustment factors has led to better correspondence to TES Limb data from 

0 to 60 km and better agreement with MGS, Mars Odyssey, and MRO data at approximately 

90–135 km. Results demonstrating the improvement of Mars-GRAM 2010 results at lower 

altitudes and AB altitudes are given in Appendix E and generate more realistic atmospheres for 

the Mars AA “truth” simulation. Improved simulations of the atmospheric density utilizing 

Mars-GRAM 2010 are vital to developing the onboard atmospheric density estimator for the AA 

Development Plan. 
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Titan-GRAM and Venus-GRAM were used to generate density data sets for AB design reference 

simulation trajectories at those destinations. Despite the much smaller data set with which to 

verify the models, these data sets still provide altitude profiles (both vertical and along a 

trajectory) GRAM perturbations (tides, gravity waves, etc.) and provided density and scale 

height values. (See Appendix E for more information.) 

All of these atmospheric models have input parameters that allow the user to control the level of 

density perturbation during an atmospheric pass. The nominal perturbations that would be 

produced for Mars, Venus, and Titan for two representative orbits are shown in Figures 7.3-2, 

7.3-3, and 7.3-4, respectively, as the ratio of the perturbed density to the mean density at that 

location and time. Each atmospheric pass has an inbound leg (pre-periapsis) and an outbound 

leg (post-periapsis). As can be seen in the figures below, the density profile sensed on the 

inbound leg can be significantly different than that of the outbound leg. 

The modeled perturbations for Mars are larger than the modeled perturbations for Venus and 

Titan. Because there have been three AB missions at Mars, there is now sufficient data to 

develop a Mars atmospheric model based entirely on flight data rather than using Mars-GRAM 

perturbed atmospheres. This is planned as part of the Phase 2 effort. Because of the limited 

flight data available for Titan and Venus, Phase 2 will look at increasing the level of 

perturbations that is provided by the models at Venus and Titan. 

Figure 7.3-2. Mars-GRAM 2010 Density Perturbations 
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Figure 7.3-3. Venus-GRAM Density Perturbations 

Figure 7.3-4. Titan-GRAM Density Perturbations 
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7.3.2 Onboard AA Models 

The following section describes the models that comprise the AADS flight software module. 

The AADS module has access to only select parameters passed to it by the spacecraft. It uses 

that information to calculate a maneuver direction, magnitude and epoch of maneuver required to 

maintain a specified corridor. 

7.3.2.1 Autonomous Atmosphere Estimator 

The purpose of the onboard Atmosphere Estimator is to determine values of relevant 

atmospheric parameters for the next AB pass by utilizing IMU accelerometer and gyroscope data 

from previous AB passes. The parameters are used to predict atmospheric density in the vicinity 

of the next periapsis, which is subsequently used to determine the maneuver required to raise or 

lower the periapsis for the next AB pass. Previous AB missions have used a variety of 

atmospheric parameterizations to analyze IMU data, but in the final analysis they reduce to an 

estimate of density at periapsis and a density scale height. In addition, radio tracking data (from 

DSN) have been used to estimate a single atmospheric parameter for each AB pass. After 

appropriate scaling, these two methods have agreed within 2 percent to 5 percent on the 

prediction of density at periapsis, well within the uncertainty of each method. Therefore, the 

methods that use IMU data have been validated and are likely candidates for onboard 

atmospheric density estimation. However, these methods benefited from having an accurate 

estimate of the spacecraft’s orbit so that the altitude of the vehicle during a pass could be 

accurately correlated with the measured acceleration due to the atmospheric forces. Onboard 

atmospheric estimation methods will likely have to be robust enough to account for ephemeris 

errors and this is probably the issue that will limit the duration of AA before the ephemeris 

requires updating based on radio-tracking data. Finally, during previous Mars AB operations, 

several schemes were used to estimate atmospheric parameters from IMU data and human 

experience was used to select the “best” solution to be used for operations. Thus, onboard 

estimation methods will make decisions based on knowledge gained from human experience. 

During Phase 1, extensive studies were performed using IMU data from the three Mars missions 

(MGS, Mars Odyssey, and MRO). There are no IMU AB data for Venus (there were no 

accelerometers onboard Magellan) or Titan (there have been no previous AB missions). 

Searches were performed to determine the data ranges and atmospheric parameterizations that 

produced the best estimate of the density at the next periapsis location. Density at the next 

periapsis was estimated using combinations of different numbers from previous orbits and 

different filtering methods. In addition, traditional, symmetric parameterizations that depend 

only on altitude were compared with unsymmetrical parameterizations that depend on time and 

altitude. To find a possible way of accommodating ephemeris errors, parameterizations that 

depend only on time were studied in an approximate manner. To evaluate the influence of large 

ephemeris errors completely would require the complete reanalysis of over 1,500 AB orbits from 

the three missions, an activity reserved for Phase 2. At the end of all these studies (in Phase 1), a 
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software system was designed for onboard atmospheric estimation that (1) uses the simplest 

reliable atmospheric parameterization and (2) is completely parameterized so that all constants 

which might vary with planet, latitude, local solar time, altitude, or season are constants in only 

two routines. This provides the ability for ground operations to occasionally update the 

algorithms to maximize performance during the course of an AB mission. (For more 

information, see Appendix F.) 

7.3.2.2 Autonomous Ephemeris Estimator 

Because all events that occur in each AB orbit depend on precise knowledge of the location and 

timing of the spacecraft in orbit, an essential element of the AA software is an algorithm that 

calculates the spacecraft ephemeris onboard for several days. The Ephemeris Estimator provides 

an on-going running estimate of the spacecraft orbital state as well as a prediction of the orbital 

state of each upcoming orbit throughout the AB mission phase. The Ephemeris Estimator is 

designed to numerically integrate the spacecraft orbital equations of motions about the planet 

using model parameters and initial conditions that are uplinked from ground-based processing. 

Once initialized, the Ephemeris Estimator processes onboard accelerometer measurements to 

account for the accelerations due to atmospheric drag and propulsive maneuvers to produce a 

trajectory prediction through the next drag pass. The Ephemeris Estimator can be re-initialized 

by up-linked ephemeris data from DSN, so that a more accurate prediction can be maintained. 

The longer the Ephemeris Estimator can maintain an accurately predicted orbital state, the longer 

the autonomous spacecraft operation can be sustained without a revision of the orbital state from 

the ground using DSN. 

The AADS provides the Ephemeris Estimator with high-level interfaces to trajectory-related data 

stored in the spacecraft memory, to the spacecraft accelerometer measurements, and to spacecraft 

event flags. The parameters include the initial spacecraft state, dynamic model parameters, and 

all required natural body ephemerides. The accelerometer data is delivered to the Ephemeris 

Estimator as time-tagged acceleration data at 10 Hz. The time tags are in ephemeris time in 

seconds past J2000 format. The accelerations are in units of meters per second squared (m/s2

) 

and are supplied as Cartesian components in Earth mean equator and equinox of J2000 

coordinates. This acceleration data includes any orbit trim maneuver that occurred on the current 

orbit followed by the acceleration data due to drag during the passage through the atmosphere on 

the current orbit. (For more information, see Appendix G.) 

7.3.2.3 Autonomous Maneuver Estimator 

Among the parameters uploaded to the AADS during a ground update are the limits for the AB 

design corridor as well as the target within that corridor. The Maneuver Estimator processes data 

from both the Ephemeris Estimator and Atmospheric Estimator to obtain a prediction of the 

control parameter at the next periapsis. If the parameter is outside of the designed corridor, then 
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the Maneuver Estimator logic determines the magnitude, direction, and execution time for the 

burn and passes that information back to the spacecraft. 

For example, at Mars, data from the Ephemeris and Atmosphere Estimators are used to estimate 

the freestream heat rate at periapsis during the next atmospheric pass. If the estimate is outside 

of the operational corridor, then a maneuver is calculated such that the predicted heat rate for the 

next periapsis is at the target location within the corridor. First, a desired change in altitude is 

calculated using: 

)ln()ln(

predicted

desired

s

predicted

desired

s

q

q Hh H





 





Eq. (7.3-1)

where ∆h is the required altitude change and Hs is the predicted atmospheric scale height. This 

change in altitude is added to the current estimated periapsis altitude, which is then added to the 

estimated apoapsis altitude to determine a new orbit semi-major axis, from which a new velocity 

at apoapsis is determined. The difference between this new apoapsis velocity and the current 

estimate of the apoapsis velocity is the required maneuver magnitude. This value is positive for 

a periapsis raise (decrease freestream heating rate) and negative for a periapsis lowering 

(increase freestream heating rate). The maneuver direction is estimated to be that of the premaneuver velocity vector at apoapsis. Since the burn duration of these maneuvers is small 

compared to the orbital period, this assumption works well, even when considering a finite burn. 

7.3.2.4 Thermal Response Surface Algorithms 

A high-fidelity thermal model of MRO was developed for use in this AA simulation study. 

Response surface equations based on 13 environmental, material, and modeling properties were 

derived from this high-fidelity MRO thermal model and integrated into the AADS. The highfidelity thermal model was developed using the Thermal Desktop®

software. The exclusive use 

of Thermal Desktop®

represents a simplification of previously developed AB thermal analysis 

methodologies. Comparisons were made between the Thermal Desktop®solutions and those 

developed for the previous AB thermal analyses performed on the MRO during AB operations. 

Thermal analysis and response surface equations were developed for AA missions at Mars and 

Venus. (See Appendix D for detailed information.) A thermal analysis was not constructed for 

Titan since an altitude corridor was used for design, and thermal constraints are not likely a 

limiting factor for a Titan mission. 

Though the thermal algorithm is used to predict solar array temperature in the AADS, it is also 

employed in the “truth” simulations as a monitor of the solar array temperature. In Phase 4 of 

AA development, thermocouple sensors onboard the spacecraft will provide further validation of 

the models. 
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7.4 AADS Model Integration 

The AADS is a suite of models and algorithms intended to demonstrate the capability of an 

AA system. Three separate AADS packages were developed for this study, one each for Mars, 

Venus, and Titan. The AADS for application at Mars and Titan consists of three distinct 

modules: (1) the Ephemeris Estimator which processes spacecraft IMU acceleration data to 

estimate current and future spacecraft states, (2) the Atmosphere Estimator which processes 

spacecraft acceleration data along with Ephemeris Estimator state data to estimate the 

atmospheric density and scale height, and (3) the Maneuver Estimator which processes data from 

both the Ephemeris and Atmosphere Estimators to determine whether a maneuver is required 

(and the direction, magnitude, and execution time if one is needed) to keep the spacecraft within 

the desired operational corridor. In addition to these three modules, the AADS for Venus 

includes a fourth module containing temperature models to predict the maximum temperature the 

spacecraft will encounter during the next atmospheric pass. 

The AADS is designed to output to the spacecraft a maneuver vector and its associated apoapsis 

time. With this information, the spacecraft can autonomously execute maneuvers at apoapsis to 

correct its periapsis altitude so that its design parameters are maintained within the specified 

corridor (e.g., heat rate, temperature, dynamic pressure, or altitude). In addition, the AADS 

outputs the atmospheric entry/exit state estimates so that the spacecraft can properly slew to AB

configuration and begin and end its atmospheric data collection at the appropriate times. 

The required AADS input data is passed into the AADS through two data structures; the first 

data structure includes parameters which are likely to change between AADS calls 

(e.g., spacecraft acceleration data), and the second data structure contains data not likely to 

change between AADS calls, but which may be changed and uploaded to the spacecraft during 

the weekly update cycle (e.g., corridor definition and target). At each AADS call, all 

calculations are performed and the required data are then passed back to the spacecraft through a 

separate data structure. At this time, the AADS can be placed in stand-by mode or terminated 

until the next AADS function call to release spacecraft resources for other activities. Onboard a 

spacecraft, the AADS will not always be running but instead is called once per orbit, typically 

after an atmospheric pass ends and prior to the next apoapsis. Some AADS data do need to be 

preserved between AADS calls (e.g., Ephemeris Estimator current state prediction and 

Atmosphere Estimator atmosphere archive data), so at least a portion of the spacecraft memory 

will be allocated and preserved while AADS is not running. Additional details regarding the 

AADS interfaces, data flow, and operation are included in Appendix H.

It is important to note that if a maneuver is commanded but for some reason is not executed 

(e.g., due to some issue with the spacecraft or some other operational consideration), this does 

not affect the AADS in any way. Each call to the AADS is distinct and independent with only 

limited information being passed from one call to the next. This information does not include 

any maneuver information. All accelerations (both from maneuvers and drag passes) are passed 
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through the IMU acceleration data. In this way, any alteration, either deliberate or due to a 

spacecraft or commanding error or complete elimination of a maneuver, will be represented in 

the acceleration data it is provided during the next call. 

The AADS has been developed for technology capability testing using generalized spacecraft 

models based on MRO (see Section 7.3.1 for more information). When a flight vehicle is 

selected for AADS implementation, the simulation aerodynamic and AADS thermal models 

must be adapted to that specific vehicle. The maneuver calculation, Atmosphere Estimation and 

Ephemeris Estimation models are not vehicle specific and do not require modification once 

validated. 

7.5 AA Simulation Results 

The performance of AADS was evaluated using two simulation methods: POST2 and the 

MESSENGER-based simulation at APL which is referred to as the AAHFS. The POST2 

analysis was conducted in 3-DOF using the forces (no moments), which provided a baseline 

analysis of the key elements of AA. The AAHFS analysis was conducted using a 6-DOF

simulation based on the flight software and truth models previously developed for the 

MESSENGER spacecraft, currently orbiting Mercury. Several advantages of the AAHFS 

analysis is the inclusion of sensor and actuator models, and the capturing of interactions between 

rotational and translational dynamics, which provides a higher fidelity testing environment that is 

closer to flight. Additional discussion of the higher fidelity captured by the AAHFS is provided 

in Section 7.5.2.

The AADS module is called from both “truth” simulations from POST2 and AAHFS, which 

provide it with only the required input parameters and IMU data described in the previous 

sections. Using the autonomous internal models, AADS made a decision to (or not to) perform a 

maneuver and passes only the maneuver vector and time of apoapsis back to the “truth” 

simulation. This section demonstrates the performance of AADS via AB mission simulations in 

both POST2 and AAHFS. Where appropriate, these simulation results have been compared 

against the reference simulations described in Sections 7.1 and 7.2, and Appendix B. 

7.5.1 AADS Performance: POST2 Analysis 

The key requirement for successful AADS operation is maintaining spacecraft safety throughout 

the AB mission. To demonstrate that AADS can accomplish this task, several AB simulation 

analyses were successfully completed for each destination: Mars, Venus, and Titan. For each 

simulation environment (POST2-based, and AAHFS), AADS predictions are compared with the 

“truth” simulation. In the AADS POST2 analyses, AADS is used to predict the upcoming 

atmospheric pass conditions; determine the spacecraft’s likely location with respect to the 

operational corridor; and if necessary, command the spacecraft to execute a maneuver at the 

following apoapsis to achieve a specified target within the corridor during the following pass. 

Unlike the reference simulation, the AADS operation allows these maneuvers to occur on each 
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and every orbit, if necessary. These operations are all done autonomously within the AADS 

software, and the maneuver commands are passed back to the “truth” simulation where their 

execution is simulated, as if AADS were running onboard the spacecraft. Updates to AADS are 

also simulated. These updates would be used in real mission operations to periodically reinitialize the Ephemeris Estimator with a new truth state, update corridor and corridor target 

parameters, etc. The goal of these analyses is to show that the AADS system can provide 

sufficient performance (with margin) without interaction from the ground for at least 1 week. 

Because of the high level of flexibility and modularity of POST2 and its extensive heritage and 

flight validation, it was possible to integrate the AADS code with POST2 in a way that is “flightlike.” The Interface Control Document for AADS can be found in Appendix J. In this 

simulation environment, POST2 takes on the role of modeling the physical environment as well 

as standing in as the spacecraft itself, where AADS is then executed through the POST2 flight 

software interface, in much the same way it would be implemented onboard the spacecraft. The 

needed interface data structures are created on the spacecraft/POST2 side and passed into the 

AADS. As would be the case onboard the spacecraft, the AADS code has no other connection to 

POST2 or the “outside world,” and vice versa, except through this data structure interface. Once 

integrated, the POST2 and AADS code are compiled into a single executable which is then run 

using the POST2 user interface. 

With the AADS software successfully integrated into the POST2 simulation environment, AADS 

performance has been assessed for application at Mars, Venus, and Titan. The “truth” simulation 

(the POST2-based simulation that utilizes AADS maneuver data) utilizes the same planetary, 

atmosphere, gravity, spacecraft, and aerodynamics models as the reference simulation (see 

Sections 7.1 and 7.2). However, to initialize the AADS, the state from the seventh orbit is 

extracted from the reference simulation results and used as the simulation initial state to allow 

data from the first seven atmospheric passes to be used for building the atmosphere archive 

needed by the Atmosphere Estimator. (During operations, this archive would likely be 

constructed during the “walk-in” phase, while there is still ground interaction and prior to 

initiation of the AADS system.) The same operational corridors as the reference simulation 

analyses are used for the “truth” simulation and AADS logic; however, because this system is 

fully autonomous and maneuvers are allowed to occur at any apoapsis, the corridor target 

selection can differ from that of the reference simulation analyses. 

7.5.1.1 AADS Module Performance at Mars 

Ephemeris Estimator Performance Assessment 

The Ephemeris Estimator performance can be assessed by examining how well the AADS 

module estimates the current (last occurring) periapsis state as compared to the POST2 “truth” 

simulation. Figure 7.5-1 illustrates this performance at Mars when assuming a perturbed 

atmosphere (using the perturbation functionality available within the Mars-GRAM “truth” 

atmosphere) and weekly ground updates, in terms of the differences in estimated periapsis time 
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and altitude. At the start of the simulation and immediately following each ground update, when 

the Ephemeris Estimator is initialized with a POST2 state, the performance is quite good and 

shows excellent agreement (sub-second and meter level) between the Ephemeris Estimator and 

POST2 estimates. As time progresses, drifting in the Ephemeris Estimator propagation (due to 

differences in integrators, etc.) and a growth in error from the lack of precision (i.e., data rate) in 

the acceleration data provided by the spacecraft (during both the atmospheric pass and 

maneuver), causes the Ephemeris Estimator estimates to diverge, but never by more than 

10 seconds or 700 meters (m). 

Figure 7.5-1a. AADS Ephemeris Estimator Performance at Mars with Perturbed Atmosphere (and 

7-day Updates): Current Periapsis Time 
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Figure 7.5-1b. AADS Ephemeris Estimator Performance at Mars with Perturbed Atmosphere 

(and 7-day Updates): Current Periapsis Altitude 

Atmosphere Estimator Performance Assessment 

The Atmosphere Estimator performance can be assessed by comparing the density and scale 

height estimates for the next periapsis against the “truth” MarsGRAM-2010 atmosphere model 

values. Since the Atmosphere Estimator is attempting to fit a mean curve to the acceleration/ 

density prediction, it is appropriate to make this comparison using an AADS run with a nominal 

atmosphere. As Figure 7.5-2 shows, the Atmosphere Estimator density prediction is generally 

within 10 percent and the scale height within ~ 1 km (~ 15 percent) of the actual from the 

Mars-GRAM 2010 model. The difference in the scale height estimates can be tied to the drift in 

the Ephemeris Estimator periapsis time and altitude (profile) estimates. As previously discussed, 

improvements to the Atmosphere Estimator to update the algorithm to be independent of altitude 
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estimates are currently planned for Phase 2 and should provide enhanced Atmosphere Estimator 

performance. 

Figure 7.5-2a. AADS Atmosphere Estimator Performance at Mars (with 7-day Updates): Predicted 

Periapsis Atmospheric Density 
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Figure 7.5-2b. AADS Atmosphere Estimator Performance at Mars (with 7-day Updates): Predicted 

Periapsis Atmospheric Scale Height 

AADS Performance Assessment 

To analyze the details of the prediction capability within the designed corridor per orbit, a 

summary of the AADS performance and margin throughout a Mars AB mission scenario using a 

perturbed atmosphere is provided in Figure 7.5-3. The capability is measured in terms of how 

well the spacecraft stays within the mission operations corridor. These plots show that the 

AADS system successfully keeps the spacecraft within the specified corridor and illustrates the 

difference between the AADS predicted freestream heat rate (red) and the estimated “truth” heat 

rate (blue), which is mainly driven by the differences between the Atmosphere Estimator density 

and scale height estimates from those of the Mars-GRAM 2010 atmosphere model. This is 

illustrated for ground update frequencies of 3, 5, 7, and 14 days. (See Figure H.2 in Appendix H 

for a more detailed description of how to interpret the mission corridor plot.) 
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Figure 7.5-3a. AADS Mission Operations Corridor Performance at Mars with a Perturbed Atmosphere 

and 3-day Updates 
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Figure 7.5-3b. AADS Mission Operations Corridor Performance at Mars with a Perturbed Atmosphere 

and 5-day Updates 
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Figure 7.5-3c. AADS Mission Operations Corridor Performance at Mars with a Perturbed Atmosphere 

and 7-day Updates 
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Figure 7.5-3d. AADS Mission Operations Corridor Performance at Mars with a Perturbed Atmosphere 

and 14-day Updates 
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As expected, this variation in update frequency has little effect on the AADS performance, as 

illustrated in Table 7.5-1, which compares the mean of the absolute value percent difference 

between predicted and “truth” heat rate and 1 variance in those percent difference values. As 

previously described, the driving constraints on the AADS performance are the drift in the 

Ephemeris Estimator integration, and to a lesser extent, the Atmosphere Estimator density 

estimate accuracy. 

Table 7.5-1. Summary of AADS Heat Rate Estimate Performance Variability for Various Ground 

Update Frequencies 

Update Frequency (days) Mean

(percent)

1

(percent)

3 11.11 10.95

5 9.55 8.69

7 11.31 10.65

14 11.34 10.99

This small variability in performance for all update frequencies is another measure of how well 

the Ephemeris Estimator and Atmosphere Estimator are performing. The perturbations in the 

atmosphere do introduce additional variability in the heat rate estimate. However, both the 

Ephemeris and Atmosphere Estimators are now working with acceleration data that reflect these 

atmospheric variations. This effect can be seen when comparing against a nominal atmosphere, 

where the corridor performance is much improved (as seen in Figure 7.5-4 and illustrated by the 

heat rate estimate performance mean being closer to 6.00 percent with a 1 variance of 

7.26 percent). 

What is most important to note from Figure 7.5-3 and Table 7.5-1, however, is that with a 

requirement of no less than 7 days between ground updates, the spacecraft could survive with 

little or no ill effects for up to at least 14 days while maintaining significant operational margin. 
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Figure 7.5-4. AADS Mission Operations Corridor Performance at Mars with a Nominal Atmosphere 

(and 7-day Updates) 

7.5.1.2 AADS Mars Comparisons to Reference Simulation 

With simulations complete for both the Mars AB reference simulation and the “truth” simulation 

with AADS implementation, it is now possible to compare the system performance between 

these two analyses. Figure 7.5-5 provides a comparison of the AB mission profile using the 

AADS (incorporating a perturbed atmosphere and 7-day updates) to the reference simulation, 

including the difference between the AB “glideslope” (orbit period versus time) and a 

comparison of the commanded maneuvers, orbit periapsis altitudes, and periapsis locations 

(areocentric latitude) as a function of time. 
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Figure 7.5-5a. AADS with Perturbed Atmosphere (and 7-day Updates) Comparison with Reference 

Simulation at Mars: Orbit Period “Glideslope” 
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Figure 7.5-5b. AADS with Perturbed Atmosphere (and 7-day Updates) Comparison with Reference 

Simulation at Mars: Commanded Maneuver ∆V 
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Figure 7.5-5c. AADS with Perturbed Atmosphere (and 7-day Updates) Comparison with Reference 

Simulation at Mars: Periapsis Altitude 
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Figure 7.5-5d. AADS with Perturbed Atmosphere (and 7-day Updates) Comparison with Reference 

Simulation at Mars: Periapsis Areocentric Latitude 

These plots demonstrate that AADS is accurately calculating maneuvers to generate AB missions 

similar to those simulated using traditional AB design methods (i.e., the reference simulation). 

The AADS mission is shorter in duration because maneuvers of any size are allowed at apoapsis 

versus the imposed constraint of one maneuver no more frequently than every 7 days in the 

reference simulation. In reality there may be some minimum engine thrust that is allowed or 

collision avoidance criteria that imposes constraints on maneuvers. These considerations will be 

evaluated in future phases. 

The comparison of the simulation using AADS against the reference simulation analysis is 

summarized in Table 7.5-2 below.
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Table 7.5-2. Summary of AADS Performance with a Perturbed Atmosphere (and 7-day Updates) 

Compared to Reference Simulation at Mars 

AADS Reference 

Simulation

AB Duration (days) 146.2 174.7

Total ∆V (m/s) 15.9 7.9

Number of Maneuvers 62 21

The reduction in the AB duration in the simulation incorporating AADS as compared to the 

reference simulation is due to the AADS ability to perform a maneuver on each and every orbit, 

if necessary, whereas the reference simulation only allows a maneuver once per week (as 

illustrated in the number of maneuvers). The increase in total ΔV is mainly a consequence of 

comparing the “truth” simulation incorporating AADS, which uses a perturbed atmosphere, 

against the reference simulation, which uses a nominal atmosphere. These atmospheric 

perturbations have a strong effect on the AADS estimates, including the required maneuver 

magnitudes. 

7.5.1.3 Effects of Changing Corridor Limits 

As discussed earlier, when the spacecraft heat rate increases, the orbital periapsis is at lower 

altitude; likewise, an elevated altitude results in a lower heat rate. It follows then that changing 

the corridor limits (and/or the target within the corridor) can have a significant effect on the AB 

mission duration as well as the number of maneuvers performed. The corridor can be modified 

to accomplish any number of objectives: to ensure proper terminal orbit conditions, to conserve 

propellant, or to increase or decrease thermal margin. To illustrate the effects of modifying the 

corridor limits, the AADS AB mission was simulated again using a tight operational corridor 

(0.02 W/cm2

in width) centered at the nominal corridor lower limit (0.11 w/cm2) and again at the 

nominal corridor upper limit (0.17 W/cm2

). Figure 7.5-6 illustrates the corridor performance for 

these cases; a summary of the mission performance is provided in Table 7.5-3.
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Figure 7.5-6a. AADS Constrained Mission Operations Corridor Performance at Mars with a Perturbed 

Atmosphere (and 7-day Updates) for a Tight Corridor Centered on the Nominal Corridor Lower Limit 
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Figure 7.5-6b. AADS Constrained Mission Operations Corridor Performance at Mars with a 

Perturbed Atmosphere (and 7-day Updates) for a Tight Corridor Centered on the Nominal Corridor 

Upper Limit 

Table 7.5-3. Summary of AADS Performance at Mars with a Nominal Atmosphere for Runs using 

the Nominal Operational Corridor, a Corridor Constrained to the Nominal Corridor Upper Limit, 

and One to the Nominal Corridor Lower Limit 

Nominal 

Corridor

Corridor at 

Lower Limit

Corridor at 

Upper Limit

AB Duration (days) 146.2 176.5 116.4

Total ∆V (m/s) 15.9 36.6 28.9

Number of Maneuvers 62 249 227
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Figure 7.5-6b does show some increased volatility in the AADS predictions as the AB mission 

progresses for the more aggressive corridor, as compared to Figure 7.5-6a which uses a more 

conservative corridor. This volatility is driven by the aggressive nature of corridor (e.g., low 

altitude = higher density) and its impact on the accuracy of the Ephemeris Estimator’s integration 

of the atmospheric pass acceleration data, and thus the Atmosphere Estimator’s density 

estimates. Since density information is estimated almost directly from acceleration data, and 

AADS will be more sensitive to these estimates due to the higher density environment, lack of 

sufficient resolution of the acceleration data will result in earlier and/or more rapid divergence 

within the AADS. As the mission progresses and the orbit period reduces, the Ephemeris 

Estimator propagation relies more heavily on acceleration data as the atmospheric passes become 

longer and more frequent. 

The accuracy at which AADS can maintain such a tight operational corridor will also be driven 

by the accuracy in the predicted freestream heat rate. Any improvements in the Atmosphere 

Estimator density and scale height estimates will narrow the spread between the predicted and 

actual, improve the required maneuver estimate to reach the target in the corridor, and thus 

further improve the overall corridor performance. 

This effect of corridor selection on mission duration can be further emphasized by evaluating the 

mission performance using AADS for a corridor with the same width as the nominal analysis 

(0.06 W/cm2), but shifted up by that same amount (0.17–0.23 W/cm2) to significantly reduce the 

time required for AB (as shown in Figure 7.5-7) without any impact to the number of maneuvers 

and/or ΔV required (which are driven more by the corridor size and target). Table 7.5-4 provides 

a comparison between the nominal and this more aggressive AB mission. Figure 7.5-7 shows 

the same immediate action line limits as for the nominal mission corridor, further illustrating the 

importance of selecting an operational corridor which ensures sufficient spacecraft safety margin 

throughout the AB mission. 
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Figure 7.5-7. AADS Mission Aggressive Operations Corridor Performance at Mars with a Perturbed 

Atmosphere (and 7-day Updates) 
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Table 7.5-4. Comparison of AADS Performance at Mars with a Perturbed Atmosphere (and 7-day 

Updates) for the Nominal and Aggressive Operational Corridors 

Nominal 

Corridor

Aggressive 

Corridor

AB Duration (days) 146.2 101.1

Total ∆V (m/s) 15.9 13.9

Number of Maneuvers 62 69

The glideslope, or plot of orbit period or apoapsis altitude reduction over time, provides the 

metric that determines how quickly an AB mission can be performed. Following the reference 

simulation glideslope is sufficient to ensure that all desired terminal orbit conditions (e.g., orbital 

period, periapsis altitude, LMST, etc) are met at the end of the AB phase. Based on the results in 

the previous section, modifying the corridor can adjust the duration and therefore the current 

glideslope of an AB mission. In this way, ground operators can easily control the glideslope of 

an AB mission by simply manipulating the corridor bounds at ground updates. To demonstrate 

this concept of glideslope control, an additional analysis using AADS was successfully 

completed using the POST2 simulation at Mars. In this simulation, after some period of time in 

nominal AB, AADS is instructed (through the spacecraft update capability) to dramatically lower 

the operational corridor. At Mars, this raises the periapsis altitude higher than it would have 

been during the nominal mission, thus reducing drag, and results in the spacecraft “falling 

behind” the nominal glideslope. After approximately 1 week, AADS is commanded to increase 

the upper corridor limit back to where it was for the nominal mission and to dramatically 

increase the lower corridor limit. This decreases the periapsis altitude target deeper into the 

atmosphere, increasing drag, steepening the glideslope, and allowing the spacecraft to eventually 

recover the nominal glideslope after about 2 weeks. A subtle, but profound implication of this 

analysis is that it demonstrates how AADS can be used to reduce risk during off-nominal AB 

operations, as the nominal glideslope was recovered without raising the upper corridor bound 

(i.e., without reducing thermal margin). Figure 7.5-8 shows the effect of this scenario on the 

glideslope profile, as compared to the reference simulation, while Figure 7.5-9 shows the effect 

on the operational corridor and resulting AADS performance. 
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Figure 7.5-8. AADS Glideslope Delay and Recovery Scenario at Mars with a Perturbed Atmosphere 

(and 7-day Updates) 
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Figure 7.5-9a. AADS Mission Operations Corridor Performance for the Nominal Corridor 
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Figure 7.5-9b. AADS Mission Operations Corridor Performance for the Glideslope Delay and 

Recovery Corridor 

Note that Figure 7.5-8 shows that not only is the nominal mission glideslope recovered, but the 

glideslope is steeper. This is a result of the spacecraft being left high in the corridor at the end of 

the recovery period, much higher than during the same time period in the nominal case (see 

Figures 7.5-9a and b). Due to the specific orbit geometry, the natural tendency is for the 

spacecraft to remain near the top of the corridor for over 2 weeks (days 70–85 in Figure 7.5-9b) 

before the first maneuver is required. If it is deemed necessary to immediately return closer to 

the nominal glideslope, this could be achieved simply by lowering the top of the corridor (which 

increases spacecraft safety margin), resulting in AADS commanding a maneuver to push the 

spacecraft lower into the corridor, until the nominal glideslope is fully recovered. At that time, 

the corridor upper limit can be returned to its nominal value. 

With AADS, this scenario is successfully achieved autonomously, with only three required 

corridor updates from the spacecraft: (1) delay the glideslope, (2) recover the glideslope, and 
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(3) return to nominal glideslope. It is accomplished simply by changing the desired corridor and 

target, thus altering when and how many maneuvers are executed during the affected time 

period. In addition, it is significant to note that all of this is accomplished without the need to 

violate the nominal mission upper corridor limit, thus introducing no additional spacecraft risk. 

With ground-based AB operations, recovery of the nominal glideslope would likely not be 

possible without increasing the upper corridor limit due to the constraint on maneuver execution 

frequency. 

7.5.1.4 AADS Performance at Venus and Comparisons to Reference Simulation 

At Venus, data from the Ephemeris and Atmosphere Estimators are used with a spacecraft 

thermal model to estimate the (spacecraft solar panel) temperature at periapsis during the next 

atmospheric pass. If the predicted temperature is outside of the operational corridor, then the 

same spacecraft thermal model is used to estimate the desired atmospheric density, given the 

predicted spacecraft orbital state at the next periapsis, and the desired target temperature within 

the corridor. From this information, a maneuver is calculated similarly to that for Mars (see 

Section 7.3.2.3). 

Many other differences exist between AB missions at Mars and at Venus which affect the 

performance of the AADS. For example, at Venus, the effects of the Sun, both in terms of third 

body gravitational effects and solar radiation pressure, have a real influence on the spacecraft 

orbit. This, coupled with the higher orbital velocities (due to the more massive planet) and the 

much higher atmospheric density, is what would likely drive a mission operations team to utilize 

a temperature corridor during AB, as opposed to the heat rate corridor used at Mars. In addition, 

the atmospheric perturbations at Venus (as provided by Venus-GRAM) are much less that those 

at Mars. This means that at Venus, as it is at Mars, an update frequency up to 14 days or longer 

will provide sufficient AADS performance to ensure spacecraft safety throughout the AB 

mission. 

A summary of the AADS performance within the mission operations temperature corridor for the 

Venus AB “truth” simulation with a perturbed atmosphere (and 7-day updates) is provided in 

Figure 7.5-10. 
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Figure 7.5-10. AADS Mission Operations Corridor Performance at Venus with a Perturbed 

Atmosphere (and 7-day Updates) and a Fixed Corridor Target 

The strong solar effects are visible where the spacecraft is pulled to either the top of the corridor 

or the bottom, depending on where the Sun is located relative to Venus and the spacecraft. To 

better take advantage of these effects, the target within the corridor can be varied during the 

mission using the weekly update capability, as illustrated in Figure 7.5-11. This approach can 

reduce the number of maneuvers required to maintain the operational corridor without the need 

to change the corridor itself. 
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Figure 7.5-11. AADS Mission Operations Corridor Performance at Venus with a Perturbed 

Atmosphere (and 7-day Updates) and a Varying Corridor Target 

Table 7.5-5 provides a summary comparing the Venus AADS baseline performance, using a 

perturbed atmosphere and 7-day updates, for both the fixed and varying corridor target, with the 

reference simulation analysis. The difference in the duration between the AADS and reference 

simulation can be attributed to the differences in the (nominal) corridor target. It is evident that 

utilizing a variable target enables a reduction in the number of maneuvers. 
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Table 7.5-5. Summary of AADS Performance with Perturbed Atmosphere (and 7-day Updates) 

Compared to Reference Simulation at Venus 

AADS 

Fixed Target

AADS 

Variable Target

Reference 

Simulation

AB Duration (days) 195.0 198.7 174.8

Total ∆V (m/s) 21.8 22.7 18.0

Number of Maneuvers 86 67 86

7.5.1.5 AADS Performance at Titan and Comparisons to Reference Simulation 

At Titan, data from the Ephemeris Estimator is used to estimate the spacecraft altitude at 

periapsis during the next atmospheric pass. If the predicted altitude is outside of the operational 

corridor, then the difference between the predicted and desired target altitude within the corridor 

is used to calculate the required correction maneuver. This change in altitude is then added to 

the current estimated periapsis altitude, which is then added to the estimated apoapsis altitude to 

determine a new orbit semi-major axis, from which a new velocity at apoapsis is determined. 

The difference between this new apoapsis velocity and the current estimate of the apoapsis 

velocity is the required maneuver magnitude. As with Mars and Venus, this value is positive for 

a periapsis raise (decrease freestream heating rate) and negative for a periapsis lowering 

(increase freestream heating rate), and the maneuver direction is estimated to be that of the premaneuver velocity vector at apoapsis. 

More so than for Venus, AB at Titan must account for strong third body effects, but in this case, 

from Saturn. These gravitational effects can once again be utilized to design the corridor target 

to minimize the number of maneuvers required to maintain spacecraft safety within the corridor. 

As was the case with Venus, the atmospheric perturbations provided from Titan-GRAM are 

small compared to those from Mars-GRAM (and are even smaller than those from VenusGRAM as well). In addition, since this Titan analysis makes use of an altitude corridor, 

atmospheric perturbations (in density) (in conjunction with the large atmospheric scale height) 

have little to no effect on the spacecraft location within the corridor itself. 

A summary of the AADS performance for the Titan AB mission with a perturbed atmosphere 

(and 7-day updates) is provided in Figure 7.5-12. Table 7.5-6 provides a summary comparing 

the AADS mission with the reference simulation analysis. As is the case with Mars and Venus, 

an update frequency up to 14 days or longer will provide sufficient AADS performance to ensure 

spacecraft safety throughout the AB mission. 
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Figure 7.5-12. AADS Mission Operations Corridor Performance at Titan with a Perturbed 

Atmosphere (and 7-day Updates) 

Table 7.5-6. Summary of AADS Performance with Perturbed Atmosphere (and 7-day Updates) 

Compared to Reference Simulation at Titan 

AADS Reference 

Simulation

AB Duration (days) 75.5 74.1

Total ∆V (m/s) 105.0 105.4

Number of Maneuvers 9 9
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7.5.2 AAHFS 

7.5.2.1 AAHFS Modeling 

AAHFS has been developed to assess the performance of the new algorithms required for an AA

mission. This 6-DOF simulation is based on the flight software and truth models previously 

developed for JHU/APL-designed MESSENGER spacecraft, currently orbiting Mercury [ref 14]. 

This AB demonstration has been developed in the MATLAB/Simulink/RTW environment. It is 

comprised of the existing MESSENGER algorithms and software, to which the AB flight system 

and truth model test bed algorithms have been added. This approach permits rapid study of the 

AADS and, in the end, generates a high degree of confidence in the technology as a precursor to 

implementation in a flight program. Another important benefit to developing the software in this 

way is that the end product is suitable for use in a flight processor, as this study uses the same 

development environment/process as the MESSENGER guidance and control flight software. 

Figure 7.5-13 shows the AAHFS software in block diagram form. Detailed block diagrams and 

descriptions further decomposing the truth model and flight software elements are provided in 

Appendix I. The color-coding of Figure 7.5-13 indicates the organization responsible for each 

software element. As previously mentioned, the JHU/APL software is MESSENGER heritage, 

although some adaptation to the AB application is necessary, particularly in the flight software. 

The truth model modifications provided by LaRC have a rich AB flight heritage. These elements 

include an atmosphere model (Mars-GRAM 2010) and an aerodynamics model (based on MRO) 

and are integrated into the MESSENGER Simulink environment to allow testing of the flight 

software. The AADS is new algorithm code developed specifically for this project and is 

described in detail in Sections 7.3 and 7.4 of this report. These algorithms perform the necessary 

calculations to ensure the spacecraft remains safe and performs AB in the desired manner with 

limited ground intervention. The AAHFS simulation is developed as a high-fidelity, reliable, 

validated test environment to demonstrate the performance of the AADS algorithms. 
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Figure 7.5-13. AAHFS 6-DOF Block Diagram 

AAHFS provides a testing environment with spacecraft dynamic behavior in addition to the 

3DOF analysis provided by the POST2 simulations. One key advantage of AAHFS is that the 

simulation environment has 6-DOF dynamics, enabling study of the interaction between the 

rotational and translational components. This is of particular importance during AB drag passes, 

where the vehicle orientation affects the drag accelerations that, in turn, change the evolution of 

the spacecraft orbit. Another example where AAHFS provides enhanced fidelity is the use of 

acceleration data in the AADS code. Instead of using the true acceleration in AADS, AAHFS 

passes this true acceleration through: (1) an IMU model which decimates the true acceleration to 

100 Hz, (2) an emulation of spacecraft command and data handling system which collects and 

buffers these raw IMU measurements, (3) a high-rate (50-Hz) data processing task which takes 

the high-rate, raw accelerations and averages them down to a more appropriate rate for use in 

AADS, and (4) a data buffer which collects the acceleration data for use in AADS. Each step in 

the process can add uncertainty (e.g., noise, bias, scaling/rotational errors, latency, etc.) to these 

true accelerations, which can impact the fidelity of the trajectory integration in AADS. All of 

these processes must occur in a flight system and are present in AAHFS. Other examples where 

AAHFS can add realism to the simulation include the maneuver implementation and execution, 

use of gyroscope and star tracker data, modeling of attitude dynamics via the real commanding 

and use of actuator models, system angular momentum modeling, lower-order dynamic effects 

(propellant slosh, structural dynamics), and additional perturbation models for forces and 

torques. 
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7.5.2.2 AAHFS Testing 

The capabilities provided by JHU/APL’s AAHFS allow for thorough testing of the AADS. As 

with the POST2 simulation results presented in Section 7.5.2.1, the AAHFS test environment 

allows evaluation of the AADS in a closed-loop simulation. All interactions with AADS in 

AAHFS are conducted autonomously, mimicking the execution of AADS for a real flight 

program. To date, the testing with AAHFS has focused on simulations at Mars, with Venus and 

Titan testing to be done in future phases of this development. The goal of the initial testing done 

with AAHFS is to demonstrate the technical capability of the AADS algorithms under nominal 

conditions. More extensive robustness testing of AADS is planned for Phase 2. It is desirable 

for the AAHFS results to show some level of consistency with the results obtained with POST2. 

In this way, the AAHFS simulation can be used to check the POST2 simulation results, and vice 

versa. Although POST2 and AAHFS have a significant number of differences, as highlighted 

earlier in this section, by configuring some benchmark simulations in a similar way, the results 

can be shown to be qualitatively similar. It is important to note that the following results are 

consistent but not identical. Identical results can be obtained in POST2 and AAHFS only when 

the AADS inputs are precisely controlled. A test where AADS was ported to the Simulink/RTW 

environment and run as a stand-alone (or unit test) model was conducted. This unit test allowed 

the inputs to be identical between a POST2 simulation and AAHFS, and under these 

circumstances, AADS produces identical results and demonstrates that the integration of AADS 

into AAHFS does not introduce any errors. For the results presented here, all AAHFS 

simulations use the 6-DOF AAHFS truth/flight software models to generate the input data to 

AAHFS, and so an identical match to the POST2 results is not feasible. 

Several simulations were done to demonstrate the technical capability of AA and to show the 

consistency of AAHFS with the POST2 simulation results described in Section 7.5.1. As the 

goal of this effort is to demonstrate the viability of AADS for a week without ground 

intervention, these initial comparisons are conducted using a ground update interval of 7 days. 

For these initial comparisons, all disturbance sources to the accelerations have been disabled in 

AAHFS to mimic the way POST2 was run. This is a recognized shortcoming of the testing to 

date and will be addressed in Phase 2 of this development effort. Additionally, the only 

environment models that were enabled for the “truth” model portion of these simulations are 

those included in the POST2 “truth” simulation. For example, the Mars gravity field uses a 

harmonic model (of degree and order 21) and the Sun as a third-body perturbation in both of the 

“truth” models. Adding fidelity to the truth models (e.g., higher order gravity field, or additional 

orbital perturbations, etc.) to study the robustness of AADS to un-modeled dynamics is left for 

Phase 2 of this development. 

Figure 7.5-14 shows the corridor performance for an AAHFS simulation using a nominal 

atmosphere at Mars. This figure shows the heat rate corridor performance of AADS versus the 

true conditions (from the AAHFS truth model), as is plotted using the same scale as the heat rate 

plots from Section 7.5.1 for easy comparison. This simulation compares favorably with the 
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results obtained with POST2, shown in Figure 7.5-5. In both the POST2 and AAHFS 

simulation, the spacecraft remains within the corridor on nearly every orbit. It is important to 

note that this is despite the AAHFS being a more challenging simulation environment, mostly 

because the simulation is exercising all 6 DOF. AADS handles the additional complications of 

imprecision in the corridor control maneuvers and more flight-like accelerometer data collection 

methods without any notable issues. Figure 7.5-15 demonstrates the accuracy of the AADS in 

predicting the orbit period between the 7-day ground updates (shown as vertical dashed red lines 

in the figure). When a ground update occurs, the AADS orbital propagation is reset to the true 

state, and the error in the periapsis timing estimate is reset. The growth of this timing error in 

AADS is simply due to imprecision in modeling, capturing, and integrating the forces on the 

spacecraft, although for the case shown in Figure 7.5-15, the error remains below ~3 seconds. 

Improving the precision in the integration will be a subject of Phase 2 investigations, as 

imprecision in predicting periapsis is one of the main factors that would require shortening the 

ground update interval. Figure 7.5-16 shows the glideslope for this AAHFS simulation versus an 

identical run with POST2. Despite the differences between the simulations, the glideslopes are 

consistent between the two runs, as expected. The lower pane of the graphic shows an expanded 

view of the differences (POST2 period minus AAHFS period), since it is difficult to discern in 

the upper pane. 

An AB phase using AADS was also simulated using a 14-day ground update interval with the 

nominal Mars atmosphere and these results are presented in Figures 7.3-17–19. While the 

corridor performance appears similar to the 7-day update case in Figure 7.3-13, the periapsis 

timing estimates from AADS are drifting farther from the true values, due to the longer time 

between ground contact. Although the overall performance of this simulation is still good (as 

indicated by the heat rate corridor), using a 14-day ground update interval is showing signs of 

stressing the AADS algorithms. Glideslope performance for this AAHFS simulation is 

compared with the POST2 results in Figure 7.3-19, demonstrating that despite the differences 

between the simulations, the AA phase is happening at a similar rate. 
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Figure 7.5-14. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Nominal 

Atmosphere and 7-day Updates 
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Figure 7.5-15. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Nominal 

Atmosphere and 7-day Updates 
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Figure 7.5-16. AAHFS Simulation – Glideslope Performance at Mars with a Nominal Atmosphere 

and 7-day Updates 
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Figure 7.5-17. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a Nominal 

Atmosphere and 14-day Updates 
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Figure7.5-18. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Nominal 

Atmosphere and 14-day Updates 
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Figure 7.5-19. AAHFS Simulation – Glideslope Performance at Mars with a Nominal Atmosphere 

and 14-day Updates 

The results shown in Figures 7.5-14 through 7.5-19 have only used the nominal atmosphere 

conditions coming from Mars-GRAM 2010. A more useful and challenging study is to use the 

Mars-GRAM 2010 perturbed densities for the AB simulations. The same two cases (7- and 14-

day ground update intervals) were repeated using AAHFS with the density perturbations 

enabled. Because these density fluctuations are captured by the accelerometer data that is 

provided to AADS for the ephemeris and atmosphere estimation, these perturbations enhance the 

realism of the simulations, but they are not expected to significantly impact the AADS 

performance. Figures 7.5-20 through 7.5-25 demonstrate that as expected, AADS continues to 

perform well, despite the atmospheric perturbations. The increased variability in the atmosphere 

does produce a handful of small deviations from the corridor as the Atmosphere Estimator in 

AADS has more difficulty producing accurate estimates of atmospheric density for the perturbed 

case. The AADS-computed periapsis timing is consistent with the nominal atmosphere 

simulations, as expected, and the glideslope remains consistent with the nominal atmosphere 

cases (and the POST2 nominal atmosphere simulation results). The steady-state deviation in 

orbital period at the end of the simulation (when comparing AAHFS perturbed atmosphere 

versus the POST2 nominal atmosphere result), shown in the lower pane of Figures 7.5-22 and 
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7.5-25, is simply an indication that the perturbed atmosphere case completed the AA phase 

slightly faster than the nominal atmosphere case. 

Figure 7.5-20. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a 

Perturbed Atmosphere and 7-day Updates 
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Figure 7.5-21. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Perturbed 

Atmosphere and 7-day Updates 
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Figure 7.5-22. AAHFS Simulation – Glideslope Performance at Mars with a Perturbed Atmosphere 

and 7-day Updates 
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Figure 7.5-23. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a 

Perturbed Atmosphere and 14-day Updates 
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Figure 7.5-24. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Perturbed 

Atmosphere and 14-day Updates 
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Figure 7.5-25. AAHFS Simulation – Glideslope Performance at Mars with a Perturbed Atmosphere 

and 14-day Updates 

Figure 7.5-6 demonstrated that the AB duration seen in the POST2 simulations could be 

manipulated by adjusting the heat rate corridor. This figure demonstrated that using a narrow 

corridor results in an increased maneuver frequency and propellant consumption necessary to fly 

the AB mission. The same conclusions can be demonstrated with AAHFS and are shown in 

Figures 7.5-26–29. It is more difficult for AADS to remain within the narrow corridor, 

particularly with the perturbed atmosphere in place, as the atmospheric variability makes 

accurate atmosphere estimation difficult. Despite this variability, AADS does a good job of 

keeping the spacecraft near the narrow corridor. This narrow corridor does have a price, for as 

with the POST2 simulations (Table 7.5-3); it is obvious from the AAHFS results in 

Figures 7.5-26 and 7.5-28 that there is a marked increase in the maneuver frequency required to 

maintain this narrow corridor. 
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Figure 7.5-26. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a 

Perturbed Atmosphere, 7-day Updates, and a Reduced Heat Rate Corridor 
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Figure 7.5-27. AAHFS Simulation – Glideslope Performance at Mars with a Perturbed Atmosphere, 

7-Day Ground Updates, and a Reduced Heat Rate Corridor 
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Figure 7.5-28. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a 

Perturbed Atmosphere, 7-day Updates, and an Elevated Heat Rate Corridor 
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Figure 7.5-29. AAHFS Simulation – Glideslope Performance at Mars with a Perturbed Atmosphere, 

7-Day Ground Updates, and an Elevated Heat Rate Corridor 

The results of Section 7.5 focused on testing the AADS with near perfect knowledge of the true 

non-gravitational accelerations. The POST2 results of Section 7.5.1 used decimated truth 

accelerations directly in AADS. The AAHFS results of Section 7.5.2 used an IMU model, but 

the error sources typically found in the accelerations had been disabled for the test results 

presented to this point. Although a full study of AADS robustness to accelerometer errors will 

be undertaken in Phase 2, it is useful to demonstrate that AADS shows promise even in the 

presence of typical accelerometer errors. Because AAHFS already has a full IMU model in the 

software, it is simply a matter of enabling it (with an appropriate parameterization) to study the 

AADS performance. The results of this simulation are shown in Figures 7.5-30 through 7.5-32, 

and the accelerometer error sources are tabulated in Table 7.5-7. These error sources were based 

on the flight performance of the MESSENGER IMU and represent typical performance of an 

interplanetary spacecraft. This simulation case was simply a repeated run of the case shown in 

Figures 7.5-20 through 7.5-22 (e.g., 7-day updates, perturbed atmosphere, nominal corridor 

bounds), and looks similar in terms of the heat rate corridor and glideslope performance. The 

AADS periapsis timing prediction is drifting more rapidly from the true value, which is not 

surprising since the orbit knowledge is largely determined by the precision of the accelerations. 
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This increased periapsis timing error does not adversely impact the corridor performance and is 

an indication of how robust AADS currently is to accelerometer errors. This case is a strong 

indicator that AADS can be used to conduct AA with a 7-day ground update interval. 

Table 7.5-7. AAHFS Simulation – Accelerometer Error Sources per Accelerometer 

Random Noise Bias Readout 

Noise

Scale 

Factor Misalignment

1.5e-4 m/s27.2e-4 m/s21 count 240 ppm 150 arcs

Figure 7.5-30. AAHFS Simulation – AADS Heat Rate Corridor Performance at Mars with a 

Perturbed Atmosphere, Accelerometer Errors, and 7-day Updates 
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Figure 7.5-31. AAHFS Simulation – AADS Orbital Period Performance at Mars with a Perturbed 

Atmosphere, Accelerometer Errors, and 7-day Updates 
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Figure 7.5-32. AAHFS Simulation – Glideslope Performance at Mars with a Perturbed Atmosphere, 

Accelerometer Errors, and 7-day Updates 

Table 7.5-8 summarizes the cases run with AAHFS. This table shows the number of maneuvers 

and total ∆V each simulation required as well as the duration of the AB phase. The relationship 

between the corridor width and the maneuver frequency (and/or ∆V requirements) is a trade 

study that will be examined in Phase 2, but it is obvious that reducing the width of the corridor 

can greatly increase the frequency of corridor control maneuvers. Despite the much higher 

frequency of burns for the narrow corridor cases, it is not expected to pose any problems for the 

spacecraft propulsion system hardware. It can be seen from Table 7.5-5 that using a perturbed 

atmosphere and/or changing the ground update interval has little impact on the number of burns 

or total ∆V. The AB duration is slightly shorter for perturbed atmosphere cases versus the 

nominal atmosphere, but the AB duration is greatly impacted by flying an elevated or reduced 

corridor, as seen in Cases 5 and 6. (Note that Case 5 only ran the simulation to 160 days, and it 

is estimated that the AB phase would have required an additional 15–20 days to complete.) For 

Cases 5 and 6, the corridor changes greatly influence the glideslope behavior, which is readily 

seen in Figures 7.5-26 and 7.5-28. The glideslope performance of these two cases demonstrates 

that the duration of AB can be managed by either raising the entire corridor, which may raise 

mission risk, or by paying a ∆V penalty to fly a narrow corridor by leaving the upper heat rate 

corridor bound alone and raising only the lower corridor bound. Table 7.5-8 demonstrates that 

when IMU error sources were enabled in Case 7, they did not negatively impact the AB metrics 

when compared to Case 3. 
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Table 7.5-8. AAHFS Simulation – AADS Performance at Mars 

Atmosphere 

Model

Ground 

Update 

Interval

(days)

Heat Rate 

Corridor 

Upper Limit

(W/m2)

Heat Rate 

Corridor 

Lower Limit

(W/m2)

Number of 

Maneuvers

∆V

(m/s)

AB

Duration 

(days)

Figure 

Numbers

Case 1 Nominal 7 0.11 0.17 70 18.2 152 7.5-14–16

Case 2 Nominal 14 0.11 0.17 64 16.7 150 7.5-17–19

Case 3 Perturbed 7 0.11 0.17 60 15.5 143 7.5-20–22

Case 4 Perturbed 14 0.11 0.17 68 16.5 147 7.5-23–25

Case 5 Perturbed 7 0.10 0.12 194 24.3 >160 7.5-26 and 

7.5-27

Case 6 Perturbed 7 0.16 0.18 222 29.4 118 7.5-28 and 

7.5-29

Case 7

(IMU 

Errors 

Enabled)

Perturbed 7 0.11 0.17 59 14.5 145 7.5-30–32

Figure 7.5-33 demonstrates the AADS heat rate performance across all AAHFS cases. The lefthand graphics show histograms of the true heat rate from each of the orbits in the various 

simulations tabulated in Table 7.5-8. The red lines on these histograms represent the corridor 

bounds used for that case. In this view, every orbit that exceeds these bounds represents one 

maneuver. With this idea, it can be seen that Cases 5 and 6 with narrow corridor bounds had a 

great number of cases outside the corridor. Those plots show that by enlarging the corridor by 

another 0.02 W/cm2, it is likely that the number of maneuvers could be greatly reduced. Another 

observation that is apparent when comparing all the cases in this way is that the corridor 

performance is not greatly affected by perturbing the atmosphere (Cases 3–4), increasing the 

ground update interval (Cases 2, 4), or adding accelerometer errors (Case 7). The right-hand 

graphics show histograms of the heat rate difference, computed as true heat rate minus AADS 

predicted heat rate. From these histograms, it is clear that perturbing the atmosphere does flatten 

the histogram versus the unperturbed atmosphere (Cases 3–7 versus Cases 1–2, respectively). 

This is not a surprising result, as the atmospheric variability will decrease the predictability and 

therefore the performance of the Atmospheric Estimator. These error statistics could be used to 

size the width of the corridor, since they provide some information about the reliability of the 

heat rate predictions for control decisions. More detailed performance estimates and trade 

studies are planned for Phase 2. 
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Figure 7.5-33. AAHFS Simulation – AADS Heat Rate Performance Histograms for all AAHFS Cases 

The results shown in Figures 7.5-14–33 demonstrate that under a number of conditions, AADS is 

able to conduct AB with limited ground interaction. In all the cases presented, the thermal loads 

on the spacecraft during every drag pass remain well within design limits. While the orbital 

evolution has been shown to be well managed by AADS, there are attitude dynamics issues to 
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consider as well. While AADS does not directly control the spacecraft attitude, reliable periapsis 

timing and state information are necessary to ensure aerodynamic stability during the drag 

passes. For a typical spacecraft, attitude commanding is generally managed with periodic 

ground involvement, but for an AA spacecraft, the attitude commanding must be autonomous as 

well. The spacecraft must be capable of taking AADS outputs and generating the necessary 

commands to configure the spacecraft for the drag passes and any corridor control maneuvers 

that are necessary. If this process fails, it could lead to an errant (or skipped) corridor control 

burn or aerodynamic instability during the drag passes. Further, the timing computed by AADS 

determines the enabling/disabling of the accelerometer data buffers, switching between reaction 

wheel and thruster control, wheel momentum dump enabling, apoapsis burn ignition timing, and 

accelerometer bias estimation. Errors in sequencing these commands can rapidly degrade the 

performance of the AA system as a whole and potentially jeopardize the vehicle. 

The aerodynamic stability of the spacecraft during the drag passes is shown in Figure 7.5-34. 

The left-hand pane of the graphic shows the performance of the aerodynamic angles (angle of 

attack, α; and sideslip, β) during an initial drag pass. The initial angles entering the drag pass are 

near enough to the aerodynamic stability point (approximately α=60, β=00) that when the 

aerodynamics overwhelms the reaction wheels as the atmospheric density increases, the vehicle 

moves to the aerodynamic stability point. After the spacecraft crosses periapsis, the atmospheric 

density decreases and eventually, the reaction wheels resume control of the vehicle. Throughout 

the deepest portions of the atmosphere, the control law uses the aerodynamic stability to dump 

the angular momentum in the wheels. During this time the thrusters are enabled for attitude 

control with wide deadbands to ensure controllability in the event of unanticipated aerodynamic 

effects. This is a simple example of how the vehicle may be controlled during a drag pass, 

although developing a control law for this purpose is beyond the scope of this project. The 

strategy used for these simulations was intended to be a typical approach. The important factors 

are that the vehicle enters the atmosphere near the aerodynamic trim point, and that the control 

law handles the atmospheric entrance and exit without any large (>30°) attitude excursions. The 

right-hand graphics show a number of consecutive (typical) orbits on the same graphic, 

indicating that as the AB phase unfolds, the attitude dynamics through the drag pass remain 

stable. In all cases, the attitude at entry (which is governed by the AADS-produced ephemeris 

information) is close to the aerodynamic trim point, so that the vehicle demonstrates the desired 

stability. The outbound portion shows some variation in the vehicle behavior, chiefly due to the 

low torque available to the reaction wheels to reign in the spacecraft body rates as the 

atmosphere dissipates. In all the simulations presented in this section, the vehicle shows this 

aerodynamic stability in all drag passes. 

The testing presented in Section 7.5 is a precursor to demonstrating the AADS algorithms under 

more challenging circumstances. This testing has used somewhat idealized circumstances, as the 

truth model for these simulations matches the AADS configuration (no unmodeled dynamics) 

and most of the significant perturbations have been disabled. Despite this shortcoming, it is 

encouraging that AADS appears to be capable of conducting AB in a safe manner without 
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ground intervention for longer durations (14 days) in the ideal cases. As noise and perturbations 

are added, it is expected that the ground update interval will be somewhat reduced. Much of this 

enhanced testing (and additional development) using AAHFS is planned for Phase 2. 

Figure 7.5-34. AAHFS Simulation – Aerodynamic Stability during Drag Passes 

7.5.3 Future Work 

Results of Phase 1 have shown the functionality of AADS and the feasibility of using AADS to 

autonomously control the computation of corridor control maneuvers onboard a spacecraft. A 

number of improvements have been identified to AADS, the simulation tools, and the analysis 

methods that test AADS, to improve the robustness of the AA system. These improvements 

include: 

AADS: 

 Reduce errors in the Ephemeris Estimator by exploring new integration methods, step 

sizes, and real-time periapsis timing correction.

 Desensitize the Atmosphere Estimator to Ephemeris Estimator timing errors and 

investigate modeling methods independent of altitude. Incorporate 3-sigma estimates 

of atmospheric density in Maneuver Estimator logic.
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 Modify the AADS software so that it is suitable for a flight implementation. This 

includes streamlining the code execution, adding error handling and fault detection 

and correction, and accommodating safe-mode events (safety triggers), off-nominal 

scenarios such as pop-up maneuvers and typical AB spacecraft contingencies. 

 Assess the feasibility of incorporating collision avoidance in AADS. 

 Add flexibility to the AADS maneuver logic and implement versatile control strategies 

that can meet project specific requirements. Currently, there are no constraints on the 

size of executed maneuvers. Operationally, there may be both lower and upper limits 

to the allowable size of maneuvers, or even a requirement to select from a menu of 

pre-selected (and pre-tested) maneuvers. 

POST2: 

 Improve the POST2 simulation capability by creating a 6-DOF “truth” simulation 

version, and by including the effects of IMUs, reaction wheels, thrusters, and other 

spacecraft models. 

AAHFS: 

 Complete the integration of Venus and Titan environment models into AAHFS and 

perform testing similar to the POST2 analyses for these bodies. (Support for any 

central body exists in AAHFS and Venus and Titan atmosphere models are already 

integrated into AADS, but the aerodynamic database and Venus-specific AADS 

version require integration and testing.) 

Analysis Methods: 

 Incorporate Mars AB flight-data-derived density profiles into “truth” simulations, 

identifying the impact of real density profiles with previously simulated “perturbed” 

atmospheres. 

 Develop model uncertainties in AADS “truth” simulations and assess AADS 

performance against a mission simulation using Monte Carlo methods to identify 

robustness and further areas of improvement of AADS.

 Stress test AADS using atmospheric random noise and bias, initial ground errors, 

modeling errors, and fault management logic. 

 Perform a sensitivity study on the required fidelity/order of the AADS (Ephemeris 

Estimator) gravity model to ensure sufficient accuracy while minimizing 

computational expenditures. This would likely trade performance accuracy against 

spacecraft resource requirements and availability. 
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 Conduct additional trade studies. Of primary interest is studying the impact of the 

accelerometer data buffer frequency on the Ephemeris Estimator orbit knowledge. 

Currently this buffering is done at 10 Hz, but lower data rates reduce the volume of 

data that must be buffered and therefore reduce the attendant processor memory 

requirements. Increasing data buffer frequency may improve Ephemeris Estimator 

performance but memory constraints may require careful architecture to allow realtime implementation in a flight processor. Additional trade studies will include 

determining accelerometer sensitivities (bias, noise, scale factor, alignment, etc.) and 

their impact on AADS; analyzing corridor width versus maneuver frequency; 

evaluating maneuver execution performance sensitivities; and quantifying the impact 

of solar radiation pressure. 

 Benchmark AADS performance on a flight processor. Ensure the proposed software 

architecture is valid and that the code can run in allotted time (and/or central 

processing unit cycles). 

8.0 Findings, Observations, and NESC Recommendations 

8.1 Findings 

The following findings were identified: 

F.1. Results from 3-DOF simulations with nominal and perturbed atmospheres at Mars, 

Venus, and Titan using POST2 indicate that AADS maintained the simulated spacecraft 

safely within or near the desired AB corridor, while allowing for 7 days between ground 

updates to the spacecraft ephemeris. 

F.2. Higher-fidelity 6-DOF results at Mars using AAHFS compared well with the 3-DOF 

results, where AADS maintained the simulated spacecraft safely within or near the 

desired AB corridor with 7-day ephemeris updates, and showed adequate performance 

with 14-day updates. 

F.3. The corridor control parameters used for all analyses were heat rate indicator at Mars, 

spacecraft temperature at Venus, and periapsis altitude at Titan. 

F.4. Differences between the corridor control parameters predicted by AADS and those 

calculated by the “truth” simulation were due primarily to errors in the ephemeris and 

Atmosphere Estimators. 

F.5. AA use may reduce AB risk by: 

a. Conducting AB maneuvers at the optimal time and executed even if DSN or other 

required ground elements are unavailable. 
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b. Narrowing the AB corridor width could provide more corridor margin for a 

spacecraft without concern for needing ground-based commands for higher 

frequency and total number of maneuvers. 

F.6. Current AADS limitations include: 

a. Does not support spacecraft attributes needed for flight implementation, including 

efficient code execution, error handling, fault detection and correction, safe-mode 

events (safety triggers), off-nominal scenarios such as pop-up maneuvers and 

typical AB spacecraft contingencies.

b. Maneuver logic may trigger excessive and unnecessary maneuver executions, 

especially in highly variable atmospheric conditions. 

c. Does not support collision avoidance. 

F.7. Adding atmospheric variability to the simulations did not significantly impact the ability 

of AADS to ensure reasonable AB corridor performance. 

F.8. Adding accelerometer errors to the simulation resulted in a more rapid divergence of the 

onboard ephemeris estimate from the “truth” orbit than atmospheric perturbations. 

F.9. Ephemeris estimates, provided by AADS at the drag pass entry and exit, are sufficient to 

control the attitude of the vehicle throughout the drag pass. 

F.10. Phase 1 analyses did not utilize uncertainty distributions on model parameters, Monte 

Carlo analyses, or stress testing of potential key error sources (e.g., ground initial 

conditions (spacecraft state and epoch), or onboard modeling errors). 

8.2 Observations 

The following observations were identified: 

O.1. Collision avoidance was a large factor in the MRO AB phase. 

O.2. Maintaining two independent and synergistic simulations aided the AA effort by allowing 

a rapid software error diagnosis in simulations and AADS and by independently verifying 

AB analyses. 

8.3 NESC Recommendations 

The following NESC recommendations were identified and directed toward the NESC (including 

the disciplines of Flight Mechanics, Aerosciences, Passive Thermal, GN&C, Software, Loads 

and Dynamics, and Human Factors) and future NASA programs and projects that may utilize 

AB: 

R.1. Further development of AA should address potential improvements to AADS. 

(F-4, F-6, O-1)
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a. Reduce errors in the Ephemeris Estimator by exploring new integration methods, 

step sizes, and real-time periapsis timing correction. 

b. Desensitize the Atmosphere Estimator to Ephemeris Estimator timing errors and 

investigate modeling methods independent of altitude. Incorporate 3-sigma 

estimates of atmospheric density in Maneuver Estimator logic. 

c. Modify the AADS software so that it is suitable for a flight implementation. This 

includes streamlining the code execution, adding error handling and fault 

detection and correction, and accommodating safe-mode events (safety triggers), 

off-nominal scenarios such as pop-up maneuvers and typical AB spacecraft 

contingencies. 

d. Assess the feasibility of incorporating collision avoidance in AADS. 

e. Add flexibility to the AADS maneuver logic and implement versatile control 

strategies that can meet project specific requirements. 

R.2. Future AA analysis should include improved analysis methods and additional stress 

testing and trade studies. (F-6, F-8, F-10, O-2)

a. Improve the POST2 simulation capability by creating a 6-DOF “truth” simulation 

version, and by including the effects of IMUs, reaction wheels, thrusters, and 

other spacecraft models. 

b. Complete the integration of Venus and Titan environment models into AAHFS 

and perform testing similar to the POST2 analyses for these bodies. 

c. Incorporate Mars AB flight-data-derived density profiles into “truth” simulations, 

identifying the impact of real density profiles with previously simulated 

“perturbed” atmospheres.

d. Develop model uncertainties in AADS “truth” simulations and assess AADS 

performance against a mission simulation using Monte Carlo methods to identify 

robustness and further areas of improvement of AADS.

e. Stress test AADS using atmospheric random noise and bias, initial ground errors, 

modeling errors, and fault management logic. 

f. Perform a sensitivity study on the required fidelity/order of the AADS (Ephemeris 

Estimator) gravity model to ensure sufficient accuracy while minimizing 

computational expenditures. 

g. Conduct additional trade studies, including studying the impact of the 

accelerometer data buffer frequency on the Ephemeris Estimator orbit knowledge; 

determining accelerometer sensitivities (e.g., bias, noise, scale factor, alignment, 

etc.) and their impact on AADS; analyzing corridor width versus maneuver 
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frequency; evaluating maneuver execution performance sensitivities; and 

quantifying the impact of solar radiation pressure. 

h. Benchmark AADS performance on a flight processor. Ensure the proposed 

software architecture is valid and that the code can run in allotted time and/or 

central processing unit cycles. 

9.0 Alternate Viewpoints 

There were no alternate viewpoints identified during the course of this assessment by the NESC 

team or the NRB quorum. 

10.0 Other Deliverables 

No unique hardware, software, or data packages, outside those contained in this report, were 

disseminated to other parties outside this assessment. 

11.0 Lessons Learned 

No applicable lessons learned were identified for entry into the NASA Lessons Learned 

Information System. 

12.0 Definition of Terms 

Corrective Actions Changes to design processes, work instructions, workmanship practices, 

training, inspections, tests, procedures, specifications, drawings, tools, 

equipment, facilities, resources, or material that result in preventing, 

minimizing, or limiting the potential for recurrence of a problem. 

Finding A conclusion based on facts established by the investigating authority. 

Lessons Learned Knowledge or understanding gained by experience. The experience may 

be positive, as in a successful test or mission, or negative, as in a mishap 

or failure. A lesson must be significant in that it has real or assumed 

impact on operations; valid in that it is factually and technically correct; 

and applicable in that it identifies a specific design, process, or decision 

that reduces or limits the potential for failures and mishaps, or reinforces a 

positive result. 

Observation A factor, event, or circumstance identified during the assessment that did 

not contribute to the problem, but if left uncorrected has the potential to 

cause a mishap, injury, or increase the severity should a mishap occur. 

Alternatively, an observation could be a positive acknowledgement of a 
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Center/Program/Project/Organization’s operational structure, tools, and/or 

support provided. 

Problem The subject of the independent technical assessment. 

Proximate Cause The event(s) that occurred, including any condition(s) that existed 

immediately before the undesired outcome, directly resulted in its 

occurrence and, if eliminated or modified, would have prevented the 

undesired outcome. 

Recommendation An action identified by the NESC to correct a root cause or deficiency 

identified during the investigation. The recommendations may be used by 

the responsible Center/Program/Project/Organization in the preparation of 

a corrective action plan. 

Root Cause One of multiple factors (events, conditions, or organizational factors) that 

contributed to or created the proximate cause and subsequent undesired 

outcome and, if eliminated or modified, would have prevented the 

undesired outcome. Typically, multiple root causes contribute to an 

undesired outcome. 

13.0 Acronyms List 

°C Degrees Celsius 

3-D Three-Dimensional 

AA Autonomous Aerobraking 

AADS Autonomous Aerobraking Development Software 

AAG Atmospheric Advisory Group 

AAHFS Autonomous Aerobraking High Fidelity Simulation 

AA PCMD Autonomous Aerobraking Planetary and Constants Document 

AB Aerobraking 

AMA Analytical Mechanics Associates, Inc. 

APL Applied Physics Laboratory (Johns Hopkins University, Laurel, MD) 

ARC Ames Research Center 

ATK Alliant Techsystems Inc. 

CCD Central Composite Design 

CFD Computational Fluid Dynamics 

CSH Constant Scale Height 

CSHIO Constant Scale Height Inbound and Outbound 

CSHT Constant Scale Height with Time 

DAC DSMC Analysis Code 

DFRC Dryden Flight Research Center 

DOE Design of Experiment 

DOF Degree of Freedom 
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DSMC Direct Simulation Monte Carlo 

DSN Deep Space Network 

EDL Entry, Descent, and Landing 

GN&C Guidance, Navigation, and Control 

GRAM Global Reference Atmospheric Model

GRETA Generic Response-Surface Equation Thermal Analysis 

GSFC Goddard Space Flight Center 

IMU Inertial Measurement Unit 

JHU Johns Hopkins University 

JPL Jet Propulsion Laboratory 

JSC Johnson Space Center 

K Kelvin 

kg/km3 kilograms per kilometer cubed 

KinetX KinetX, Inc. 

km kilometer 

LaRC Langley Research Center 

LM Lockheed Martin 

LMST Local Mean Solar Time 

LST Local Solar Time 

LTST Local True Solar Time 

m meter 

Mars-GRAM Mars Global Reference Atmospheric Model 

MESSENGER MErcury Surface, Space ENvironment, GEochemistry and Ranging 

(Discovery mission) 

MGCM Mars Global Circulation Model 

MGS Mars Global Surveyor 

MITS MSFC Information Technology Services 

MOI Mars Orbit Insertion 

MOLA Mars Orbiting Laser Altimeter 

MRO Mars Reconnaissance Orbiter

m/s meters/second 

MSFC Marshall Space Flight Center 

MTSO Management and Technical Support Office 

MTGCM Mars Thermospheric Global Circulation Model 

NCSU North Carolina State University 

NESC NASA Engineering and Safety Center 

NIA National Institute of Aerospace 

OD Orbit Determination 

PDS Planetary Data System 

POST2 Program To Optimize simulated Trajectories II 

PTE Periapsis Timing Estimator 
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PVO Pioneer Venus Orbiter 

rms root mean square 

RTW Real Time Workshop 

SA Solar Array 

SME Subject Matter Expert

SRP Solar Radiation Pressure 

TDT Technical Discipline Team 

TES Thermal Emission Spectrometer 

VIRA Venus International Reference Atmosphere 

w/cm2 watts per centimeter squared 

14.0 References 

1. Spencer, D.A., Tolson, R.H., “Aerobraking Cost and Risk,” Journal of Spacecraft and 

Rockets. Vol. 44, No. 6, November–December 2007, pp 1285–1293.

2. Hanna, J.L. and Tolson, R.H., “Approaches to Autonomous Aerobraking at Mars,” 

AAS/AIAA, Astrodynamics Specialist Conference, Quebec City, Canada, 

July 30-August 2, 2001. AAS 01-387.

3. Lyons, Daniel T., “Aerobraking Automation Options,” AAS-01-385, AAS/AIAA 

Astrodynamics Specialist Conference, Quebec City, California, 2001. 

4. Hanna, J.L., Tolson, R.H., Cianciolo, A.M.D., and Dec, J.A., “Autonomous Aerobraking at 

Mars,” presented at 5th International ESA Conference on Guidance Navigation and Control 

Systems and Actuator and Sensor Product Exhibition, Frascati, Italy, October 22–25, 2002. 

(ESA SP-516, February 2003.) 

5. Willcockson, W.H. and Johnson, M.A., “Mars Odyssey Aerobraking: The First Step Toward 

Autonomous Aerobraking Operations,” 2003 IEEE Aerospace Conference, Big Sky, 

Montana. March 9-14, 2003. 

6. Tolson, Robert H. and Prince, Jill L., “Onboard Atmospheric Modeling and Prediction for 

Autonomous Aerobraking Missions,” AAS 11-477, AAS/AIAA Astrodynamics Specialist 

Conference, Girdwood, Alaska, 2011. 

7. D.J. O’Shaughnessy et al., “Autonomous Aerobraking Algorithm Testing in a Flight 

Software Simulation Environment,” AAS 11-471, AAS/AIAA Astrodynamics Specialist 

Conference, Girdwood, Alaska, 2011. 

8. Prince, J.L. and Striepe, S.A., “NASA Langley Simulation Capabilities for the Mars 

Reconnaissance Orbiter,” AAS/AIAA Space Flight Mechanics Conference, Copper Mountain, 

Colorado, January 23-27, 2005.

9. Bird, G.A., Molecular Dynamics and the Direct Simulation of Gas Flows, Oxford 

University Press, Oxford, United Kingdom, 1994. 
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10. Wilmoth, R.G., LeBeau, G.J., and Carlson, A.B., “DSMC Grid Methodologies for 

Computing Low-Density, Hypersonic Flows About Reusable Launch Vehicles,” 

AIAA Paper 1996-1812, 1996. 

11. LeBeau, G.J., “A Parallel Implementation of the Direct Simulation Monte Carlo Method,” 

Computer Methods in Applied Mechanics and Engineering, Vol. 174, No. 3–4, 1999, 

pp. 319–337.

12. LeBeau, G.J., Boyles, K.A., and Lumpkin III, F.E., “Virtual Sub-Cells for the Direct 

Simulation Monte Carlo Method,” AIAA Paper 2003-1031, 2003.

13. Borgnakke, C. and Larsen, P.S., “Statistical Collision Model for Monte Carlo Simulation of 

Polyatomic Gas Mixture,” Journal of Computational Physics, Vol. 18, No. 4, 1975, 

pp. 405-420.

14. D.J. Carrelli et al., “Autonomous Aerobraking for Low-Cost Interplanetary Missions,” 

9

th Annual Low-Cost Planetary Missions Conference, Laurel, Maryland, 2011. 

15.0 Appendices 

Appendix A. Autonomous Aerobraking Planetary Constants and Models Version 0.07 

(Supplement to Section 7.2) 

Appendix B. Mission Design Appendix (Supplement to Section 7.2) 

Appendix C. Aerodynamics and Aerothermodynamics Computational Methods 

(Supplement to Section 7.3.1.2) 

Appendix D. Thermal Modeling (Supplement to Section 7.3.2.4) 

Appendix E. Mars-GRAM 2010 (Supplement to Section 7.3.1.3) 

Appendix F. Onboard Atmospheric Modeling and Prediction for Autonomous Aerobraking 

Missions (Supplement to Section 7.3.2.1) 

Appendix G. Ephemeris Estimator User’s Guide (Supplement to Section 7.3.2.2)

Appendix H. AADS (Supplement to Section 7.5.1) 

Appendix I. AAHFS (Supplement to Section 7.5.2) 

Appendix J. AA Interface Control Document 
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Models Version 0.07 (Supplement to Section 7.2) 

 
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Appendix B. Mission Design Appendix (Supplement to Section 7.2) 

Generalized spacecraft geometry and mass properties (as described in Section 7.3.1.1) were used 

as simulation inputs. Planetary constants and models and the atmosphere GRAM models for 

each destination were used and are detailed in the AA PCMD (Appendix A) and in Section 7.2. 

Aerodynamics models developed specifically for use with this spacecraft at each destination 

were utilized and are described in Section 7.3.1.2. Solar radiation pressure and the Sun as a 

third-body perturbation were included for each destination. Additionally, Saturn was included as 

a third-body perturbation at Titan, and a thermal model as described in Section 7.3.2.4 was used 

in the Venus reference simulation. 

For the Mars reference simulation, an initial orbital state was selected from the MRO flight 

profile after the "walk-in" phase of the AB mission was completed, and an initial epoch near 

Ls=250 degrees was used to ensure the Martian dust storm season was encompassed during the 

AB duration. A full AB mission was then simulated until the apoapsis altitude reached 450 km. 

Maneuvers were constrained to occur no more frequently than once a week. The estimated 

freestream heat rate at periapsis was used as the corridor control parameter to which the 

spacecraft must be kept during the main AB phase. This is the same constraint utilized in both 

the Odyssey and MRO AB missions. For this analysis, the corridor was set to 0.11 watts per 

centimeter squared (w/cm2) to 0.17 W/cm2. Since maneuvers were constrained to once a week, it 

was necessary to bias the target within this corridor as a function of orbit period: 80 percent of 

the total corridor width for orbit periods greater than 2.5 hours and 30 percent for orbit periods 

less than 2.5 hours. This bias was necessary to ensure the corridor was maintained (upper limit 

not exceeded) throughout the AB mission while meeting the maneuver frequency constraint. 

Figure B.1 shows the operational corridor performance for the reference simulation at Mars. 
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Figure B.1. Mars Reference Simulation Corridor Performance 
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For the Venus reference simulation, a 24-hour initial orbit period was selected and a full AB 

mission was simulated until the apoapsis altitude reached 450 km. Due to the third-body effects 

of the Sun at Venus pulling the spacecraft periapsis altitude higher at some times during the 

mission and lower at others, maneuvers are required more frequently than at Mars to keep the 

spacecraft within the operational corridor and thus were allowed to occur once per day. Because 

of higher solar flux and greater periapsis velocities at Venus, there is increased aerodynamic 

heating experienced during drag passes than at Mars. Therefore, the temperature of the 

spacecraft at periapsis was used as the operational corridor to which the spacecraft must be kept 

since temperature limits are the driving constraint in the structural integrity and functional 

performance of the spacecraft. For this analysis, the temperature corridor was set from 275 to 

375 °C. (The temperatures seen at Venus in this analysis are artificially high because the 

spacecraft utilized in the analysis was not specifically designed for AB at Venus.) Because the 

temperatures experienced at periapsis are a direct function of the periapsis velocity and hence 

orbit period, it was necessary to bias the target within this corridor as a function of orbit period: 

80 percent for orbit periods greater than 10 hours, 90 percent for orbit periods less than 10 hours 

and greater than 2.17 hours, and 5 percent for orbit periods less than 2.17 hours. This bias was 

necessary to ensure the corridor was maintained (upper limit not exceeded) throughout the AB 

mission while meeting the maneuver frequency constraint and to maintain the desired AB rate 

even with the perturbing effects of the Sun. Figure B.2 shows the operational corridor 

performance for the reference simulation at Venus. 
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Figure B.2. Venus Reference Simulation Corridor Performance 
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AB at Titan is different than at Mars and Venus due to the perturbing effects of Saturn’s and 

Titan's large atmospheric scale height. Saturn can induce large changes in periapsis and apoapsis 

altitudes and these effects are dependent on the orbit conditions and orientation relative to 

Saturn. For instance, Saturn can cause shifts in periapsis altitude of over 100 km from one orbit 

to the next in a 20-hour period orbit studied in this analysis. Whether the altitude swing is 

upward or downward is dependent on the orbit orientation relative to Saturn. As the orbit period 

and apoapsis altitudes decrease, the effects of Saturn lessen. In an 8-hour period orbit with the 

same orbit orientation relative to Saturn as the 20-hour orbit, Saturn causes shifts in periapsis 

altitude on the order of only 10 km from one orbit to the next. Saturn's pull on the apoapsis and 

periapsis altitudes is less pronounced when the orbit plane is nearly normal to Saturn. 

Due to Saturn's effects, the overall ΔV requirement for corridor control at Titan can be large 

(e.g., up to 4 m/s per day spent in AB (averaged)) when starting in the initial orbit period of 

20 hours examined in this analysis. Without Saturn, AB can be performed using the same initial 

20-hour orbit period for less than 0.1 m/s ΔV per day (averaged) because the large atmospheric 

scale height at Titan means that there is less orbit-to-orbit variability in density during AB. 

The large atmospheric scale height has the effect of increasing the size of corridor control 

maneuvers as compared to the sizes at Mars and Venus.) Thus, Saturn's effect at Titan is to 

decrease the typical ΔV savings achieved by AB in comparison to the savings at Mars and Venus 

because of the ΔV required for corridor control when AB for any significant duration. 

One method to minimize the corridor control ΔV at Titan is to aerobrake as quickly as possible. 

Short AB durations (7–20 days when starting in an initial 20-hour period orbit) are feasible at 

Titan while meeting spacecraft heating constraints because the periapsis velocities at Titan are 

lower than they are at Mars and Venus, and the spacecraft can therefore experience higher 

densities for the same heating rate as found at Mars and Venus. However, AB at Titan 

represents an opportunity for in situ atmospheric sampling which would be of great benefit to 

science. This science return would be enhanced as the AB duration increases. Hence, a trade 

space exists when designing a Titan mission where there is some balance between the AB 

duration and the ΔV required for corridor control to still provide reasonable ΔV savings to justify 

AB versus all propulsive maneuvering. 

This trade space is heavily dependent on the initial orbit conditions relative to Saturn and has not 

been extensively examined here. Rather, an initial 8-hour period orbit was selected for the Titan 

reference simulation since this orbit period seemed to be the threshold where Saturn's effects on 

the corridor control ΔV could be reduced to an average value of ~1 m/s per day spent AB. 

Additionally, even though it is possible to begin AB at Titan from a larger orbit period (such as 

the 20-hour period orbit mentioned previously), it only takes a few atmospheric passes before the 

orbit period is reduced to approximately 8 hours. These first few atmospheric passes in the 

larger orbit period are similar to the walk-in phase of AB at Mars and Venus where the 

atmosphere is being sampled and therefore would not be utilized with AA. 
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A full AB mission was simulated from the initial 8-hour orbit period with the same epoch as was 

used in the Mars case until the apoapsis altitude reached 1500 km. The initial orbit was nearly 

polar and had the periapsis located near the South Pole, similar to a previous Titan AB study 

[ref. B.1]. An initial periapsis altitude of 810 km was selected to ensure that AB occurred from 

the beginning of the simulation. A periapsis altitude corridor was chosen for this analysis 

because it provides a more straightforward control approach in the presence of Saturn than other 

corridor types when the desire is to stretch the duration of AB. The corridor was set at 750 km to 

900 km and an altitude of 870 km was used as the corridor target for the entire AB duration. 

Both the corridor and target within the corridor were selected with the objective of achieving 

~2-month AB duration. 

Figure B.3 shows the operational corridor performance for the reference simulation at Titan. 

Note that there are regularly occurring periods of time spanning ~2 days where the periapsis 

altitude remains almost constant rather than dropping steadily from one orbit to the next. An 

examination of the Saturn-Titan-Probe angle as seen in Figure B.4 indicates a relationship exists 

between the Saturn-Titan-Probe angle and the periapsis behavior. As the Saturn-Titan-Probe 

angle approaches 90 degrees (i.e., Saturn is nearly normal to the orbit plane examined in this 

analysis), the periapsis altitude remains almost constant. The occurrences of the Saturn-TitanProbe angle being near 90 degrees take place at regularly spaced intervals of ~8 days since the 

orbit period of Titan around Saturn is just under 16 days. Once the spacecraft orbit period 

shrinks to ~4.5 hours, the effects of Saturn lessen on the periapsis altitude. This can be seen 

between days 65–70 in Figure B.3 where the periapsis altitude does not remain quite as steady 

when the Saturn-Titan-Probe angle is near 90 degrees. 

By setting a constraint that maneuvers can only take place when the Saturn-Titan-Probe angle is 

~90 degrees, and then setting the corridor limits and target within the corridor such that the 

spacecraft has reached or is below the bottom of the corridor when the Saturn-Titan-Probe angle 

is ~90 degrees, the amount of required corridor control ΔV is reduced. This is illustrated in 

Figure B.5 where another full AB mission was simulated at Titan using the same initial 8-hour 

period as presented in Figures B.3 and B.4. The corridor was set at 825 km to 875 km at the 

onset of AB but was changed to 750 km to 875 km once the orbit period reached just under 

4.5 hours. Although the lower corridor limit could have been set to 750 km at the onset of AB, 

the lower limit would have needed to be shifted upward repeatedly as AB progressed to ensure 

the spacecraft was in the desired location of the corridor when the Saturn-Titan-Probe angle was 

~90 degrees and a periapsis raise maneuver was triggered to prolong AB. Dropping the lower 

corridor limit to 750 km later in AB was done specifically in this case to avoid performing 

another periapsis raise maneuver only to reach the desired apoapsis altitude soon after the 

maneuver. In some mission simulations analyzed, performing another maneuver targeting near 

the top of the corridor is advantageous to the AB duration rather than unfavorable as was the 

case with this simulation. The corridor target was an altitude of 860 km for the entire AB 

duration in this mission. 
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The strategy used here to prolong AB while reducing corridor control ΔV can be utilized to 

increase the AB duration even more than shown for this case if preferred. One such simulation 

provided 122 days in AB for 120 m/s ΔV when beginning from the same initial conditions versus 

the 69 days and 72 m/s ΔV shown here. Further study in the relationship of periapsis/apoapsis 

altitude behavior to orbit orientation/conditions relative to Saturn will likely provide additional 

insight into methods that can be employed to optimize an AB mission design at Titan. 

Table B.1 summarizes several parameters of interest for the Mars, Venus, and Titan reference 

simulations. 

Figure B.3. Titan Nominal Reference Simulation Corridor Performance 
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Figure B.4. Saturn-Titan-Probe Angle during Nominal Reference Simulation 
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Figure B.5. Titan Reduced ΔV Reference Simulation Corridor Performance 
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Table B.1. AB Summary 

Mars Venus Titan Nominal Titan Reduced 

ΔV

Initial Periapsis Altitude 

(km) 101.65 142.58 810.86 810.86

Initial Orbit Period (hours) 33.43 23.78 8.19 8.19

Range of Periapsis 

Altitudes (km) 99.06 - 127.03 126.31 - 148.62 750.50 - 870.57 738.34 - 860.32

Maximum Qdot (W/cm2) 0.16 1.18 0.007 0.009

Maximum Dynamic 

Pressure (N/m2)

0.41 1.20 0.034 0.05

Maximum Density (kg/m3) 5.13e-8 2.50e-8 1.78e-8 2.35e-8

Reference 

Ref. B.1: Lyons, D. and Strange, N., “Aerobraking at Titan,” AAS/AIAA Astrodynamics 

Specialist Conference, Pittsburgh, Pennsylvania, August 9–13, 2009. 
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Appendix C. Aerodynamics and Aerothermodynamics 

Computational Methods (Supplement to Section 7.3.1.2) 

C.1 Computational Methods 

The DSMC calculations were performed using Distributed DSMC Analysis Code, the parallel 

implementation of the program DAC (DSMC Analysis Code) [refs. 2–4]. In DAC, the gas 

molecular collisions are modeled using the variable hard-sphere model developed by Bird 

[ref. 1], and the Larsen-Borgnakke model is used for internal energy exchanges [ref. 5]. The 

surface geometry is represented by unstructured triangular elements that are embedded in a 

two-level Cartesian grid for the flowfield calculation. The solution from the first level of grid 

cells, which are uniform in size, is used for grid refinement to create the second-level cells. The 

grid is refined based on local conditions, thus allowing the program to meet the spatial resolution 

requirements without excessive global refinement. The grid cells are typically refined such that, 

on average, the second-level cells have dimensions less than the local mean free path. The local 

simulation parameters are set such that there are nominally 10 simulated molecules in each cell 

and the local time step is typically dictated by the local flow time for the problems considered. 

The simulation is allowed to progress until there is approximately a constant number of particles 

in the flow domain, then it is run in a steady state mode until a sufficient number of surface 

collisions are sampled. 

For all calculations, the wall collisions were assumed to be fully diffusive; that is, an 

accommodation coefficient of one was specified, with the spacecraft wall temperature at a 

constant 300 K. The free stream parameters used for the atmospheres of Mars, Venus, and Titan 

are presented in Tables C.1-1, C.1-2, and C.1-3, respectively. The baseline vehicle geometry 

was that of the MRO and can be seen in Figure C.1-1. The surface grid was derived from a 

computer-aided design file provided by LM Astronautics and represents the best preflight 

estimate of the nominal AB configuration. The spacecraft itself is about 12 m wide from the 

outside tip of one solar array to the other. At each trajectory point, angles of attack and side-slip 

angles of 0 deg, ±5 deg, and ±10 deg were simulated to span the expected range of orientations 

expected. 
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Figure C.1-1. Space Craft Surface Geometry 

Table C.1-1. Mars Simulation Parameters 

n∞ (1/m3)  (kg/m3

) V∞

(m/s)

T∞ (K) XCO2 XN2 XO XCO XHe XN

7.80E+16 5.60E-09 4811 144.77 0.9537 0.0463 0.0000 0.0000 0.0000 0.0000

1.39E+17 1.00E-08 4811 144.77 0.9537 0.0463 0.0000 0.0000 0.0000 0.0000

2.48E+17 1.78E-08 4811 144.77 0.9537 0.0463 0.0000 0.0000 0.0000 0.0000

4.40E+17 3.16E-08 4811 144.77 0.9537 0.0463 0.0000 0.0000 0.0000 0.0000

1.39E+18 1.00E-07 4811 144.77 0.9537 0.0463 0.0000 0.0000 0.0000 0.0000

2.09E+18 1.50E-07 4211 144.77 0.9537 0.0463 0.0000 0.0000 0.0000 0.0000

3.48E+18 2.50E-07 3911 144.77 0.9537 0.0463 0.0000 0.0000 0.0000 0.0000

4.87E+18 3.50E-07 3611 144.77 0.9537 0.0463 0.0000 0.0000 0.0000 0.0000
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Table C.1-2. Venus Simulation Parameters 

n∞ (1/m3)  (kg/m3

) V∞

(m/s)

T∞ (K) XCO2 XN2 XO XCO XHe XN

1.08E+15 3.42E-11 9000 127.4 0.0659 0.0548 0.7893 0.0671 0.0175 0.0054

7.10E+15 3.13E-10 9000 127.4 0.3552 0.0842 0.4537 0.1009 0.0033 0.0026

1.09E+17 6.85E-09 9000 127.6 0.7310 0.0676 0.1427 0.0575 0.0003 0.0008

5.53E+17 3.69E-08 9000 128.0 0.8267 0.0539 0.0845 0.0344 0.0001 0.0005

2.92E+18 2.02E-07 9000 129.0 0.8887 0.0461 0.0455 0.0194 0.0001 0.0002

Table C.1-3. Titan Simulation Parameters 

n∞ (1/m3)  (kg/m3

) V∞ (m/s) T∞ (K) XN2 XCH4 XH2

3.34E+16 1.54E-09 6500 174.63 0.9837 0.013 0.0033

7.01E+16 3.23E-09 6500 171.90 0.9850 0.0124 0.0026

1.55E+17 7.16E-09 6500 166.79 0.9867 0.0117 0.0017

3.67E+17 1.69E-08 6500 159.74 0.9878 0.0111 0.0011

9.37E+17 4.32E-08 6500 151.42 0.9887 0.0106 0.0007

C.2 Database Uncertainty Analysis for Aeroheating 

With any database, some uncertainty must be assigned to the heating levels reported. While 

some uncertainties are generalized and apply to any data set, there were several that needed to be 

quantified for the present databases. For the current work, an analysis was performed on the 

Martian atmosphere and is assumed to be valid for the atmospheres of Venus and Titan as well. 

C.2.1 Effect of Chemical Reactions 

For the Martian database, a two-species, non-reacting chemistry model was implemented while a 

nine-species, reacting chemistry model was implemented for the Venus and Titan databases. To 

assess the uncertainty associated with the differing chemistry models, comparisons were made at 

the highest expected density at Mars (32 kg/km3). The variation of the non-dimensional incident 

heating coefficient, CH, was compared and the maximum difference was estimated to be less than 

5 percent at the edges of the solar panels. 
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C.2.2 Effect of Surface Grid Resolution 

The next uncertainty examined was the effect of changing the surface grid resolution at the 

highest expected Martian density (32 kg/km3). The nominal surface grid was compared with a 

surface grid for which the size of the surface elements was decreased by approximately one-half. 

The greatest differences observed were near the corners of the solar panels and were estimated to 

be less than 1 percent. 

C.2.3 Effect of Surface Temperature 

The final simulation parameter to be examined for uncertainty was the variation of the incident 

heating rate with the wall temperature specified for the spacecraft, once again at the highest 

expected Martian density (32 kg/km3). The nominal wall temperature was chosen to be 300 K. 

Off-nominal surface temperatures of 150 K and 600 K were chosen for comparison. The value 

of 600 K was obviously higher than any expected in-flight temperature but is included to get the 

maximum uncertainty level. As it turns out, the 150 K off-nominal temperature was lower than 

any of the temperatures observed near the atmospheric entry portion of the MRO AB maneuver, 

but it provided a reasonable lower bound. The greatest differences observed were approximately 

5 percent. 

C.2.4 Summary of Database Uncertainty 

A summary of the uncertainties included in the overall estimate of database uncertainty is 

presented in Table C.2-1. The main sources of uncertainty are computational errors (statistical 

sampling, gridding errors), physical model errors (gas collision model used, accommodation 

coefficient used, chemical reactions), boundary conditions (atmospheric temperature, surface 

temperature), and any errors in the computational geometry model used (whether the multilayer 

insulation was applied correctly, simplifications to some parts, etc.). While this may not be an 

all-inclusive list of possible sources of error, the major contributors have been included and 

examined. 

The database uncertainty has been reported with and without the inclusion of the accommodation 

coefficient uncertainty. The thermal analysis team used the uncertainty with this value because 

their analysis includes the reflected heating rate in addition to the incident heating rate. The 

accommodation coefficient affects the incident heating only slightly (by varying the number 

density near the surface). The total uncertainty was calculated by taking the square-root-of-thesum of the squares of the contributing uncertainties. 

The grid, chemical reaction, and surface temperature have already been addressed here. The 

statistical sampling error was estimated by approximating the uncertainty as

1 / N

, where N is 

the number of surface collisions. Because most of the surface elements accumulated on the order 

of one million collisions, this uncertainty was estimated to be ±0.1 percent. The gas collision 

model, accommodation coefficient, and atmospheric temperature uncertainties are historic values 
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that have been used with confidence in previous planetary missions. The geometry error was an 

uncertainty to which it was difficult to assign a value. This uncertainty is only mentioned and 

was not assigned a value because a direct comparison between the computational model and the 

spacecraft in flight cannot be made. The final database uncertainties are therefore assigned 

values of ±7.9 and ±9.4 percent, with and without the inclusion of accommodation coefficient 

uncertainty, respectively. 

Table C.2-1. Summary of Uncertainties 

Source of Uncertainty Aeroheating (percent) Aerodynamics (percent)

Computational errors

 Statistical sampling ±0.1 ±0.05

 Grid ±3.0 ±1.0

Physical errors

 Gas collision models ±2.0 ±1.0

 Accommodation coefficient ±5.0 ±2.5

 Chemical reactions ±5.0 ±1.0

Boundary Conditions

 Atmospheric temperature ±0.2 ±0.1

 Surface temperature ±5.0 ±0.5

Geometry Small Small

RMS uncertainty (excl. acc. coef.) ±7.9

RMS uncertainty (incl. acc. coef.) ±9.4 ±3.08

C.3 Database Uncertainty Analysis for Aerodynamics 

The sources of uncertainty for the aerodynamics databases are the same as for the aeroheating 

databases, but the sensitivity of the force and moment coefficients is much smaller than for the 

heating coefficient. The resulting uncertainties for the aerodynamic databases are listed in 

Table C.2-1. 

C.4 Database Trends 

The following section gives the reader a general knowledge of how the aerodynamic and 

aeroheating coefficients vary as the density and orientation vary through an atmospheric pass. 

No specific comparisons will be given between atmospheres since the free stream conditions 

vary widely depending on which planet/moon is being considered. 
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C.4.1 Aeroheating Database 

Due to the elliptic nature of AB orbits, a range of densities is generally encountered, from the 

free-molecular regime down through the maximum density allowed by the thermal limit lines 

(as determined by the Thermal Team) where the flow may become transitional. Heating results 

for a range of densities from the Martian atmosphere simulations are presented in Figure C.4-1. 

Although the non-dimensional heating may be decreasing as the density increases, it should be 

noted that the heating rates are increasing since the density is increasing. The value of Ch

decreases with density because the kinetic energy of the incident molecules is decreasing due to 

the increasing number of collisions in the flow. 

Figure C.4-1. Effect of Density on Ch at  = 0-deg,  = 0-deg 

As discussed, a variety of angles-of-attack and side-slip angles were examined for each 

trajectory. A sample of how the distribution of Ch varies with these parameters is presented in 
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Figure C.4-2. The spacecraft is assumed to pass through the atmosphere with the science 

instruments pointed downward towards the surface, so in this figure, the ground is “up.”

Figure C.4-2. Effect of Orientation on Ch
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Figure C.4-3. Variation of Forces and Moments with Orientation at 750 km at Titan 

C.4.2 Aerodynamic Database 

Samples of the aerodynamics database for Titan are presented in Figures C.4-3 and C.4-4 for 

altitudes of 750 km and 800 km, respectively, for the six forces and moments (these results are 

not non-dimensionalized) at various spacecraft orientations. The trends between the two 

altitudes are generally similar except for the rolling moment (My) where the slope of the curve 

changes sign somewhere between 750 km and 800 km. 
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Figure C.4-4. Variation of Forces and Moments with Orientation at 800 km at Titan 

C.5 References 

1. Bird, G.A., Molecular Dynamics and the Direct Simulation of Gas Flows, Oxford 

University Press, Oxford, United Kingdom, 1994. 

2. Wilmoth, R.G., LeBeau, G.J., and Carlson, A.B., DSMC Grid Methodologies for 

Computing Low-Density, Hypersonic Flows About Reusable Launch Vehicles, AIAA 

Paper 1996-1812, 1996. 

3. LeBeau, G.J., “A Parallel Implementation of the Direct Simulation Monte Carlo 

Method,” Computer Methods in Applied Mechanics and Engineering, Vol. 174, No. 3–4, 

1999, pp. 319–337.
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4. LeBeau, G.J., Boyles, K.A., and Lumpkin III, F.E., Virtual Sub-Cells for the Direct 

Simulation Monte Carlo Method, AIAA Paper 2003-1031, 2003.

5. Borgnakke, C. and Larsen, P.S., “Statistical Collision Model for Monte Carlo Simulation 

of Polyatomic Gas Mixture,” Journal of Computational Physics, Vol. 18, No. 4, 1975, 

pp. 405–420.
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Appendix D. Thermal Modeling (Supplement to Section 7.3.2.4) 

A high-fidelity thermal model, originally developed in MSC Software PatranTM ref. [

i

] and 

Thermal Desktop® ref. [

ii] for MRO AB operations ref. [iii], was modified to develop the response 

surface equations for this AA simulation. Originally, Thermal Desktop® was used to compute 

the view factors to space and the solar heating. The PatranTM model was used to compute the 

temperatures during the drag pass, utilizing the view factor and solar heating data from Thermal 

Desktop®, and the aerodynamic heating from the DSMC code as boundary conditions. The 

Thermal Team assessed the effect of reflected heating only on the solar panel. They made no 

direct assessment of the heating reflected from the solar panel to other spacecraft surfaces. In the 

DSMC calculations, particles reflected from the solar panel surfaces that impinge on other 

spacecraft surfaces are included in the calculated Ch value for that surface. Vice versa, particles 

reflected from other spacecraft surfaces impinging on the solar panel are included in the 

calculated incident Ch value. The original high-fidelity PatranTM thermal model was used as a 

starting point because the model was already correlated to flight data, ref. [iv]. One of the 

objectives of the AA study was to consolidate the thermal analysis models into one universal 

model that would compute the view factors, solar heating inputs, and solar array temperatures. 

To accomplish this objective, the original MRO thermal model (shown in Figure D.0-1) was 

converted to Thermal Desktop®and correlated to MRO flight data, ref.[v]. The results of the 

correlation effort compare well to flight data. An example of the correlation results is provided 

in Figures D.0-2 and D.0-3 for orbit pass 262. 

Figure D.0-1. Original MRO Solar Array Model and Sensor Locations 
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Figure D.0-2. Correlation of the Calculated Temperatures to Flight Data for Drag Pass 262 ref. [v] 
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Figure D.0-3. Peak Temperature Distribution for Drag Pass 262 (°C) 

After the MRO model was converted to Thermal Desktop®and correlated to flight data, several 

modifications were made to utilize the model as a tool for AA and response surface 

development. First, the model was parameterized to allow variation in the key environmental, 

material property, and modeling variables needed for response surface development. This 

parameterization involved creating symbols within the model that either explicitly define the 

value of specific variables, or, as in most cases, establish a multiplier or bias to known values to 

represent the defined uncertainty of the variable. 

The next modification of the model is made to enable autonomous running of multiple analyses 

in parametric mode with multiple variables, where the user can select a desired number of 

variables and change the values between a defined upper and lower limit. Currently, Thermal 

Desktop®

has no design of experiment (DOE) capabilities; the code only has the built-in ability 

to run in parametric mode while varying a single variable. For response surface equation 

development of the MRO model, it is necessary to vary between 12 and 15 parameters. 

Therefore, custom logic and operation blocks are added to the Thermal Desktop® model that 

allows multiple cases to be run with variation of a user-defined number of variables. 

Additionally, these logic blocks allow specification of the total number of cases to run as well as 

the nominal, the high, and the low values of each variable. 

The logic block provides the ability to input a matrix of numbers that define the values of each 

parameter for each run. For a DOE, this matrix would be N by M elements, where N represents 

the number of cases in the study and M represents the number of variables being investigated. 

The values in the matrix consist of either a 0 or ±1. In the case of the MRO model, 0 indicates 

the nominal value of the variable used in the study and ±1 indicates that the ±3 σ value is used. 
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The variables are coded to range between -1 and +1 so that they are all on the same scale. This 

matrix is then input to an array data block, within the Thermal Desktop®logic manager. While 

this approach limits the user to only the nominal, high, and low values, minimal effort would be 

required to populate this matrix with any values between -1 and +1, based on either a uniform or 

Gaussian distribution, and the variable set according to the corresponding value, thus allowing 

the user to run Monte Carlo analyses, but that aspect is beyond the scope of this study. 

D.1 Design of Experiments, Sensitivity Study, and Response 

Surface Development 

For an AA mission, it is impractical (from a time perspective), given current onboard spacecraft 

computer technology, to run a high-fidelity thermal model onboard the spacecraft. For AA, the 

spacecraft must be able to compute the temperatures within seconds, or minutes at the most. One 

solution to satisfy this calculation speed requirement is to develop a response surface model for 

the temperatures, which is derived from the high-fidelity thermal model. A response surface 

model is typically a polynomial equation that can be used to determine how a given response is 

affected by a set of quantitative independent variables or factors over a specified range. In the 

case of a high-fidelity thermal model the response is the temperature at a discrete point. The 

general form of the response surface equation representing the thermal response of the spacecraft 

solar arrays is given in Eq. (D.1-1), ref [vi].

 

1 2 1

2

0

1 1 1 1 1 1 1

n n n n n n n

m i i ii i ij i j ijk i j k

i i i j i i j i k j

T b b x b x b x x b x x x

  

         

           

 Eq. (D.1-1) 

Eq. (D.1-1) captures the main effects (first- and second-order interactions) and non-linearities 

with the quadratic terms and third-order interaction terms. Main effects are how the response of 

the system changes as a single factor changes. Interactions occur when the effect of one factor 

on the response depends on the level of another factor, ref. [vii]. 

Without a priori knowledge of how the temperatures (calculated via a thermal analysis of a 

complex system) will respond to variations and uncertainty in the input parameters, analysts are 

forced to include every variable they can think of in the development of a response surface 

representation of the thermal analysis. One way to generate the data necessary to create a 

response surface is to perform a DOE. A DOE is a systematic way of varying the design 

variables so that the data obtained can be analyzed to yield valid and objective conclusions, 

ref [vii]. In the case of the thermal analysis for AA, the objective is to create a response surface 

model of the high-fidelity thermal model. As the number of variables (or factors, as they are 

called in statistics) increases, the number of runs required for the DOE and thus, required to 
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define the response surface increases dramatically. For example, in a full factorial design, which 

is a DOE that includes all possible combinations of the factors, if there are three levels for each 

factor and ten factors, then the number of required runs of the thermal analysis model would be 

59,049, or 

k l

, where l is the number of levels and k is the number of factors. A level is defined as 

a discrete value for a particular factor, hence three levels represents three discrete values for a 

factor. Typically, when three levels are used the minimum, maximum, and midpoint values are 

used. 

There are other types of DOEs that reduce the number of runs, but the trade off is that not every 

combination of the factors is represented. A face-centered central composite design (CCD) for 

example is one type of DOE that reduces the number of runs. A face-centered CCD is made up 

of three parts: center points, axial points, and fractional factorial points. For the same example 

of 10 factors at three levels, if a face-centered CCD is chosen with two center points and a 

1⁄4 fractional factorial contribution, the number of runs required of the thermal model would be 

reduced to 278. The variation in the number of required runs as a function of the number of 

analysis variables for a full factorial design and a face-centered CCD are compared in 

Figure D.1-1. 

The trends in Figure D.1-1 indicate that the number of factors being used to create the response 

surface should be minimized to reduce the number of required runs of the thermal model. In 

practical terms, if the thermal model takes 2 hours for one run, the 10-factor face-centered CCD 

requiring 278 runs would take over 23 days running on a single computer to generate the data 

required to create the response surface. For AA, updates to the thermal response surface may be 

required so minimizing the number of required runs, and thus, the time necessary for an update is 

essential. Additionally, reducing the number of factors reduces the amount of data that needs to 

be passed back and forth and maintained within the AA simulation software. 
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Figure D.1-1. Comparison of Required Runs for Different DOEs 

To minimize the number of factors, a sensitivity study can be performed to determine which 

initially selected factors are significant contributors to the solar array temperature response. 

Creating a screening DOE is a way to examine which of the factors’ main effects and which 

interactions are important. A screening DOE is similar to a CCD, except that a screening DOE 

does not include axial points; may or may not include center points; and the fraction factorial 

portion is much, much smaller. If a factor is deemed insignificant, it does not mean that the 

particular factor contributes nothing to the response; it just means that the particular factor’s 

variation is insignificant. 

For this study, the MRO spacecraft is used to simulate AA around both Mars and Venus. 

The thermal model described in Section 7.1.4.1 is used for both the Mars and Venus mission 

scenarios. The only differences in the model come from the external heating environments. 

At Mars, the solar heating input is relatively low and the effect of solar occultation on the initial 

temperatures is large. The atmospheric density and corresponding aerodynamic heating 

encountered during the drag pass are relatively low, but due to the low initial temperatures prior 

to the drag pass, only the aerodynamic heating dominates the thermal response during the drag 

pass. At Venus, the solar heating inputs are relatively high and the effect of solar occultation in 

lowering the initial temperatures is lessened. The density and corresponding aerodynamic 

heating are relatively high and combined with the solar heating; both dominate the thermal 

response during the drag pass. The differences in the corresponding thermal response for both 
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mission scenarios necessitate that a screening sensitivity study be performed for each mission 

scenario. 

Starting with the initial list of factors used in the MRO AB thermal response surface analysis, 

ref. [viii], a screening DOE was generated using the JMP® statistical software, ref. [ix]. The 

factors and their definitions are given in Table D.1-1. The factors can be classified into three 

general categories: environmental, material property, and modeling. For these 15 factors, the 

screening DOE only required 129 runs, 128 from the fraction factorial part and 1 center point. 

The JMP®software performed an analysis of variance on the resulting temperatures calculated 

for each case in the DOE matrix. The statistical p-value was an indication of whether the 

variation in the factor contributes significantly to the analysis. P-values less than 0.05 typically 

indicate a significant contribution. For the Mars AA mission, the main effects for factors that 

had p-values greater than 0.05 are summarized in Table D.1-2. If the only concern were the 

main effects, all six of these factors could be eliminated from the subsequent DOE and would not 

be carried in the response surface equation. However, the interactions between factors must be 

examined. In the Mars mission scenario, interactions between all but two of the factors had 

p-values less than 0.05 when interacting with other factors. The only factors that could be 

dropped were the drag pass duration and the solar cell emissivity; therefore the face-centered 

CCD DOE for generating the response surface equation for the Mars mission scenario will 

contain 13 factors. 

Table D.1-1. MRO Thermal Analysis Variables 

Category Factor Abbreviation

Environmental

Drag pass duration DP

Density RHO

Heat transfer coefficient CH

Periapsis velocity V

Initial solar array temperature IT

Orbital heat flux Qs

Material Property

M55J graphite emissivity FSE

ITJ solar cell emissivity ITJE

M55J graphite thermal conductivity FSk

M55J graphite specific heat FSCp

Aluminum honeycomb core thermal conductivity ALk

Aluminum honeycomb core specific heat ALCp

Modeling

Outboard solar panel mass distribution OFM

Solar cell layer mass distribution MD

Contact resistance CR
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Table D.1-2. Factor Screening for Mars Mission Scenario 

Factor Abbreviation p-value

Drag pass duration DP 0.8100

Orbital heat flux Qs 0.5987

ITJ solar cell emissivity ITJE 0.6443

M55J graphite thermal conductivity FSk 0.7929

Outboard solar panel mass distribution OFM 0.4642

Contact resistance CR 0.7929

Since different environmental conditions are encountered for the Venus mission scenario, the 

screening sensitivity must be performed again. The drag pass duration was replaced by the 

orbital period. This new factor was used since it was deemed a better representation of the 

variation in the orbit geometry, which was the original intent of the drag pass duration factor. 

Following the same procedure as in the Mars mission scenario, an identical screening DOE was 

generated and the resulting data analyzed. For the Venus AA mission, the main effects for 

factors that had p-values greater than 0.05 are summarized in Table D.1-3. 

Table D.1-3. Factor Screening for Venus Mission Scenario 

Factor Abbreviation p-value

Orbital period P 0.1097

Periapsis velocity V 0.7999

M55J graphite specific heat FSCp 0.5526

M55J graphite thermal conductivity FSk 0.5232

Aluminum honeycomb core thermal conductivity ALk 0.9832

Aluminum honeycomb core specific heat ALCp 0.5684

Solar cell layer mass distribution MD 0.5291

Outboard solar panel mass distribution OFM 0.5496

Contact resistance CR 0.5081

For Venus, some of the factors that are found to be insignificant are the same as in the Mars 

mission scenario; however, there are others that are insignificant for Venus but were significant 

for Mars, and vice-versa. The difference arises due to how different the missions are in terms of 

their environment and underscores the need to repeat the screening study for every mission 

scenario. Both scenarios illustrate the need to examine the interaction between factors. It was 

found that all but two factors had significant interactions with other factors. For Venus, the 

periapsis velocity and the contact resistance are dropped; hence the face-centered CCD DOE for 

generating the response surface equation for the Venus mission scenario will contain 13 factors. 

D.2 Response Surface Goodness of Fit Determination 

A face-centered CCD with 13 factors was generated using the JMP statistical software. The 

CCD had 26 axial points, 10 center points, and 128 points from the fractional factorial 
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contribution. JMP®automatically reduces the fraction used to compute the fractional factorial 

contribution as the number of factors increases; in this case the fraction was 1/64th. The 

temperatures calculated for each of the 164 total runs for both Mars and Venus were analyzed 

using JMP® where a least squares fit was constructed using the stepwise regression option in 

JMP®. The result of the regression is a quadratic equation, one unique to the Mars mission 

scenario and one unique to the Venus mission scenario. The coefficient of determination or R2

adjusted value was measured and used to determine how well the assumed functional form of the 

response measures the variability of the supplied data. In this case, the R2

adjusted value 

measured how well the quadratic response surface represented the variability in the temperatures 

generated by the DOE cases. In the Mars mission scenario, the resulting response surface 

equation had an R2adjusted value of 0.9948. For the Venus mission scenario, the R2 adjusted 

value was 0.9991. An R2adjusted value greater than 0.9 was desirable but not sufficient to 

determine the goodness of fit of the response surface. 

To get a clear picture of how well the response surface equation is fitting the response data from 

the DOE runs, a plot of the actual versus predicted values, a plot of the residual versus predicted 

values, and the model fit distributions must be examined. The actual versus predicted plot shows 

the temperatures calculated by the thermal model for the cases described in the DOE plotted 

against the temperatures calculated by the quadratic response surface equation and is given in

Figure D.2-1for the Mars mission scenario and Figure D.2-2 for the Venus mission scenario. 

Note that the temperatures for the Venus mission scenario are unrealistically high. The reason 

the temperatures were unrealistically high is due to the fact that the solar heating was almost 

4.5 times higher at Venus as compared to Mars, in addition to a higher aerodynamic heating. 

Furthermore, the MRO spacecraft was not designed to aerobrake at Venus and hence, the thermal 

response was not consistent with a spacecraft specifically designed for Venus AB. For the AA 

simulation at Venus (for demonstration purposes) the maximum temperature obtained from the 

thermal analysis was scaled to match the maximum temperature calculated for a proposed Venus 

AB spacecraft; a spacecraft which had a more robust thermal design and had solar panels tailored 

to minimize the aerodynamic heating. 
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Figure D.2-1. Mars Mission Scenario Actual versus Predicted Temperatures 

Figure D.2-2. Venus Mission Scenario Actual versus Predicted Temperatures 
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The centerlines of the plots in Figures D.2-1 and D.2-2 represent a perfect fit of the data; the 

plots show that the data points lie close to the center line, which indicates a good fit. The 

residual is the error in the fitted model and is the difference between the temperature calculated 

by the thermal model and the temperature calculated by the response surface equation. The 

residual for the maximum solar panel temperature versus the predicted maximum temperature is 

plotted in Figure D.2-3 for the Mars mission scenario and Figure D.2-4 for the Venus mission 

scenario. 

Figure D.2-3. Mars Mission Scenario Maximum Solar Panel Temperature Residual versus Predicted 

Maximum Temperature 
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Figure D.2-4. Venus Mission Scenario Maximum Solar Panel Temperature Residual versus Predicted 

Maximum Temperature 

 

In general, the data points are randomly scattered in Figures D.2-3 and D.2-4, indicating a good 

fit of the temperature data. However, there are two areas on Figure D.2-3 and one on 

Figure D.2-4 where the data points are clustered together; this clustering indicates that one of the 

factors may be dominating the response. For AB, the peak temperatures are highly influenced by 

the peak density, which is the primary reason for this clustering. One way to alleviate the 

occurrence of clustering is to break the density into smaller intervals and develop a different 

response surface equation for each interval as in ref. [viii]. For simplicity in implementing the 

response surface equations into the AA simulation, a goal is to try to have a single response 

surface equation. As a result of the goodness of fit analysis, it is recommended that the density 

be broken into three ranges and three separate response surface equations used. 

One final check of the goodness of fit is to examine the model fit and model representation error 

distributions. Both model error distributions should approximate a normal distribution with a 

mean around zero and a standard deviation less ≤ 1.0. The model fit error is how well the 

response surface fits the temperature data in the DOE. The model fit error distribution for the 

maximum temperature for the Mars mission scenario is plotted in Figure D.2-5 and for the Venus 

mission scenario is plotted in Figure D.2-6. The model fit error distribution for the Mars 

response surface equation is approximately normal and has a mean of 0.0158 and a standard 

deviation of 1.0359. The standard deviation is greater than 1.0, but is sufficiently close to 1.0 to 

conclude that the model is accurately fitting the DOE temperature data. 
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Figure D.2-5. Mars Mission Scenario Model Fit Error Distribution 

Figure D.2-6. Venus Mission Scenario Model Fit Error Distribution 

The model fit error distribution for the Venus response surface equation is approximately normal 

and has a mean of -0.0085 and a standard deviation of 0.7616. Both the mean and standard 

deviation fall within the desired range, therefore it can be concluded that the model is accurately 

fitting the DOE temperature data. 
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The model representation error is how well the response surface fits temperatures calculated by 

the thermal model for points other than those on the DOE. For the Mars mission scenario, the 

model representation error for the maximum temperature is plotted in Figure D.2-7. For the 

Venus mission scenario, the model fit distribution is plotted in Figure D.2-8. The model 

representation error distribution for the Mars response surface equation is approximately normal 

with a mean of -0.1103 and a standard deviation of 0.6177. Hence, it can be concluded that the 

response surface equation is an accurate representation of the high-fidelity thermal model. 

The model representation error distribution for the Venus response surface equation is 

approximately normal and has a mean of 0.778, but a standard deviation of 3.48. The response 

surface equation for Venus is modeling the high-fidelity thermal model accurately, but there is a 

lot of room for improvement. Referring back to Figure D.2-4, there is a region on the plot 

between 205–355 °C where it appears that there is no temperature response for the runs made 

from the DOE. The model representation error distribution is found by randomly setting the 

model factors and calculating the temperatures using both the high-fidelity thermal model; this is 

due to an error made while constructing the response surface. Unfortunately, the error was not 

discovered in time to correct for this report. The orbital period was a new variable introduced for 

the Venus mission scenario and replaced drag pass duration as a way to better track how the 

variation in orbit geometry affects the thermal response. The error was made by using the early 

20-hour orbit period and resulting orbit geometry and only varying this orbit by 



1.0 hours. 

The way it should have been varied was to select the 20-hour orbit as the +1 point in the DOE 

table, selecting a short period ~2-hour orbit as the -1 point in the DOE table and an orbit 

somewhere in the middle of the range ~11-hour orbit as the 0 point in the DOE table. After 

discovering the error, the response surface equation was regenerated eliminating the orbital 

period from the equation. Some fidelity was lost in eliminating the orbital period variation but 

the response surface equation is still accurate enough for the purposes of demonstrating the 

temperature corridor AB strategy as shown by the goodness of fit tests. Correcting this error and 

breaking the density range into three separate response surface equations will be the first thing 

accomplished for Phase 2. 
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Figure D.2-7. Mars Mission Scenario Model Representation Error Distribution 

Figure D.2-8. Venus Mission Scenario Model Representation Error Distribution 

The model fit and model representation errors are accounted for in the response surface equation 

when the temperature calculation is made from within the AA simulation to provide a 

conservative temperature. Another error is added as a bias to the temperature calculated by the 

response surface. This error is present because the high-fidelity thermal model will typically not 

be correlated to the AB flight temperature data. This error is typically unknown until the first 

couple of drag passes are made and the flight temperatures and predicted temperatures compared. 
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Therefore, a short calibration period is required but this can be accomplished during walk in 

which makes up the first initial orbits where the spacecraft’s periapsis is gradually lowered into 

the AB altitude corridor. One important aspect of response surface modeling that must be 

emphasized is that the response surface equations are only valid over the range for which they 

are defined. It must be stressed that even a small amount of extrapolation in any factor included 

in the equation can produce invalid results. 

D.3 AA Simulation Software 

A generic response-surface equation thermal analysis (GRETA) computer program was written 

for use in the AADS. There are two versions, one written as a standalone program which 

includes the ability to run Monte Carlo simulations, the other for use directly with AADS which 

does not have a Monte Carlo simulation. AADS accesses the GRETA routines via an external 

function call. This architecture is beneficial in that the response surface equation coefficients or 

GRETA routines can be updated independently of AADS. The main feature of GRETA is that 

GRETA will accept any number of variables and hence any number of response surface equation 

coefficients so long as the program follows the form of Eq. (D.1-1). GRETA will allow the user 

to modify any set of factors and thus calculate a new response. Additionally, GRETA allows the 

user to input a value for the response and calculate the value of one specific factor, holding all 

others constant. For AA, the ability to calculate the value of a factor is crucial. For AA the 

response is the temperature and the factor which needs to be determined is the atmospheric 

density. During the AA simulation a temperature within the temperature corridor is sent by 

AADS to GRETA and the density is calculated. Hence, the temperature can be used to control 

the spacecraft during AB. Using the temperature represents a major step forward since the 

temperature is measured directly onboard the spacecraft and can be used to determine what 

temperature is input to GRETA for the next orbit pass. The temperature and corresponding 

density for the Mars Mission simulation is shown in Figures D.3-1 and D.3-2.
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Figure D.3-1. Periapsis Temperature for a Mars Mission Scenario 

Figure D.3-2. Periapsis Density for a Mars Mission Scenario 
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D.4 References 

iMSC/PATRAN User Manual, MacNeal-Schwendler Corporation, Version 2010, February 2010. 

iiThermal Desktop User Manual, Cullimore and Ring Technologies, Inc., Version 5.3, 

January 2010. 

iiiDec, John A., Gasbarre, Joseph F., and Amundsen, Ruth M., “Thermal Modeling of the Mars 

Reconnaissance Orbiter’s Solar Panel and Instruments During Aerobraking,” 07ICES-64, 

37th International Conference On Environmental Systems, Chicago, Illinois, July 2007. 

ivAmundsen, Ruth M., Dec, John A., Gasbarre, Joseph F., “Thermal Model Correlation for Mars 

Reconnaissance Orbiter,” 07ICES-17, 37th International Conference on Environmental Systems, 

Chicago, Illinois, 2007. 

vAmundsen, Ruth M., “Aeroheating Mapping to Thermal Model for Autonomous Aerobraking 

Capability,” 22nd Annual Thermal Fluids and Analysis Workshop, Newport News, Virginia, 

2011.

viBreyfogle, F. W., Implementing Six Sigma: Smarter Solutions Using Statistical Methods, 

2

nd Ed., John Wiley & Sons, Inc., Hoboken, New Jersey, 2003. 

viiNIST/SEMATECH e-Handbook of Statistical Methods, 

http://www.itl.nist.gov/div898/handbook/, 2011. 

viiiDec, J. A., Probabilistic Thermal Analysis During Mars Reconnaissance Orbiter 

Aerobraking, AIAA Paper 2007-1214, January 2007. 

ixJMP®

, Version 8. SAS Institute Inc., Cary, North Carolina, 1989-2011. 
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Appendix E. Mars-GRAM 2010 (Supplement to Section 7.3.1.3) 

E.1 Mars-GRAM 2010 

The Mars-GRAM is an engineering-level atmospheric model widely used for diverse mission 

applications. Applications include systems design, performance analysis, and operations 

planning for AB; entry, descent, and landing (EDL); and aerocapture. Mars-GRAM’s 

perturbation modeling capability is commonly used, in a Monte-Carlo mode, to perform highfidelity engineering end-to-end simulations for EDL1

. Mars-GRAM 2005 has been validated2

against Radio Science data and both nadir and limb data from the TES3.

There are several traditional Mars-GRAM options for representing the mean atmosphere along 

entry corridors. The first option is mapping Year 0, with user-controlled dust optical depth and 

Mars-GRAM data interpolated from ARC’s Mars Global Circulation Model (MGCM)4results 

driven by selected values of globally uniform dust optical depth. The second is the auxiliary 

profile option in which the user can read and use any auxiliary profile of temperature and density 

versus altitude in the mapping Year 0 option. In exercising the auxiliary profile Mars-GRAM 

option, the values from the auxiliary profile replace data from the original MGCM databases. 

Examples of auxiliary profiles include data from TES (nadir or limb) observations or Mars 

mesoscale model output at a particular location and time. The final option is mapping Years 

1 and 2, with Mars-GRAM data coming from MGCM results driven by the observed TES dust 

optical depth during TES Years 1 and 2. From the surface to 80 km altitude, Mars-GRAM is 

based on the ARC MGCM. Above 80 km, Mars-GRAM is based on the University of Michigan 

Mars Thermospheric Global Circulation Model (MTGCM)5. Mars-GRAM and MGCM use 

surface topography from MGS Mars Orbiting Laser Altimeter (MOLA), with altitudes 

referenced to the MOLA constant potential surface (areoid). 

Mars-GRAM standard inputs are geographic position and time. The user can adjust the optical 

depth of the uniformly mixed background dust level, add a seasonal dust optical depth, set the 

dust particle diameter and density, and provide the starting Ls, position, duration, intensity, and 

radius of a dust storm. Mars-GRAM outputs include density, temperature, pressure, winds, and 

selected atmospheric constituents. Three Mars-GRAM parameters allow standard deviations of 

Mars-GRAM perturbations to be adjusted: rpscale can be used to scale density perturbations up 

or down, rwscale can be used to scale wind perturbations, and wlscale can be used to adjust 

wavelengths (spectral range) of the perturbations. 

E.1.1 References 

1

Striepe S. A. et al., (2002) AIAA Atmospheric Flight Mechanics Conference and Exhibit, 

Abstract # 2002-4412. 

2

Justus C. G. et al., (2005) “Mars Aerocapture and Validation of Mars-GRAM with TES Data,” 

53rd JANNAF Propulsion Meeting. 
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3

Smith M. D. (2004) Icarus, 167, 148-165. 

4Haberle, R. M., Pollack, J. B., Barnes, J. R., et al., (1993) “Mars Atmospheric Dynamics as 

Simulated by the NASA Ames General Circulation Model 1. The Zonal-Mean Circulation,” 

Journal of Geophysical Research, Vol. 98, No. E2, pp. 3093-3123. 

5Bougher, S.W., et al., (1990) “The Mars Thermosphere: 2. General Circulation with Coupled 

Dynamics and Composition,” Journal of Geophysical Research, Vol. 95, No. B9, pp. 14,811-

14,827. 

E.2 Mars-GRAM 2010 Adjustment Factors 

E.2.1 Adjustment Factor Requirements 

The adjustment factors generated by this process had to satisfy the gas law: p = ρRT as well as 

the hydrostatic relation: dp/dz = -ρg. If T is assumed to be unchanged and both p and ρ are 

adjusted by a common factor (F), both relations are preserved. The adjustment factors 

[F(z,Lat,Ls)] were expressed as a function of height (z), latitude (Lat), and areocentric solar 

longitude (Ls). This adjustment factor (F), is applied to the daily mean ARC MGCM density and 

pressure (0–80 km) and University of Michigan MTGCM density and pressure (above 

80 km). The pressure scale height (RT/g) is unchanged by this process. However, since the 

pressure has been changed by the adjustment factor, the height of the 1.26 nbar pressure level, 

referred to as ZF in Mars-GRAM, has been changed. 

The daily mean MGCM or MTGCM density, DTA0, and the daily mean MGCM or MTGCM 

pressure, PTA0, depend on height (z), latitude (Lat), solar longitude (Ls), dust amount (tau), and 

solar activity parameter (F10). The adjusted values of DTA0′ and PTA0′ are computed from the 

adjustment factor (F) using the following equations: 

DTA0′ = DTA0 * F(z, Lat, Ls) Eq. (E.2-1) 

PTA0′ = PTA0 * F(z, Lat, Ls) Eq. (E.2-2) 

where the adjustment factor (F) has been determined. 

Adjustment factor (F) is used to adjust ZF by the relation: 

ZF′ = ZF + H ln(F) Eq. (E.2-3) 

where H is local pressure scale height. 
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E.2.2 Development of MTGCM Factors 

The Mars-GRAM density and pressure need to be consistent at 80 km, where the transition from 

MGCM to MTGCM data occurs. Thus, the assumption was made that F(80, Lat, Ls) for the 

MTGCM data had to be the same as the adjustment factor at 80 km for the MGCM data. After 

adjustment factors F(80, Lat, Ls) were determined from the MGCM analysis, they were used to 

determine MTGCM adjustment factors by use of the following equation: 

F(z, Lat, Ls) = F(80, Lat, Ls)*(1 + A + B

2

) Eq. (E.2-4) 

where the height parameter = (z – 80) and the coefficients A and B depend on Lat and Ls. 

Final adjustment factors F(z, Lat, Ls) for MTGCM data were implemented into Mars-GRAM and 

a validation run comparing Mars-GRAM 2010 versus MGS, Mars Odyssey, and MRO AB data 

from the Planetary Data System (PDS) was completed. Any residual variation of AB density 

about mean values that became apparent during this process was used to update the height 

dependence of Mars-GRAM perturbation standard deviations. 

E.3 Improvement in Mars-GRAM 2010 Results 

E.3.1 Improvement of Mars-GRAM 2010 at Lower Altitudes 

Application of adjustment factors for the ARC MGCM data yields improved comparisons 

between Mars-GRAM and TES limb data, as shown by density ratios (Mars-GRAM/TES Limb) 

given in Figure E.3-1. Prior to adjustment these density ratios were as low as 0.65 near 60 km. 

Figure E.3-1.Latitude-Height Contours of Density Ratio (Mars-GRAM/TES Limb) after 

Application of MGCM Adjustment Factors
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Mars-GRAM 2005 and Mars-GRAM 2010 Map Year = 0 results have been compared for three 

locations at Local True Solar Time (LTST) 2 and 14. 

 Location 1 (L1) = 22.5o S, 180o E, Ls = 90 ± 5, tau=.11

 Location 2 (L2) = 22.5o S, 180o E, Ls = 75 ± 5, tau=.12

 Location 3 (L3) = 2.5o N, 180o E, Ls = 210 ± 5, tau=2.65 *Dust Storm case*

Figure E.3-2 provides the density ratios of Mars-GRAM to TES for Mars-GRAM 2005. As

Figure E.3-3 shows, the application of the adjustment factor in Mars-GRAM 2010 results in 

ratios of approximately 1 at lower altitudes. 

Figure E.3-2. Density Ratio (Mars-GRAM/TES) for Mars-GRAM 2005 
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Figure E.3-3. Density Ratio (Mars-GRAM/TES) for Mars-GRAM 2010 

At the higher altitudes, Mars-GRAM 2010 results have corrected the effect of the underestimated 

dust aloft in the MGCM. At location 3, the Mars-GRAM 2010 density ratio has shifted closer to 

1. This demonstrates that the addition of adjustment factors to Mars-GRAM 2010 has improved 

the results for the Map Year = 0 cases for large tau values. 

E.3.2 Improvement of Mars-GRAM 2010 at Aerobraking Altitudes 

Mars-GRAM modeled data output has improved at AB altitudes by adding University of 

Michigan MTGCM adjustment factors which included height parameters and thermosphere 

coefficients. Improvement has been quantified by examining all of the profile data density ratios 

for each PDS orbiter. The 99th percentile profile shows the most extreme cases of ratio values 

while eliminating outliers that do not contribute to the standard profile. Density ratios for the old 

and updated Mars-GRAM versions will be shown versus height and latitude globally for Mars; 

these results will show the variability in certain regions on the red planet. All of these results 

will show that the updated Mars-GRAM is producing more realistic results, which will assist in 

future AA procedures. 

All of the density ratios from the PDS profile datasets are shown in Figures E.3-4 through E.3-6. 

Each of these figures shows the density ratio of the PDS density to the Mars-GRAM output 

density versus height, with the blue lines representing the old Mars-GRAM output and the red 

lines showing the updated Mars-GRAM 2010 output using the thermosphere coefficients. Each 

one of the datasets showed an improvement with the ratio values for the latest version of MarsGRAM. The MGS/Mars-GRAM density ratio originally was an average 2.6 with a maximum 

value of 16.1, but the updated Mars-GRAM 2010 ratio data averaged 1.8 with a maximum value 

of 10.7. The initial MRO/Mars-GRAM density ratio reached a maximum of 10.0 and averaged 

2.0, whereas the new ratio only reached a maximum of 3.6 and averaged 0.9—close to the 
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optimal 1.0 ratio. The Mars Odyssey /Mars-GRAM ratio exceeded all of the other ratios with a 

maximum ratio of 39 but had an average of 3.9, which means that there were several outlying 

profiles that skewed the average profile. However, the newly modeled Mars Odyssey/MarsGRAM 2010 ratio only reached a maximum of 8.2 with an average of 0.99. As these results 

show, the updated Mars-GRAM 2010 with MTGCM adjustment factors including thermosphere 

coefficients greatly improves the results of the modeled data when compared to observed data. 

Figure E.3-4. Density Ratios of MGS Data to the New and Old Mars-GRAM Output Data

Figure E.3-5. Density Ratios of MRO Data to the New and Old Mars-GRAM Output Data
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Figure E.3-6. Density Ratios of Mars Odyssey Data to the New and Old Mars-GRAM Output Data

Taking the 99th percentile of all the density profiles illustrates the significant change the updated 

Mars-GRAM 2010 has on the profile density ratios. As shown in Figure E.3-7, the least amount 

of change was observed in the MGS data over the 99th percentile profile data, with an overall 

change of 2.0 units across the altitude range. The MRO data showed a significant improvement 

from the old version of Mars-GRAM, reducing the higher altitude ratios from 6.0 to close to the 

optimal value of 1.0 on the updated data. However, the greatest change in ratio values occurred 

with the Mars Odyssey data where the older data reached values close to 20.0, but the newer data 

brought the ratios down to a range between less than 1.0 to over 4.0 at the higher altitudes. All 

of the ratio values of the datasets improved from the old Mars-GRAM data output to the updated 

Mars-GRAM 2010 version; therefore, the inclusion of MTGCM adjustment factors has shown to 

be valid in providing more realistic output to be used in future endeavors. 
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Figure E.3-7. The 99th Percentile Density Ratios of the Profile Data from MGS, MRO, and Mars 

Odyssey to Mars-GRAM 2010 Output Versus Height 

Although AA procedures are sensitive to density values at certain altitude levels, showing the 

density ratio values according to latitude is beneficial for mission planning operations. Figures 

E.3-8 and E.3-9 show the ratio of the observed density values to the Mars-GRAM output values 

for the old version and the updated Mars-GRAM 2010 version versus height and Mars latitude. 

Before the MTGCM adjustment factors including thermosphere coefficients were added to the 

Mars-GRAM code (Figure E.3-8), the ratio values were higher than the optimal value of 1.0, 

especially at locations toward the poles. The contour lines are tight near the poles, meaning lots 

of variability exists with the comparisons. In the updated plot shown in Figure E.3-9, a large 

area of the map is covered with the 1.0 ratio value, especially between 30°S and 15°N. Although 

a large discrepancy of ratio values still exists toward the poles, the variability has decreased with 

the inclusion of the adjustment factors. Improvement in density ratio values across latitudes can 

be beneficial for planning AA procedures on Mars.
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Figure E.3-8. Contour Plots of the Ratio of Observed PDS Density Values to Mars-GRAM Output 

Values (before Adjustment) versus Height and Latitude 

Figure E.3-9. Contour Plots of the Ratio of Observed PDS Density Values to Mars-GRAM 2010 

Output Values (after Adjustment) versus Height and Latitude 
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Appendix F. Onboard Atmospheric Modeling and Prediction for 

AA Missions (Supplement to Section 7.3.2.1) 

F.1 Introduction 

The first planetary AB mission, Venus Magellan, took 70 days and over 700 passes1through the 

atmosphere to enhance the scientific return of the extended mission. AB was performed to 

reduce the orbital eccentricity after the primary science mission thereby lowering apoapsis 

altitude and improving the resolution of the gravity mapping. Based on the successful Magellan 

experience, AB became an enabling technology for recent Mars orbiting missions. These 

missions had AB operational phases that took about 850 orbits for MGS, 77 days and 325 orbits 

for Mars Odyssey, and 145 days and 420 orbits for MRO. MGS was anomalistically long due to 

a broken solar array which constrained the maximum dynamic pressure during an AB pass. 

These missions used the solar arrays as the primary drag area and consequently, except for MGS, 

the temperature of the solar arrays was the limiting atmosphere dependent factor in designing the 

AB corridor1, although other subsystems had to be considered. 

Although AB has numerous benefits, there are cost and risk. The greatest costs are the large 

operations team and DSN coverage that have been required to maintain the AB schedule. The 

greatest risk2has been the inability to predict the orbit-to-orbit variability of the Martian 

atmosphere. One of the functions performed on an orbit-by-orbit basis is an estimation of the 

atmospheric density profile. These profiles were recovered using telemetric accelerometer and 

gyroscope data from the IMU. After the AB pass, these data were related to aerodynamic forces 

and then mapped into atmospheric density at 1-second intervals along the orbit. The recovered 

density profiles were analyzed to determine atmospheric temperature, gravity wave phenomena, 

orbit-to-orbit variability, longitude dependent waves, latitudinal gradients, and other 

information.3 To predict upcoming atmospheric conditions, this information was evaluated on a 

day-by-day basis by a team of atmospheric scientists, the Atmospheric Advisory Group (AAG). 

Implementation of AA will require the development of robust, reliable, and simple methods for 

the estimation of atmospheric density profiles from the IMU data and the prediction of future 

atmospheric conditions without the human interpretation provided by the AAG. 

Mars, Venus, and Titan are targets for AA missions. It is well known that the Mars atmosphere 

provides a challenging environment for AB because of the high orbit-to-orbit variability in 

atmospheric density3. An abundance of AB data provides adequate information for testing AA at 

Mars. High orbit-to-orbit variability has been detected near the terminator and on the night side 

of Venus4

. Even though there are no accelerometer data for detection of small-scale variations, 

Pioneer Venus Orbiter (PVO) mass spectrometer data provide some insight. 

Little is known about the variability of the Titan atmosphere on the temporal and spatial scales of 

interest for AB. However, during the Huygens descent through the atmosphere, significant wave 

structure was found in the density and temperature profiles in the altitude range of interest5, and 
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Cassini mass spectrometer measurements during Titan flybys in the altitude range from 1,000 km 

to 1,600 km identified relevant vertical and horizontal wave structure in various constituents and 

in total density.6

The current paper presents various potential methods for representing density profiles derived 

from IMU data during AA, for recovering profile parameters from IMU data, and for optimal 

combinations of profiles for prediction. Algorithms are evaluated based on simplicity, 

robustness, and applicability to onboard limitations. The atmosphere of Mars is the primary 

focus due to the wealth of data, but Venus and Titan are discussed briefly. 

F.2 Atmospheric Estimations during Past AB Missions 

Magellan entered orbit in August 1990 with an orbit eccentricity of about 0.4. After the 4th 

Venusian day, spanning over 7,000 orbits, the AB phase was initiated and reduced the 

eccentricity to about 0.03 after 70 days and over 700 AB passes. During AB, the active side of 

the solar array was turned away from the free stream direction to minimize the temperature 

encountered by the cells, adhesives, and structure. Maximum solar array (SA) temperature was 

the limiting factor constraining the rate of AB1. Pre-AB studies provided a relationship between 

free stream dynamic pressure and maximum SA temperature, but atmospheric density was 

required to determine dynamic pressure. The method for determining atmospheric density 

during each Magellan pass relied on Doppler radio tracking data. Pre-pass and post-pass 

tracking data were processed in a single orbit determination (OD) that included density at a 

specified altitude as a solution parameter. This approach provides continuity of the equations of 

motion across the unobserved AB pass. To provide a unique solution for density, a model for 

density versus altitude was used. The contemporary Venus International Reference Atmosphere 

(VIRA) model7 provided density every 5 km and a constant scale height was used for 

interpolation. Density at 140-km altitude was the solution parameter in the OD process and the 

scale heights from the VIRA model were used to map density to other altitudes. For a 

hydrostatic atmosphere, this is equivalent to assuming that the temperature profile is given and 

the density profile is defined within a multiplicative factor. 

Magellan AB was so successful that AB was considered a validated technology and was enabled 

for the MGS mission in 1997. The MGS AB corridor was again defined in terms of the 

surrogate variable, free stream dynamic pressure. However, after the discovery of the broken 

solar array on orbits 11 through 15, the corridor criteria changed from limiting SA temperature to 

limiting torque on the broken SA yoke8and for the only time, the maximum dynamic pressure 

became the most relevant control variable. 

During MGS operations, density at periapsis was estimated by two different methods. Members 

of the AAG used the IMU data at a one per second sample rate to model the atmospheric density 

profile. IMU accelerometer measurements were mapped to the vehicle center of mass using the 

IMU angular rate data and the resulting center of mass acceleration was converted to 
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atmospheric density using a database of aerodynamic force coefficients. Density at periapsis and 

density scale height were extracted using a least squares solution from three data sets that 

included all data within 1, 1.5, and 2 scale heights of periapsis.9 The “best” model was selected 

by visual comparison of the model and the data density profiles. Estimated scale heights were 

averaged over a few orbits and provided to the Navigation Team to be used for corridor control 

maneuver calculations and orbit determination. The Navigation Team used this scale height to 

estimate the density at periapsis using radio tracking data in the same way as was done for 

Magellan. The need for more autonomy10 was recognized well before the end of the 15 months 

required to complete MGS AB. When adjusted for the different between predicted and observed 

scale height, the AAG and navigation estimates of periapsis density were within 5 percent, 1

The periapsis altitude, latitude, density at periapsis, local solar time (LST), density scale height, 

and solar longitude as determined during operations, are shown in Figure F.2-1. In an idealized 

atmosphere, density scale height is proportional to temperature, so this variable can be thought of 

as the local average atmospheric temperature. The first 202 orbits of MGS were termed “phase 

1,” after which there was a 6-month “hiatus” while periapsis regressed over the North Pole at a 

periapsis altitude near 170 km. AB “phase 2” began on orbit 573 and ended on orbit 1285 about 

2 weeks after periapsis regressed over the South Pole during the winter. 

Figure F.2-1. Summary of AB Conditions for MGS, Mars Odyssey, and MRO 
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Mars Odyssey, the most aggressive AB mission to date, went to the lowest altitude and 

experienced the highest densities, unintentionally reaching 107 kg/km3

on orbit 106. Like MGS 

and MRO, the science orbit required a particular LST, which meant that the AB phase had to end 

within a few days of the planned final day. Both Mars Odyssey and MRO used Mars-GRAM11

to define the density profile and the OD process to determine the density by solving for a 

multiplier to be applied to the Mars-GRAM density profile. In addition, as the latitude of AB 

precessed toward the North Pole, it was expected that the thermospheric temperature would 

decrease. Instead the temperature increased dramatically as indicated by the density scale height 

in Figure F.2-1. The inferred temperature increase has been interpreted as a polar warming12 and 

led to accelerometer derive density scale heights between 7 km and 14 km with an average above 

10 km. The nominal atmosphere scale height was expected to be closer to 6 km and did return to 

that value after the latitude was south of 60°N. The difference in scale height partially led to the 

large density differences between Mars-GRAM and the IMU-derived densities. 

Mars Odyssey tested new techniques. Though Mars Odyssey used maximum dynamic pressure 

to define the AB corridor, it was the first mission to have a near real time prediction of the solar 

array temperatures for a comparison with the measured temperatures.13 Based on this comparison 

over a number of orbits, the AB safety margin was reduced, permitting Mars Odyssey AB to 

proceed at a faster rate. During this mission, the first onboard algorithm14, called the Periapsis 

Timing Estimator (PTE) and designed to reduce the work load of the ground flight team, was 

tested. 

MRO had a less risky AB phase than Mars Odyssey because there were 6 months between Mars 

Orbit Insertion (MOI) and the time when the orbit would have the proper LST. AB was initially 

performed with nearly a 200 percent safety margin as opposed to the 100 percent margins used 

for MGS and Mars Odyssey. However, as suggested by the significant increase in density after 

orbit 200, MRO fell behind the time line during the early conservative approach and AB was 

more aggressive for the last 200 orbits. PTE was used operationally during this mission with an 

estimated saving of about $1M. The operational process for atmospheric estimation was 

essentially the same as Mars Odyssey. 

F.3 Atmospheric Prediction Performance during Operations 

During Mars AB operations, the AAG monitored the characteristics of recent AB passes to 

anticipate major changes in the atmosphere. The simplest variation used for modeling the 

density () profile was the exponential or constant scale height (CSH) model 

Eq. (F.3-1)

h p

h hp– – 

H

s

= exp ----------------------
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where density, as determined from IMU data9, is a function only of the altitude (h) above some 

reference or base altitude, here taken as periapsis. Hs is called the density scale height. Such a 

model results for a homogeneous, isothermal atmosphere in hydrostatic equilibrium, and the 

density scale height is related to the atmospheric temperature (T), the local gravity acceleration 

(g), and the mean molecular weight by Hs=kT/mg, where k is the Boltzmann constant. Using 

this as the basic model, the AAG studied density and temperature latitudinal gradients, amplitude 

of gravity waves, and among others, the accuracy of predicting the periapsis density for the 

upcoming orbit using the density and scale height from the current orbit. This latter metric was 

called “persistence’ and is a measure of the atmospheric variability that the AB system must 

accommodate. The ratio of observed to predicted periapsis density for orbit n+1 is 

 Eq. (F.3-2)

where the altitudes are provided by the OD process and “observed” density and scale height are 

determined from IMU data. Orbit n is called the “base’ orbit and orbit n+1 is the “predict” orbit.

Figure F.3-1 provides the persistence for all three Mars missions. The means over the entire 

missions are between 1.06 and 1.08, with the deviation from unity mostly being an artifact of 

averaging a positive ratio. Mars Odyssey has the largest 19 orbiting running mean at 1.38 and a 

maximum standard deviation of 1.10 (i.e., over a factor of two) variation orbit to orbit. Missionwide standard deviations range from 37 percent for MRO to 47 percent for Mars Odyssey. The 

large Mars Odyssey value is perhaps due to the large variations early in the mission between 

70°

and 80°latitude. Except for Mars Odyssey during this time, the deviations from the means 

are much smaller at high latitudes than in the mid latitudes and equatorial regions. Poleward of 

60°

latitude, the 1 deviations are generally between 20 percent and 30 percent. From a 

geometric argument, it might be expected that the deviations would become smaller near the pole 

since great circle distances between successive periapsis locations become shorter. The large 

Mars Odyssey deviations near the pole are likely due to the polar warming producing strong 

winds and large, asymmetric temperature variations around the pole.12, 15 In the tropics, 

persistence is the largest for all three missions likely due to the global scale tides that appear as 

stationary waves.16 These waves were sufficiently persistent and observable during MGS that 

models were developed during operations to include their influence on predicting subsequent 

periapsis densities and to plan orbit trim maneuvers.17 Latitude-dependent empirical models were 

developed post flight for inclusion of such waves in Monte Carlo simulations of AB missions.18

These waves appeared for brief periods during Mars Odyssey and MRO, but not with sufficient 

persistence to be included in operational decisions. 

obsn + 1

predn + 1

-------------------

obsn + 1

obsn

-----------------

hn + 1hn–

Hsn

= exp ------------------------
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Figure F.3-1. Persistence for MGS, Mars Odyssey, and MRO Missions. Dots are data and lines are 

the 19 Orbit Running Mean and Mean +/1 1. Full Mission  and  are shown. Dots and lines 

change color as periapsis regresses past the pole. 

Ignoring the latitudinal, seasonal, diurnal, and other dependencies and considering the orbit-toorbit variability as a random process provide similar results for all three missions. It was found18

that persistence can be reasonably represented by a gamma probability distribution. Maximum 

likelihood estimates (95 percent) of the two gamma distribution parameters for each mission 

result in probability density distributions shown in Figure F.3-2. The histograms are from the 

same ratios shown in Figure F.3-1. Within the 95 percent confidence interval, the values of 

and  are indistinguishable from each other and compare well with the simple standard 

deviations in Figure F.3-1.

Since underestimating density usually causes higher mission risk than underestimation, these 

distributions can be used to approximate the probability associated with any ratio of obs to pred. 

For example, for MGS, Mars Odyssey, and MRO, the probabilities that the ratio will be less than 

2 are 98.5 percent, 97 percent, and 98.6 percent, respectively. These probabilities are consistent 

with the AB rule of thumb requiring a design safety factor of 2 for the uncertainty in density. 

The distributions might be used for Monte Carlo simulations of AB missions. 
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Figure F.3-2. Gamma Probability Density Distribution Based on Maximum Likelihood Fit to 

Persistence Data for Three Mars AB Missions 

F.4 Relevant Atmospheric Parameters for Aerobraking 

The relevant atmospheric parameters depend on the criterion selected to define the AB corridor. 

If the limiting condition is related to maximum aerodynamic force or torque, then maximum 

dynamic pressure is likely the relevant parameter. If maximum temperature is the limiting factor 

for a component with rapid thermal response, maximum free stream heat flux might be the 

relevant parameter. If temperature is the limiting factor for a component with slow thermal 

response (e.g., high thermal inertia or low radiative cooling), total or integrated heat flux may be 

most relevant. Here thermal response time is relative to the duration of the AB pass. To 

calculate any of these parameters requires knowledge of some characteristic of atmospheric 

density along the trajectory. To predict the variation for subsequent orbits requires an 

atmospheric model. For this discussion, consider Figure F.4-1, which shows the recovered 

density versus time and versus areodetic altitude for a typical Mars AB orbit. A least squares fit 

to data with > 2 kg/km3

using the CSH model produced the “model” results. For this orbit, 

maximum density occurs 57 seconds before periapsis, a feature not captured by CSH. There is 

considerable asymmetry in the time profile, with density rising faster than it falls. If maximum 

dynamic pressure or maximum heat flux are the selected corridor criteria, then recovering the 

density at periapsis using the data or the model is inadequate. Further, when maximum 

temperature is the criterion, the shape of the heat flux as well as the total heat flux could become 

a consideration and only a detailed thermal analysis19 can address these issues. The CSH scale 

height of 8.9 km, which might be used to predict density for the next orbit, represents the 

inbound, outbound, and mean density profiles reasonably well. Maximum density occurs 2 km 

above periapsis and density varies by nearly a factor of 3 within this altitude range. This 

gradient is likely due to a strong along track density gradient. Within this altitude range, Mars 

Odyssey spent about 110 seconds and traveled about 360 km along track. The high-frequency 

deviation from a “smoothed” density profile is generally attributed to gravity waves20 and is a 

common feature at high latitudes. Note that accelerometer noise becomes relevant above 
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altitudes of 125 km. Early and late in the AB pass, accelerometer data noise dominates the 

signal and the recovered “density” is often negative. These phases of the pass are used to 

determine a time linear approximation to the accelerometer bias, which is used to correct the data 

during the pass.9

Figure F.4-1. Mars Odyssey Orbit 159 Atmosphere Density Inferred from Accelerometer Data 

Although the density variation is usually modeled as a function of only altitude, along track 

variations may dominate over the altitudinal. Large-scale variations in atmospheric properties, 

from those assumed for the simple CSH model, might be expected to include an along track 

variation () in base density and/or base temperature, and an altitudinal variation in temperature. 

Examples of how such variations affect the density profiles are shown in Figure F.4-2. 

Figure F.4-2. Effects of Along Track and Altitudinal Density and Temperature Gradients on Density 

Profiles 
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There are obvious deviations in the altitudinal profiles but the differences in the temporal 

variation are more subtle. The CSH model is of course a straight line in the two right panels and 

for this case has a scale height of 7 km. Assuming base density varies linearly with along track 

angle () provides different inbound and outbound profiles and a substantial difference in the 

two densities within a kilometer or two of periapsis that is comparable to the altitudinal variation 

in density. An along track linear temperature variation produces a linear variation in scale height 

resulting again in different inbound and outbound profiles. This variation causes little density 

differences in the vicinity of periapsis but an increasing difference with altitude. The model with 

temperature increasing linearly with altitude (T(h)) has the same inbound and outbound altitude 

profiles and no significant deviation in the first 10 km, but deviates significantly 20 km above 

periapsis and higher. One can assume that some combination of these and other effects influence 

every AB pass. For AA, the first issue is to quantify such effects and the second issue is to 

decide whether or not to include them in the atmospheric estimation process. 

As examples of some of the multiplicity of effects on real AB passes, consider Figure F.4-3 

which provides examples of Mars Odyssey profiles that are representative of the types of 

phenomena seen during all the Mars AB missions. The noticeable increase in data noise level is 

due to halving the sample rate on orbit 134 and again on orbit 270. The “bell-shaped” density 

variation with time, shown for the CSH model in Figure F.4-2, is not representative of any of 

these orbits. For orbit 44, the factor of two change in density over 10 seconds is not atypical for 

Mars. The time and altitude of maximum density are meaningless concepts for pass 157. The 

large asymmetry for orbit 159 results in maximum density occurring a full minute before 

periapsis. Generally solar power and Earth communications are lost during the AB pass. Thus, 

there are clear reasons to want to minimize the duration that the vehicle is in the AB orientation. 

The AB phase is usually designed to be centered on periapsis. With such large asymmetries, 

extra time may have to be allocated, or if the asymmetries are consistent from orbit-to-orbit, 

biasing the center of the pass away from periapsis may be desirable. The AB passes for orbits 

157 and 159 are 7 hours apart in time, 2 km apart in altitude, and essentially at the same latitude, 

yet the profiles and the maximum density are dramatically different. These phenomena are the 

sort of natural orbit-to-orbit variabilities that are difficult to predict and therefore must be 

included as uncertainties in the design of any AB mission. They require a particularly robust 

design for an AA mission. It will be seen that there is some orbit-to-orbit persistence in the 

density, density scale height, and temporal asymmetry. 
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Figure F.4-3. Four Odyssey Orbits 

Near factor of two density spikes like P280 are uncommon. They would be important if 

maximum density or heat flux is the consideration and not so important if total heat flux is the 

consideration. Even in the former case, the characteristic response time of the system will play a 

role. At Mars, the lack of persistence in the shape and maximum value of the density profile 

from orbit to orbit and the small-scale deviation are attributed to global scale longitudinal waves 

and vertically propagating gravity waves. The longitudinal waves during MGS have been 

modeled18 and are attributed to non-migrating thermal tides16 in the lower atmosphere that 

propagate to the upper atmosphere in the equatorial and mid-latitude regions. On the other hand, 

the source of the gravity waves is not known, but they are believed to originate in the lower 

atmosphere, and at high latitudes, and to propagate vertically while increasing in amplitude with 

subsequent “breaking” in the lower thermosphere.20 Their latitudinal, seasonal, and diurnal 

variations of root mean square (rms) amplitude have been partially defined from previous AB 

data.3 Whether they are significant for a particular mission depends on the criteria that limit AB. 

In the modeling approaches that follow, neither of these wave types will be a consideration as 

they are difficult to model on time scale of interest to AB. 

The observed density asymmetries in time could be due to either an along track density gradient 

at a fixed altitude or to the areodetic altitude gradient at a constant distance from the center of the 
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planet. First consider a possible density gradient. Mars Odyssey, like the other Mars AB 

missions, is in a near polar orbit so along track is essentially latitudinal. The polar regions are 

generally colder than the tropics and consequently the density scale height is smaller in polar 

regions. This would suggest that, for a fixed altitude, a lower density would be expected near the 

pole than in the tropics and strong latitudinal density gradients have been seen in all three Mars 

missions. On the second possible reason for a density asymmetry, periapsis is the point in the 

orbit that is closest to the center of mass; but, due to planetary flattening, does not usually 

correspond to the point of lowest areodetic altitude. Planetary flattening is defined by the 

reference ellipsoid which approximates the equipotential surface at the surface of the planet. The 

reference ellipsoid is selected to approximate such a surface by defining an equatorial radius 

(a) and a flattening (f) that give a polar radius of a(1-f). For the Earth, the ellipsoid can be 

thought of as defining “mean sea level.” On solid, ocean-less planets, the ellipsoid is selected to 

provide an equatorial radius that approximates the physical mean radius and the flattening is 

usually selected to represent the equipotential defined by the central gravitational potential, J2,

and the centrifugal potential due to planetary rotation. In an idealized, isothermal atmosphere, 

surfaces of constant planetodetic altitude correspond to surfaces of constant pressure and density. 

Hence, in a real atmosphere, density should be approximately constant on surfaces of constant 

planetodetic altitude. Many empirical atmospheric models, as will this paper, use this surface as 

the reference from which altitude is measured. 

Density: In this paper it is assumed that the AB corridor is defined in terms of variables that 

require a knowledge of atmosphere density. But readers should remember that density is often a 

surrogate for some other physical quantity that defines the limits on the execution of AB. 

Density Scale Height: Density scale height plays two roles in AB. First, for maneuver 

calculations to stay within a density corridor, the density scale height, or equivalent, must be 

known to calculate the required V. Second, if total heat flux or integrated density is important, 

the integral depends on the reference altitude density and the scale height as discussed in Section 

F.5.2 below. 

Asymmetry of Density Profile: As mentioned, during AB at Venus or Mars, the vehicle would 

be generally turned from sun-point and would be operating on batteries. In this case it may be 

desirable to minimize the time in the AB orientation. If the density profile is skewed or 

asymmetric in time, an allowance may be made for the potential skewness. If the skewness is 

predictable, then it can be included in the design and the AB pass can be accordingly biased in 

time. 

Figure F.4-4 shows the influence of planet flattening on shifting the density profile for a Mars 

AB mission. The upper left chart provides the variation of altitude above periapsis (blue line) 

along the orbit for three scale heights (21 km). The orbit parameters are given in the figure. The 

green line shows altitude of the reference ellipsoid relative to periapsis along the ground track. 

The upper right panel provides the altitude above the reference ellipsoid. The lowest areodetic 

altitude and highest density occur 64 seconds before periapsis. The 0.59 km difference in 
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altitude would cause a 9 percent higher density than the density at periapsis. This shift would 

cause a least squares density estimation process, centered on periapsis, to overweight the 

outbound leg of the pass. The time and altitude shifts for other latitudes and orbit periods are 

shown in the lower two panels. The differences approach zero at the equator and pole, are 

maximum at mid latitudes, and decrease rapidly with orbit period. This latter effect is due to 

shortening of the AB pass as eccentricity increases with orbital period. Non-polar orbits will 

show smaller effects at every latitude. The size of the altitude difference and time shift are 

increased with planetary flattening, AB pass duration, and angular velocity at periapsis. This 

phenomenon is not an issue at Venus due to slow rotation and the nearly spherical gravity field. 

The Titan rotational period is 15.9 days and Saturn produces tidal bulges of less than one 

kilometer resulting in a flattening that is less than 1/10 of that at Mars, so the effects on Titan AB 

are likely ignorable. 

Figure F.4-4. Mars Reference Ellipsoid Flattening Effect on Density Profiles 
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F.5 Potential Atmospheric Models 

Here it is assumed that no preflight empirical model of the atmosphere exists that is sufficiently 

accurate to enable AB to be performed without using onboard data to adjust model parameters 

during the flight. Selection criteria for onboard atmospheric models include (1) capture the 

relevant characteristics of the atmosphere, (2) be robust against unexpected phenomena, 

(3) allow for linear estimation of the parameters, (4) permit prediction of atmospheric properties 

for the next AB pass, and (5) support the calculation of corridor control maneuvers. Several 

models are discussed and evaluated using Mars AB data. All the models assume that 

atmospheric density data have been derived from an onboard source (e.g., IMU accelerometer 

and gyro data).9

F.5.1 Models That Require Altitude Knowledge 

Empirical atmospheric models are almost always modeled with altitude as one of the parameter. 

An onboard Ephemeris Estimator is required to provide altitude versus ephemeris time. On the 

other hand, onboard density estimation is done using IMU data which has spacecraft time as the 

independent variable. If these two time references loose synchronization, significant errors, as 

will be seen in Section F.6 can be produced in the estimate of the variation of density with 

altitude. Such a loss of synchronization is likely not due to a clock failure, but rather an 

ephemeris integration error that causes associating an erroneous time with the time of periapsis 

passage. In anticipation of such issues, the methods studied are divided into those that depend on 

knowledge of altitude and those that do not. 

F.5.1.1 Constant Scale Height 

The CSH model given Equation (F.3-1) was used successfully as the fundamental model during 

the MGS mission. Successful use of this model, or any model using altitude, depends on an 

accurate representation of altitude versus. time. This could be an issue for onboard ephemeris 

integration and is discussed in F.6. There are two disadvantages to using this form for 

estimation. First, the density is not linear in the estimation parameters (hp) and Hs and second, a 

simple least squares process will overweight residuals at the lowest altitude and nearly ignore 

residuals a few scale heights above the reference altitude. One approach is to use log() as the 

observable and use 

 Eq. (F.5-1)

where a and b are the regression parameters. The equation is linear in a and b and the least 

squares method, within the linear regime, now minimizes the sum of squares of the density 

difference divided by the density, i.e., the fractional deviation in the density. This approach 

provides equal weight to high or low density data and is more suitable when scale height is 

logh a b h hp= +  – 
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among the estimated parameters. This model can, to a limited extent, provides asymmetric 

temporal variation like the left panel in Figure F.4-1, but the inbound and outbound altitude 

profiles will be identical so that the model is a straight line in the left panel. Equation (F.5-1) is 

not applicable early and late in the AB pass when accelerometer data noise produces negative 

density. This model is simple and captures the dominant local variations in density. It permits 

prediction of the atmospheric density at the next periapsis by assuming that the scale height is the 

same for the next orbit and that the density at periapsis can be obtained equation (F.3-1) at the 

next periapsis. Since the AB pass is not vertical, the two parameters in this model absorb an 

unknown amount of along track variation. The persistence results in Figure F.3-1 show the real 

world limitations to this approach. 

F.5.1.2 Constant Scale Height with Linear Time 

As seen in Figure F.4-3, density profiles need not be symmetric in time from periapsis or in 

geodetic altitude so models should be considered that might include such asymmetries. One of 

the simplest models is the hybrid model (constant scale height with time (CSHT)), with constant 

scale height but different inbound and outbound density profiles. One approach can be obtained 

by adding a linear time term to get 

 Eq. (F.5-2)

where the reference altitude and time are taken at periapsis. The model permits some variation in 

local scale height with altitude. It is unlikely that this model should be used to extrapolate 

beyond the data interval, since, unless c=0, the predicted density will eventually increase with 

altitude. 

F.5.1.3 Constant Inbound and Outbound Scale Heights 

Another asymmetric three parameter hybrid model (constant scale height inbound and outbound 

(CSHIO)) permits different inbound and outbound scale heights and one density at periapsis 

given by 

 and Eq. (F.5-3)

where the first equation is used for the inbound part of the pass and the second model is used for 

the outbound phase. The parameter a=log(p), b= -1/Hsin inbound and c= -1/Hsout outbound. 

logh t a b h hp –  c t t

p

= + +  – 

logh a b h hp= +  –  logh a c h hp= +  – 
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F.5.2 Models that Depend Only on Time 

In the definitive reference on drag effects on satellite orbits,22 King-Hele provides a derivation to 

show that the CSH altitude model is well represented by the bell shaped Gaussian density 

function in time. That equation is derived below in a more focused manner and other relations 

relevant to AB are developed. 

F.5.2.1 Temporal variation of the CSH model for two body motion 

Consider an AB pass during for which atmospheric density can be modeled with a constant scale 

height (equation (F.3-1)), so that the density as a function of altitude above periapsis is 

 Eq. (F.5-4)

where hp is the periapsis altitude and Hs is the density scale height. To produce the familiar 

“bell” shaped density versus. time profile, assume two-body motion about a spherical planet and 

expand the altitude in a Taylor series about the time of periapsis to get 

 Eq. (F.5-5)

where 

)( pth



is the second derivative of altitude with respect to time evaluated at periapsis. 

Under the identified assumptions, altitude is symmetric in time so odd derivatives vanish and the 

truncated terms are of order (t-tp)

4

 and negligible except for very low eccentricity orbits. 

Eliminating altitude in equation (F.5-4) in favor of time in equation (F.5-5) yields the “bell” 

shape variation of density with time. 

 Eq. (F.5-6)

It is of interest to write 

)( pth



in terms of the orbital elements. Starting with the radial 

acceleration equation for the two-body problem 

Eq. (F.5-7)

h  hp 

h hp– – 

Hs

= exp ---------------------

ht h t

p

 

1

2

--h

··

t

p

  t t

p

 – 

2

O t t

p

 – 

4

= + +  

t  t

p

 

h

··

t

p

  t t

p

 – 

2

–

2Hs

= exp ----------------------------------

r

··

r

·

2 

r

2

= – ----
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where  is the gravitational constant for the planet and  is the angular position in orbit. At 

periapsis r=rp=a(1-e) and 

 Eq. (F.5-8)

where Vp is the velocity at periapsis and e is the orbital eccentricity. Since 

rh 





for a spherical 

planet, equation (F.5-7) reduces to 

 Eq. (F.5-9) 

To relate the orbital and atmospheric parameters, start with the Gaussian density function 

 Eq. (F.5-10) 

where  is the mean and  is the standard deviation and 

 

Eq. (F.5-11) 

Equation (F.5-10) and equation (F.5-6) suggest the substitution 

 Eq. (F.5-12) 

with e>0, leading to equation (F.5-6) in the desired form 

Eq. (F.5-13) 

r

2



·

2

Vp

2

1 + e r

p

= = 

f(x,,)

1

 2

--------------

x – 

2

2

2

= exp –------------------

fxdx

–





= 1



2

Hsh

··

p

 Hsr

p

2

= =  e

t  t

p

 

2r

p

2

H

s

e

------------------

1

 2

--------------

t t

p

 – 

2

–

2

2

exp ---------------------- p

t t

p

 – 

2

–

2

2

= = exp ----------------------

h

··

t

p

  e r

p

2

= 
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From equation (F.5-11), the integral over the entire pass is 

 Eq. (F.5-14) 

where again e>0 is assumed. This result shows that the area under the curve is proportional to 

the density at periapsis times the square root of the scale height, sometime called the “square root 

of scale height law.” Since the orbital velocity decrease due to drag is approximately 

proportional to the integral of density, over estimation of the scale height will result in an 

underestimation of the density as determined by an orbit determination approach that process 

tracking data before and after the unobserved AB pass. 

The only approximation to arrive at equation (F.5-13) is the truncation of the Taylor series in 

equation (F.5-6) and as long as the scale height is small compared to the periapsis altitude the 

higher order terms are not significant. For example, for Mars with e=0.1, Hs=7 km, hp=125 km, 

and p=50 kg/km3, the error in altitude is less than 1 km and the error is density is less than 

0.1 kg/km3over an altitude range from periapsis to 5 scale heights above periapsis. 

The integrals of dynamic pressure (0.5V

2

) for total drag effect or heat flux (0.5V

3

) for total 

heat input may be more important variables than density. Under the same assumptions for which 

equation (F.5-6) is valid, the velocity variation throughout the AB pass varies by only a few 

percent from the value at periapsis. So the total heat input during a pass is closely approximated 

by the value of the heat flux at periapsis times the radical equation (F.5-14).

Finally, the “drag duration” (Td) is often defined as the time from the inbound occurrence of 

1 percent of maximum density to the outbound time when the density is 1 percent of maximum 

density, then the drag duration is twice the time for the spacecraft to increase in altitude above 

periapsis by 4.6Hs. From equation (F.5-6) and equation (F.5-14) 

 Eq. (F.5-15) 

Equation (F.5-15) has been used to define the AB duration for some AB missions. 

F.5.2.2 Quadratic time 

Under the identified assumptions, the CSH model can be represented in time by 

tdt

–





 t

p

 

2r

p

2

Hs

e

= ------------------

Td2

9.2H

s

r

p

2

e

= ------------------
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 Eq. (F.5-16) 

where 

 Eq. (F.5-17) 

depends on orbit parameters and scale height. Again, to assure linear estimation, log is used as 

the observable and a=logp and b=-1/2

2

are the parameters. This model has the advantage that a 

precision trajectory is not required to generate altitude versus time. To predict to other altitudes, 

the scale height can be approximated from the solution for 

2

. It is seen that a disadvantage is 

that the model is symmetric in time about the time of periapsis and that maximum density occurs 

at periapsis, whereas few of the Martian density profiles satisfy either of these conditions and 

further, if one is only relying on the IMU time tags, the time of periapsis is unknown. A shift in 

the time of maximum density is easily accomplished by adding a linear term to get 

 Eq. (F.5-18) 

which is still symmetric in time but centered at the model maximum density which occurs at 

tmax=tp-b/2c and has a value of exp(a-b2/2c). This model (QdT) does however permit different 

inbound and outbound altitude profiles, but with the same scale height. 

F.5.3 Cubic and Quartic Time 

One can introduce both asymmetry and a shift in the time of maximum density by extending the 

quadratic model to either a cubic (CubT) or a quartic model (QtT) in time, for example: 

 Eq. (F.5-19) 

The quartic term might be included to assure that density decreases with altitude outside the data 

set or to provide a better estimate of the maximum density during the pass. There are profiles for 

which the coefficient e has a value greater than zero, so this model would not be recommended 

for extrapolation. For both models, Hs can be extracted from the quadratic coefficient. 

However, it was found that the (t-tp)

4 term often absorbed enough of the quadratic dependence 

that the Hs estimates were substantially biased. Consequently, no further consideration will be 

given to the quartic representation. 

t p

t t

p

 – 

2

–

2

2

= exp ----------------------



2

Hsr

p

2

=  e

logt a b t t

p

 –  c t t

p

 – 

2

= + +

logt a b t t

p

 –  c t t

p

 – 

2

d t t

p

 – 

3

e t t

p

 – 

4

= + + + +
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F.5.4 Periapsis Timing Estimator 

Satellite ephemeris propagation errors are usually dominated by along track deviations which for 

AB are manifested as time of periapsis errors. The PTE14 was consequently designed to adjust 

the flight sequence so that it would be centered on the centroid of the density history. Based on 

the PTE t from one orbit, the initiation of the AB sequence for the next orbit is adjusted by t. 

PTE was run in shadow mode and validated during Mars Odyssey and was operational for MRO. 

Although the details are not exactly known, results of the models will be compared to an 

implementation based on Reference 14. The implementation is a simple density weighted time 

from periapsis to provide the location of the density centroid relative to periapsis 

 Eq. (F.5-20) 

where time is measured from periapsis and the sum is taken over all the density data above a 

threshold determined by the density noise level. 

F.5.5 Single Orbit Examples 

Each of these models was applied to the four Odyssey orbits in Figure F.4-3. Data within 14 km 

altitude of periapsis are used for the LS solutions. Results are shown in Figure F.5-1 for both 

density versus. time and density-altitude profiles, where the density data are shown as dots. 

Relevant solution parameters for these orbits are tabulated in Table F.5-1. For the QdT and 

CubT models, the scale height was calculated using Equation (F.5-17) where the position and 

velocity at periapsis was used to calculate the eccentricity. For orbits 44, 157 and 280, little 

difference between the models is seen in the plots. For these orbits, the CSHT and time 

quadratic (QdT) models are nearly identical and the differences in the parameters in Table F.5-1 

are ignorable. Examination of the orbit 44 profile shows that the cubic (CubT) model is 

beginning to diverge above 110 km and =10 kg/km3 with one branch going to zero density and 

the other going to an infinite density with further increase in altitude. To fit the “flat” top of 

orbit 157, all models produced a large scale height near 23 km, whereas the remaining orbits 

have scale heights of less than 11 km. Similar statements can be made for the time of the 

maximum density. 

t t

i

  i  i= 
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Figure F.5-1. Density Model Least Squares Fit to Four Odyssey Orbits. Data Altitude Range 

h=14 km 

Estimation of the scale height is consistent among the models, but of course all the orbit 

157 estimates are much greater than estimates from nearby orbits and it would likely be unwise 

to use the large scale height for orbit 157 to predict the density for orbit 158. To do so would 

give 21.8 kg/km3

verses the measured value of 38.8. Predicting orbit 159 from the 157 values 

gives 21.9 kg/km3. Orbits like this demonstrate the need to combine estimates from a number of 

orbits and even then, large differences might be expected. 
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Table. F.4-1. Model Comparisons for Four Mars Odyssey Orbits

Model

Odyssey Orbit

44 157 159 280

max, kg/km3

Data 40.8 27.8 68.1 51.8

CSH 31.5 24.9 45.0 33.6

QdT 31.6 25.0 48.0 33.5

CSHT 31.6 25.0 48.1 33.6

CubT 31.7 25.1 54.5 33.6

tmax, sec

Data 20.0 -44.5 -58.5 29.5

CSH 5.0 -3.5 -4.5 -49.4

QdT 9.0 -15.5 -34.5 -45.4

CSHT 9.0 -15.5 -34.5 -46.4

CubT -1.0 -19.5 -48.6 -44.4

PTE 6.8 -5.4 -28.6 -41.3

Hs, km

CSH 8.6 23.1 8.9 5.1

QdT 8.7 23.6 9.2 5.0

CSHT 8.6 23.1 8.9 5.1

CubT 8.3 23.8 9.7 5.0

F.5.6 Multiple Orbit Comparisons 

The four algorithms in Table F.5-1 and the CSHIO algorithm were applied to all three Mars 

missions. Only data during the “main” AB phase were included. In addition, MGS data for 

orbits 910 through 980 were excluded because of an onboard computer issue that significantly 

reduced the quality of the accelerometer data. There is a subtle difference in how the data are 

selected for the three constant scale height models and the two time polynomial models. For the 

former, data are selected within a specified altitude range of periapsis, which for all these results 

is 14 km or about 2 density scale heights. Unless periapsis is at the equator or a pole, planetary 

flattening results in these data being asymmetric in time. Conversely, for the latter two models, 

the data are selected symmetric in time around periapsis with a time interval that corresponds to 
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a planetocentric radius change of 14 km. The resulting in planetodetic altitude distribution is 

generally asymmetry. This small difference has a noticeable effect on the results. 

Density: As a basis for comparison, the “mean” density for each orbit was calculated by 

averaging all five solutions for density at periapsis. Results are presented as ratios of recovered 

density to this mean density. For MGS it was found that this ratio varied from 0.92 to 1.06. The 

orbit average difference between CSH and CSHIO had a 0.0045 with and between QdT 

and CubT <10-5 and <10-3. Because these pairs of recoveries are so similar, only one of the 

pair will be shown for some of the results. Figure F.5-2 shows these ratios for the CSH, CSHT 

and QdT methods. There are a couple of general trends evident. First, when the CSH ratios are 

generally greater than one, the QdT ratios are generally less than one. Second, the CSHT 

method provides results closest to unity over the entire mission. Third, there are two places 

where all three methods give nearly the same density, near orbits 860 and 1190. 

It will be seen in the next paragraph that a couple of these trends can be explained in terms of 

(1) the method of selecting data as discussed and (2) the time between periapsis and the 

minimum planetodetic altitude. The Mars Odyssey and MRO analyses showed similar trends in 

ratio ranging from 0.92 to 1.06, model agreement near the pole, and CSH and QdT providing 

opposite deviations from unity. The CSHT model provides results closer to the mean than the 

other two models, but with slightly larger deviations than MGS. 
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Figure F.5-2. MGS Estimated Periapsis Density for Three Methods Normalized by Mean Periapsis 

Density of all Five Methods

Time of Maximum Density: Consider Figure F.5-3 which shows the time from periapsis to the 

time when the various models predict the maximum density. For the CSH model, this is time 

from periapsis to minimum planetodetic altitude, i.e., the same “time to minimum altitude,”

presented in Figure F.4-4. Time difference changes slowly because latitude and orbit 

eccentricity are changing slowly until near the final orbits when the orbit is nearly circular. 

During the first 200 orbits, MGS is passing from north to south as periapsis regresses northward. 

Consequently, minimum altitude occurs after periapsis. The CSHT and QdT results suggest 

there is an additional effect that further delays the time. This would be consistent with an 

equator-ward increase in density, which is the climatological trend. The periapsis regresses past 

the equator on orbit 860 and here the altitude data distribution will be symmetric in time and 

conversely. So, the models should predict essentially the same atmospheric parameters. It is 

seen from Figure F.5-2 that this is true for density, but not so for the t values. Again there is an 

along track density gradient that delays the epoch of maximum density. At the risk of over 

analysis, one possibility is that the maximum density is occurring in the northern hemisphere 
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since during all of phase 2, Ls (Figure F.2-1) is between 0° and 90°, so it is hemisphere spring and 

the Sun is in the northern hemisphere. The balance of the orbits after 860 is readily explained by 

a minimum density occurring near the pole. Maximum positive t occurs near orbit 1060 as 

periapsis regresses past 45° latitude, the region of maximum gradient in the planetocentric 

altitude. As periapsis passes over the pole, there will be symmetry in the data distributions and 

the densities are nearly identical. One final note, the difference between the t for CSHT and 

QdT has a =0.2 second and =1.9 second. These two methods are providing excellent 

agreement in t.

Figure F.5-3. MGS Time from Periapsis to Time of Maximum Density as Predicted by Three Models 

Mars Odyssey and MRO analyses provided similar results. MRO had generally smaller 

deviations from the t caused by flattening than MGS. Mars Odyssey on the other hand, while 

periapsis regressed toward the pole, showed up to 40 seconds positive t deviations which 

rapidly switched to negative values up to -40 seconds while moving away from the pole. 

Perhaps these large, rapid variations were due to the polar warming. 

Density Scale Height: Hs is the final variable of interest for predicting the periapsis density at 

subsequent orbits. As might be expected, the estimation of scale height is more sensitive than 

density to the altitude span of the data set. Orbit 157 in Figure F.5-1 illustrates the difficulty. 
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The solution used data within h=14 km of periapsis, i.e., about two expected scale heights. The 

resulting Hs=23 km given Table F.5-1 is not a realistic value to use for predicting density at the 

next periapsis. From the figure it can be expected that as the altitude range h is increased, the 

value of Hs would decrease perhaps to more realistic values, but the estimated periapsis density 

will likely increase. The data above 100 km appears to follow a straight line with a scale height 

of about 7.5 km, but using just these data would yield a periapsis density of about 100 kg/km3. 

Hence, using a much larger data set would lead to a significantly higher density prediction. Orbit 

158 occurred 1 km lower in altitude than 157 and had a density of 41 kg/km3. So the predictions 

using a 14 km altitude range underestimated the density for 158 and using a very large altitude 

range would have overestimated the density. Studies for all missions using h=7, 11, 14, and 

21 km altitude ranges showed that for orbits with “bell shaped” density histories, even with time 

shifts, the estimates of Hs generally differed by less than 0.5 km between the 11 and 14 km cases 

and 0.3 km between the 14 and 21 km cases. Differences between the 7 and 14 cases were 

around 1 km. For orbits that vary significantly for the “bell shape,” the results are mixed. Using 

an altitude interval of h=2Hs seems to be a reasonable compromise. 

Like the other parameters, the estimation of Hs within a family of methods, e.g., (CSH, CSHT, 

CSHIO) or (QdT, CubT) were consistent with standard deviations for the differences of less than 

=50m. Between the two families, 500m. Consequently, only the CSHT results are shown in 

Figure F.5-4. The means of the three MGS data segments (Hs=6.9, 7,3, 6.6 km) have trends that 

are consistent with temperature decreasing toward the poles. The standard deviations are 1.1, 0.7 

and 1.1 km, from left to right. Mars Odyssey scale heights (i.e., temperature) were the means of 

discovering the polar warming but outside the polar region the mean scale height drops to about 

5.6 km, well below the expected value. Global circulations model simulations of a polar 

warming15 show strong adiabatic heating near the pole due to subsiding flow and an adjacent 

region of cooling. This cool region may be the reason for these small scale heights. In this 

region =0.76 km. MRO shows a decreasing Hs trend as periapsis regresses toward the pole. If 

there was a south polar warming, it occurred after periapsis passed the pole. Averaging over 100 

orbit blocks, Hsvaries from =6.9 and =0.86 to =5.7 and =1 km over the mission. 
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Figure F.5-4. Density Scale Height Recovered using the CSHT Method and a Data Altitude Range of 

h=14 km 

F.6 Influence of Along Track Ephemeris Errors 

Studies of numerical solutions of two body satellite orbits usually show that the largest position 

error is along track23and increases with t, t3/2 or t2

depending on the numerical integration scheme, 

computer specifications and problem formulation. An example is shown in Figure F.6-1 using a 

simple Runge-Kutta-Fehlberg 4/5 integration method. The nature of the errors is typical, but the 

deviations will vary in magnitude with integration method particulars. The orbit starts at 

periapsis at an altitude of 125 km. The initial periapsis location is in the equator on the x-axis 

and the orbit inclination is 30°. 
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Figure F.6-1. Numerical Integration Errors for a RKF 4/5 Method Applied to a Mars Satellite in an 

AB Orbit with a 12-hour Period 

The upper left panel shows, for 100 orbits, the difference between subsequent periapsis position 

and the initial position. Note the errors are predominately in the y and z directions, i.e., normal 

to the position vector at periapsis. The upper right panel shows the angle () between the 

position error vector and the periapsis velocity vector. After just the first orbit, the predominant 

position error is essentially along track and becomes even more closely aligned as orbit number 

increases. From an osculating orbital element view point, the dominate error is in the time of 

periapsis passage. In anticipation of using equation (F.5-17) to obtain an estimate of scale 

height, note from the lower panels that the errors in rp and orbit eccentricity are negligible over 

100 orbits. To obtain a first order evaluation of the effects of such errors on the estimation of 

atmospheric density and scale height, the following study was performed. Assuming a two body 

orbit and a CSH atmosphere with periapsis density of 1 kg/km3and a density scale height of 

7 km, density versus time was generated to simulate the onboard recovery of density purely from 

IMU data. Altitude versus time was generated from the two body equations. Then, the altitude 

versus time ephemeris data was shifted in time to simulate an ephemeris time of periapsis offset. 

The CSH, CSHT and QdT methods were then used to recover density at periapsis and scale 

height using the equations (F.5-1), (F.5-2), (F.5-16), and (F.5-17), respectively. 
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Figure F.6-2. Effect of Ephemeris along Track Offsets on CSH Estimation of Density and Density 

Scale Height 

Figure F.6-2 shows the effect of an ephemeris offsets from 0 to 30 seconds for a range of orbital 

periods from 3 to 36 hours. The blue line in the upper figures corresponds to IMU derived data 

except for the left-most figure where the line corresponds to the altitude if there were no 

ephemeris offset. The red line corresponds to the ephemeris values with a 30-second delay in the 

ephemeris time. The magenta line corresponds to the CSH model estimation results. The CSH 

maximum density occurs near the same IMU time as the ephemeris maximum density. As 

shown in the lower two plots, regardless of the ephemeris offset or the orbital period, the CSH 

model always underestimates the maximum density and overestimates Hs. Larger offsets can be 

tolerated more readily by low eccentricity orbits. For the high eccentricity orbits, a 10-second

offset leads to a 10 percent underestimation of maximum density and about a 1 km over 

estimation of Hs. For Mars, these deviations are within the 1 natural variability in both density 

(Figure F.3-1) and Hs (Figure F.5-4) and may be acceptable. It was evident that 30-second

offsets would not be acceptable. 
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Figure F.6-3. Effect of Ephemeris along Track Offsets on CSHT Estimation of Density and Density 

Scale Height 

When the linear time term is added to the CSH model to obtain the CSHT model (equation 

(F.5-2)) the influence of the ephemeris offset becomes almost nil. The results are shown in 

Figure F.6-3. Here, only every third magenta point is plotted so the blue and magenta results can 

be distinguished. In the top center frame, the difference is negligible and the CSHT model 

recovers the maximum density to 5 decimal places and Hs to within a few meters over the entire 

period and time offset sweep. This method still requires a model that produces an altitude profile 

versus time. The model can either be a precision ephemeris or an approximation based on a set 

of osculating or mean elements. As a backup to the precision ephemeris, consideration should be 

given to utilizing other approaches to obtaining altitude vs. time profiles. 
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Figure F.6-4. Effect of Ephemeris along Track Offsets on OdT Estimation of Density and Density 

Scale Height 

Finally, the QdT (equation (F.5-18)) method was tested with the results (Figure F.6-4) being 

similar to those of the CSHT results. The main difference is in the estimates of the max. density 

and Hs. Here, an orbital period dependent bias is seen in each parameter and these biases are 

essentially independent of the time offset. The biases are due to truncating the Taylor series 

expansion in equation (F.5-9) and are much larger than the errors produced by the ephemeris 

time offset. The latter are illustrated by the two lower panels in Figure F.6-3. This model has 

the advantage of only requiring a reasonable estimate of rp and orbital eccentricity as seen in 

equation (F.5-17).

This study was done near the end of the Phase 1 of the project and is by no means complete. The 

next step would be to apply an ephemeris offset to MGS, Mars Odyssey and MRO density sets to 

evaluate the effects. This can be done in a relatively short time but is not complete. The 

complete study would include ephemeris offsets in the density recovery process itself. Though 

probably a small effect, the ephemeris influences the density recovery in that the position and 

velocity are necessary to calculate the velocity relative to a rotating atmosphere to determine 

angles of attack and sideslip for interpolation into the aero data base. The exact influence will 

vary from orbit to orbit depending on the phasing of the attitude oscillation relative to the time of 
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periapsis. A second study will be required to determine the accuracy with which periapsis radius 

and orbit eccentricity are determined by the particular numerical method use for the onboard 

ephemeris generation. A third study should include determining the precision with which the 

altitude vs. time profile must be known. The current approach is based on a precision 

ephemeris, but these results suggest a less precise trajectory may be required. The results of 

these studies could ameliorate the effects on an ephemeris time offset and substantially extend 

the duration of AA before human intervention is required. 

F.7 Aerobraking Corridor Maintenance 

As mentioned earlier, a model of atmospheric density has a couple of purposes: (1) to quantify 

characteristics of the atmosphere for the current pass which might be used for heating 

calculations19, (2) to provide a prediction of the characteristics of the next pass, and (3) provide 

information needed to calculate the orbit trim maneuvers to stay in the AB corridor. 

F.7.1 Corridor Maintenance Maneuvers 

To maintain the AB corridor, orbit trim maneuvers are generally performed near apoapsis to 

adjust the altitude of subsequent periapses and thereby control the atmospheric density.21 For 

tangential, impulsive maneuvers, the first order Va required at apoapsis to raise periapsis 

altitude by an amount rp is first given for two body motion and secondly is given by relating the 

altitude change through the CSH model to obtain the desired fractional change in periapsis 

density p/p.

 Eq. (F.7-1)

where rp has been approximated by hp, n is the orbital mean motion, ra (rp) is the apoapsis 

(periapsis) radius and Hs and p are the expected density scale height for the next orbit. Even 

without a precision trajectory, the previous results strongly suggest that the latter two variables 

are likely to contribute the majority of the uncertainty in calculating the desired Va. 

F.7.2 Predicting Atmospheric Parameters for the Next Pass 

For AA it will be necessary to have a prediction of atmospheric density for the next pass through 

the atmosphere. From past experience with Mars AB it is clear that there are likely to be large 

variations between predicted and observed density that are not within the current ability to 

predict from either empirical or numerical models of the atmosphere. Any of the density models 

discussed might be used to generate parameters for predicting the conditions at the next periapsis 

as was demonstrated in the study of “persistence.” All the models have persistence values that 

Va

n

4

--

r

a

r

p

---- r

p

n

4

– --

r

a

r

p

----H

s

p

p

--------

 

 

 

= =
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deviate up to a factor of 2 from unity. This naturally raised the question if some averaging of the 

estimates would produce a better “prediction” ratio. As mentioned, for both Magellan and MGS, 

some form of atmospheric density was averaged over a number of orbits to be used to predict the 

density at the next periapsis. Using the extensive set of data from Mars, a study was performed 

of two averaging methods over a range of altitudes (h) used to obtain model coefficients and 

over the number of orbits used in the averaging process. One would anticipate both of these 

variables would influence the results. Only the CSH and CSHT models were included as CSH is 

the simplest model and CSHT provided prediction results that were the closest to the average of 

all the methods. The data collection altitude ranges studied were h=7, 10, 14 and 21 km. This 

range starts near the mean Hs averaged all latitudes and times. The values of 10 and 14 can be 

thought of as 1.5 or 2 times the Hs=7 km value or 1 and 1.5 times the Hs~10 that was seen during 

the polar warming. The number of orbits for the averaging was varied from 1 to 20. It might be 

anticipated that a low number of averaging orbits will have a large standard deviation for the 

prediction ratio while estimates using long data arcs may be biased by the time dependent 

(latitudinal, seasonal, diurnal) variations in atmospheric characteristics. 

Figure F.7-1 shows the results for MGS. The prediction  is the standard deviation over all the 

values of the ratio of observed to predicted density across the entire mission. Two simple 

averaging methods were explored for both the CSH and CSHT models. For notational convince, 

let n+1 be the orbit number at which density is to be estimated using model values from orbits n, 

n-1,...n-k+1, where k is the “number of orbits in the estimate.” When the number of orbits in the 

estimate k=1, the prediction value is the standard deviation of all the points in Figure F.5-2 for 

each model. For the “CSH AVG” results the previous k values of ‘a’ and ‘b’ in equation (F.5-1) 

are used to get a value of ‘a’ at the periapsis altitude of orbit n+1. These k values are simply 

averaged to obtain the “estimated” density at orbit n+1. This value is used in the denominator of 

the prediction ratio. A similar process is used for the CSHT model where the time dependence in 

this model is ignored in the prediction. The second averaging method attempted to account for 

the “accuracy” of the estimated parameters. The LS process was turned into a WLS method by 

using the reciprocal of the rms deviation between observed and model predicted density to 

“weight” the data. Orbits with large deviations, like orbit 159 (Figure F.5-1), would be weighted 

lower than orbits which had a smaller rms, like orbit 280. So the second method is the weighted 

sum of the estimates, much like a minimum variance linear combination of random variables. 

No probabilistic interpretation is attempted for these results for obvious reasons. 
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Figure F.7-1. Density Prediction Capability of Various Methods for the MGS Mission 

Referring to the figure, the standard deviation across all orbits starts near 40 percent 1. The 

initial downward trend as the number of orbits increases is to be expected. From a practical 

standpoint little is to be gained in reducing  after 10 to 15 orbits and the AVG results start to 

increase slightly after 10 orbits are averaged. The three lower values of h provide similar 

results and noticeable lower than the h=21 case, although this different is likely not significant 

from an AA standpoint. This residual deviation of about 28 percent is interpreted as the natural 

variability from the “mean” atmosphere and cannot be reduced without significantly more 

knowledge of the atmosphere than is available from onboard measurements alone. 

The standard deviation does not tell the whole story on prediction for AA. The probability of the 

ratio being greater than a specified value may be more relevant. The gamma distributions shown 

in Figure F.3-2 provide a more rigorous means of making probabilistic statements. Here, a 

simpler approach is taken by just tracking the fraction of total orbits for which the ratio of 

observed to predicted density ratio exceeds 1.5. For MGS this result is shown in Figure F.7-2 for 

the same methods and data as Figure F.7-1. There appears to be little advantage to using more 

than 10 to 15 orbits for the prediction and WLS provides about 1 to 2 percent improvement over 
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the AVG approach. Note that WLS is computationally more cumbersome than the AVG 

approach, which is a consideration for onboard computation. For prediction the shorter data 

spans, h<10 provided a small advantage, for Figure F.7-2 the lines cross repeatedly with h=14 

being lower than the others in more cases. Setting h at about 2 scale heights may be a good rule 

of thumb and unless time of maximum density is a desirable parameter to estimate, the simple 

CSH method seems like a good candidate. Selecting between AVG and WLS is less obvious. 

Figure F.7-2. Fraction of Total MGS Orbits for which the Ratio of Observed to Predicted Density 

Exceeded 1.5 

Just to complete this story, similar results are shown for Mars Odyssey and MRO in Figure F.7-3 

for just the CSH model and the WLS prediction method. The Mars Odyssey prediction has a 

minimum at 0.3 which is 10 percent higher than either MGS or MRO, but still over a 30 percent 

reduction below the initial persistence values. This higher variability appears in the prediction 

greater than 1.5 have nearly 10 percent of the orbits above this limit. The longer the span of 

orbits used in the prediction, the smaller the . The h=21 appears to be optimal for Mars 

Odyssey, consistent with Mars Odyssey having Hs>10 km for a significant fraction of the 
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mission. Of course, MRO behaves in a different manner from the other two missions with an 

initial rise in followed by a steep fall eventually becoming 0.28 like MGS. The decline in the 

1.5 fraction is slower than MGS, but does get near 5 percent eventually. 

Figure F.7-3. Prediction and Orbit Fractions > 1.5 for Mars Odyssey and MRO 

F.7.3 Prediction Errors 

Although not an active part of the current AA strategy, it is of interest to have an estimate of the 

uncertainty of the predicted density at the next periapsis shown in Figure F.7-1, Figure F.7-2, and 

Figure F.7-3. The only method tested during Phase 1 was to simply calculate the standard 

deviation over the number of orbits used to obtain the predicted density for MGS for the CSH 

method. For example, in Figure F.7-1 the upper right panel shows the prediction sample 

standard deviation averaged over the entire MGS mission for the CSH “average” prediction 

method. The prediction accuracy varies throughout the mission due to the latitudinal, season and 

diurnal natural variability of the atmosphere. One method to capture this local variability is to 

determine the sample standard deviation for each orbit prediction. Figure F.7-4 shows this 

variation for the MGS case with h=14 km and a 7 orbit averaging, the red line in Figure F.7-1, 

upper right. 
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Figure F.7-4. Prediction Standard Deviations for CHS Method Based on Seven MGS Orbit Samples 

The upper panel of Figure F.7-4 shows the ratio of the observed density at the next periapsis 

location to the predicted density based on the indicated CSH method. The standard deviation 

over all these orbits would provide one point on the red curve in Figure F.7-1, upper right. The 

variation here is similar to the persistence shown in Figure F.3-1 for MGS. The local sample 

standard deviation is shown in the lower panel Figure F.7-4. This sample s can be interpreted as 

the ability to predict the density at periapsis of the next pass. This approach provides a “trailing” 

and highly variable indicator of variability. Phase 2 studies are proposed to improve this simple 

method, to expand the study to other methods (e.g., CSHT, QdT, etc.) and to quantify the 

accuracy of this and similar approached. 

F.7.4 Summary 

1. Mars is a challenging environment for AA due to the large, natural orbit to orbit variability in 

the density profiles. With the plethora of data from MGS, Mars Odyssey and MRO, some 

latitudinal, seasonal trends have been identified, but the best that has been done to date is to 

reduce the variability by about one third by averaging over a number of orbits. 
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2. Thermospheric waves, due to thermal tides in the lower atmosphere, produce nearly twice the 

average variability in temperate latitudes than at polar latitudes. AA strategies should be 

designed to take advantage of this well documented latitudinal variation, recognizing of 

course that a polar warming can upset the trend. 

3. Five different formulations for the density variation with altitude and time were investigated. 

If maximum density or the time of maximum density is not relevant, then the simple CSH 

model performs nearly as well as more complicated models. If time is important, the hybrid 

CSHT is the likely choice. 

4. Models that depend on altitude are likely to be sensitive to ephemeris errors and combined 

studies of atmospheric model parameterization and ephemeris propagation errors should be 

performed to better quantify this interaction. Consideration should be given to using 

atmospheric data to adjust the ephemeris time of periapsis passage. If ephemeris errors in 

altitude versus time become too large, models that depend only on time can be considered 

without loss of performance. The extent to which such models are applicable should be 

evaluated. Such models should be considered as the primary onboard algorithm. 

5. Two methods were used to combine data from numerous orbits to improve the prediction for 

subsequent orbits. A weighted least squares method performed a little better than simple 

averaging, but at the cost of additional software on the vehicle. Both methods reduced the 

variability by about 30 percent. The remaining 1 deviations of about 30 percent are likely 

due to natural variability that will have to be included in vehicle design. 

6. The AA strategies to date do not rely on statistical considerations to improve performance or 

to quantify risk. Studies should be performed to determine the advantages and limitations of 

including a more statistical based approach. 

7. Due to the limited data, the extensive analyses reported here cannot be performed for AB at 

Venus and Titan. However, significant orbit to orbit variation has been noted at Venus and 

gravity waves have been seen at both bodies. PVO4and Magellan orbit determination results 

show modest orbit to orbit variability on the day side of Venus and large variability on the 

night side and near the terminator. PVO mass spectrometer data provides some insight into 

gravity wave structure. Based on these limited data, studies should be performed for Venus 

AB similar to those performed herein for Mars. 

F.8 References 

1. Willcockson, W. H., Magellan Aerobraking Control Corridor: Design and Implementation, Adv. 

Astronautical Sciences, Vol. 87, Part II, 1994, pp. 647-662. 

2. Spencer, D.A. & Tolson, R.H., “Aerobraking Cost and Risk,” J. Spacecraft and Rockets, 

Vol. 44, No. 6, Nov.-Dec., 2007, pp.1285-1293 
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3. Tolson, R.H., Keating, G.M., Zurek, R.W., Bougher, S.W., Justus, C.J., Fritts, D.C., “Application 

of Accelerometer Data to Atmospheric Modeling During Mars Aerobraking Operations.” J. 

Spacecraft and Rockets, Vol. 44, No. 6, 2007, pp. 1171-1179. 

4. Konopliv, A.S. & Sjogren, W.L., “Venus Gravity Handbook,” JPL Pub.96-2, Jan. 1996. 

5. Striepe, S.A., Blanchard, R.C., Kirsch, M.F., Fowler, W.T.,”Huygens Titan Probe Trajectory 

Reconstruction Using Traditional Methods and the Program to Optimize Trajectories II,” 

AAS/AIAA Space Flight Mechanics Meeting, Sedona, AZ, 2007, AAS 07-226. 

6. Muller-Wodarg, I. C.F., Yelle, R.V., Borggren, N., Waite, J.H., “Waves and Horizontal 

Structures in Titan’s Thermosphere,” J. Geophysical Research, Vol. 111, A12315, 

doi:10.1029/2006JA011061, 2006. 

7. Keating, G.M., et al., “Models of Venus Neutral Upper Atmosphere: Structure and Composition,” 

Adv. Space Res., Vol. 5, No. 11, 1985, pp. 117-171. 

8. Lyons, D.T., Beerer, J.G., Esposito, P., Johnston, M.D., “MGS: Aerobraking Mission Overview,” 

J. of Spacecraft and Rockets, Vol. 36, No. 3, 1999, pp. 307-313. 

9. Tolson, R.H., Keating, G.M., Cancro, G.J., Parker, J.S., Noll, S.N., and Wilkerson, B.L., 

“Application of Accelerometer Data to Mars Global Surveyor Aerobraking Operations,” 

J. Spacecraft and Rockets, Vol. 36, No. 3, May-June, 1999, pp. 323-329. 

10. Hanna, J.L. & Tolson, R.H., “Approaches to Autonomous Aerobraking at Mars,” AAS/AIAA 

Astrodynamics Specialist Conference, Quebec City, Canada, July 30-August 2, 2001. AAS 

01-387 

11. Justus, C.G., Duvall, A., Keller, V.W., “Atmospheric Models for Aeroentry and Aeroassist,” 

Proceedings of the 2nd International Planetary Probe Workshop, NASA Ames Research Center, 

Moffett Field, CA, pp 41-48, August 23-27, 2004. Also published in NASA/CP-2004-213456, 

April 2005. 

12. Keating, G.M., et al., “Detection of Winter Polar Warming in Mars Upper Atmosphere,” Paper 

PS1.02-1TH2A-006, EGS XXVII General Assembly, Nice, France, April 2002. 

13. Dec, J. A., Gasbarre, J.F., George, B.E., “Thermal Analysis and Correlation of the Mars Odyssey 

Spacecraft’s Solar Array During Aerobraking Operations,” AIAA/AAS Astrodynamics 

Conference, Monterey CA, August 5-8, 2002.

14. Willcockson, W.H. & Johnson, M.A., “Mars Odyssey Aerobraking: The First Step Towards 

Autonomous Aerobraking Operations” 2003 IEEE Aerospace Conference, Big Sky, MT, 

March 9-14, 2003. 

15. Bougher, S.J., Bell, J.M., Murphy, J.R., Lopez-Valverde, M.A., Withers, P.G., “Polar Warming in 

the Mars Thermosphere: Seasonal Variations Owing to Change in Insolation and Dust 

Distributions,” Geophysical Research Letters, Vol. 33, 2006. 

16. Wilson, R.J., “Evidence for Nonmigrating Thermal Tides in the Mars Upper Atmosphere from 

the MGS Accelerometer Exp.,” Geophys. Res. Lett., 27(21), 3563-3566, 2002. 
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17. Tolson, R.H., Keating, G.M., Noll, S.N., Baird, D.T., Shellenberg, T.J., “Utilization of Mars 

Global Surveyor Accelerometer Data for Atmospheric Modeling,” Astrodynamics 1999, 

Advances in the Astronautical Sciences, pp. 1329-1346, 2000. 

18. Dwyer, A.M., Tolson, R. H., Munk, M.M., Tartabini, P.V., “Development of a Monte Carlo 

Mars-GRAM Model for Mars 2001 Aerobraking Simulations,” J. of the Astronautical Sciences, 

2001, Vol. 109, pp 1293-1308. 

19. Dec, J.A. & Thornblom, M.N., “Autonomous Aerobraking: Thermal Analysis and Response 

Surface Development,” AAS/AIAA Astrodynamics Specialist Conference, July 31-August 3, 

2011, Gildwood, Alaska, AAS 11-474. 

20. Fritts, D.C., Wang, L., Tolson, R.H., “Mean and Gravity Wave Structured and Variability in the 

Mars Upper Atmosphere Inferred from Mars Global Surveyor and Mars Odyssey Aerobraking 

Densities,” J. Geophy. Res.,Vol. 111, 2006. 

21. Maddock, R.W., et al., “Implementation and Simulation Results Using Autonomous Aerobraking 

Development Software,” AAS/AIAA Astrodynamics Specialist Conference, July 31-August 3, 

2011, Gildwood, Alaska, AAS 11-476. 

22. King-Hele, D.G., “Satellite Orbits in an Atmosphere: Theory and Applications,” Blackie and 

Sons, Ltd., Glasgow and London, 1987, ISBN 0-216-92252-6. 

23. Arakida, H. & Fukushima, T., “Long-Term Integration Error of K-S Regularized Orbital 

Motion,” Astronomical Journal, Vol. 120, pp. 3333-3399, December 2000. 
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Appendix G. Ephemeris Estimator User’s Guide

(Supplement to Section 7.3.2.2) 

G.1 Introduction 

The Ephemeris Estimator is one of the models in the AADS software package intended for use 

on-board spacecraft that are placed in orbit around Venus, Mars, or Titan to implement AA. The 

Ephemeris Estimator provides the AADS a running estimate of the spacecraft orbital state 

through each atmospheric pass as well as a prediction of both the apoapsis and periapsis of the 

next orbit to be traversed. With occasional updates of the spacecraft orbital state, this 

information is provided orbit by orbit throughout the AB mission phase. 

Written in C, the Ephemeris Estimator is a package of subroutines that integrates the orbit of a 

spacecraft in the gravitational field of its central body taking into account the gravitational 

effects of other relevant bodies including the Sun, the effects of solar radiation pressure, and the 

effects of orbit trim maneuvers and atmospheric drag as provided by accelerometer data gathered 

on-board the spacecraft. The integrator itself is an eighth order Runge-Kutta integrator with 

Fehlberg constants and seventh order automatic step sizing, which can be used for all 

integrations. Alternatively, a specified fixed step size can be used when integrating either or 

both of the orbit trim maneuvers and atmospheric drag accelerometer data types. 

A list of C extern variables, most of which are associated with the AADS "iload" data, and the 

arguments of five of the Ephemeris Estimator routines comprise the complete data interface 

between the Ephemeris Estimator and the AADS. Many of the C extern variables are constants 

associated with the mission at hand, while the arguments to the five subroutines and the 

remaining C extern variables are running variables. The arguments can be further categorized as 

either inputs to the Ephemeris Estimator from the AADS or outputs from the Ephemeris 

Estimator to the AADS, but never both. There is a programming interface that includes 

providing the built-in data for the central body nxn gravitational arrays, i.e., the C and S matrices 

as well as the J array of zonal coefficients, and the requisite C code modifications that are needed 

to run the Ephemeris Estimator either as a standalone program or as part of the AADS. Two 

auxiliary subroutines are provided. One extracts the needed parts of natural body ephemeris files 

and the other unloads acceleration data from ASCII files generated by the AADS when it is used 

in a simulation. Both of these are needed as input arrays to the Ephemeris Estimator when used 

as a standalone program. 

G.2 Extern Variable Interface 

Below is a table containing all C extern variables of this interface. At the top of the table are the 

19 C extern variables that are associated with the specified AADS "iload" data structure element 

names, although one of these (“ephinit_gm_saturn”) is only present when Titan is the central 

body. To the left of each equal sign ("=") is the C extern variable in the Ephemeris Estimator; to 
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the right of each equal sign ("=") is the associated AADS "iload" data structure element name. 

Two of these element names (“ee_ae_re” and “ee_ae_rp”) are divided by a thousand in the table 

to convert from meters to kilometers. At the bottom of the table are two C extern variables that 

have no associated AADS "iload" data structure element names. These control error handling 

and printing. 

double ephinit_gm_sun = ee_sun_mu; /* Sun gravitational

 constant [km^3/s^2] 

*/

double ephinit_gm_saturn = ee_saturn_mu; /* Saturn gravitational

 constant [km^3/s^2]

 (only present when 

Titan

 is the central body) 

*/

double ephinit_gm = cb_mu; /* central body

 gravitational 

constant

 [km^3/s^2] */

double ephinit_alpha = ee_ae_pole_ra; /* right ascension of 

cental

 body rotational pole

 (EMEJ2000) [deg] */

double ephinit_delta = ee_ae_pole_dec; /* declination of central

 body rotational pole

 (EMEJ2000) [deg] */

double ephinit_w = ee_IAU_pm; /* prime meridian with

 respect to central

 body IAU vector at

 epoch [deg] */

double ephinit_wdot = ee_ae_omega; /* central body rotation

 rate [deg/day] */

double ephinit_radius = ee_ae_re/1000.; /* central body equatorial

 radius [km] */

double ephinit_radius_polar = ee_ae_rp/1000.; /* central body polar 

radius

 [km] */

double ephinit_radius_oblate = ee_oblate_radius; /* central body oblateness

 radius [km] */

double ephinit_deltat_atm = ee_deltat /* time offset [s] from

 atmosphere entry and

 exit times */

double ephinit_alt_atm = ee_alt_atm; /* bodydetic altitude to

 use as atmospheric

 interface [km] */

double ephinit_stepsize = ee_stepsize; /* integrator step size

 initial guess [s] */

double ephinit_relative_error = ee_relative_error; /* integrator relative
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 error [] */

double ephinit_absolute_error = ee_absolute_error; /* integrator absolute

 error [] */

double ephinit_mnvr_step = ee_mnvr_step; /* fixed step size to use

 during maneuvers [s]

 (0. causes variable

 step size) */

double ephinit_atmos_step = ee_atmos_step; /* fixed step size to use

 during atmospheric

 passes [s] (0. 

causes

 variable step size) 

*/

double ephinit_sc_area = sc_area; /* spacecraft aerodynamic

 reference area [m^2] 

*/

double ephinit_sc_mass = sc_mass; /* spacecraft mass [kg] */

int ephdriver_error_handling; /* 0 = error off with

 appropriate 

message

 (default)

 1 = immediately return

 with status code 

*/

int ephdriver_print; /* 0 = no printed results

 1 = interface argument

 printed results

 from "ephdriver"

 (default)

 2 = all printed results

 with debugging

 except from inside

 of integrator

 3 = all printed results

 with debugging

 even from inside

 of integrator */

What follows are the built-in data for the C extern variables whose values are common to all 

three central bodies as specified by the "Autonomous Aerobraking Planetary Constants and 

Models" document [1]. 

ephinit_stepsize = 60.; /* integrator step size

 initial guess [s] */

ephinit_relative_error = 1.e-11; /* integrator relative

 error [] */
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ephinit_absolute_error = 1.e-11; /* integrator absolute

 error [] */

ephinit_gm_sun = 0.13271244004094400e+12; /* Sun gravitational

 constant [km^3/s^2] 

*/

What follows is the built-in value for the lone C extern variable that is only present when Titan is 

the central body as specified by the "Autonomous Aerobraking Planetary Constants and Models" 

document [1]. 

ephinit_gm_saturn = 37931207.6129; /* Titan */ /* Saturn gravitational

 constant [km^3/s^2] 

*/

What follows are the built-in data for the C extern variables whose values differ by central body 

as specified by the "Autonomous Aerobraking Planetary Constants and Models" document [1]. 

ephinit_gm = 42828.376212; /* Mars */ /* central body

ephinit_gm = 8978.1394; /* Titan */ gravitational 

constant

ephinit_gm = 324858.592079; /* Venus */ [km^3/s^2] */

ephinit_alpha = 317.68143; /* Mars */ /* right ascension of 

cental

ephinit_alpha = 36.41; /* Titan */ body rotational pole

ephinit_alpha = 272.76; /* Venus */ (EMEJ2000) [deg] */

ephinit_delta = 52.8865; /* Mars */ /* declination of central

ephinit_delta = 83.94; /* Titan */ body rotational pole

ephinit_delta = 67.16; /* Venus */ (EMEJ2000) [deg] */

ephinit_w = 176.630; /* Mars */ /* prime meridian with

ephinit_w = 189.64; /* Titan */ respect to central

ephinit_w = 160.20; /* Venus */ body IAU vector at

 epoch [deg] */

ephinit_wdot = 350.89198226; /* Mars */ /* central body rotation

ephinit_wdot = 22.5769768; /* Titan */ rate [deg/day] */

ephinit_wdot = -1.4813688; /* Venus */

ephinit_radius = 3396.19; /* Mars */ /* central body equatorial

ephinit_radius = 2575.; /* Titan */ radius [km] */

ephinit_radius = 6051.8; /* Venus */
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ephinit_radius_polar = 3376.20; /* Mars */ /* central body polar 

radius

ephinit_radius_polar = 2575.; /* Titan */ [km] */

ephinit_radius_polar = 6051.8; /* Venus */

ephinit_radius_oblate = 3396.2; /* Mars */ /* central body oblateness

ephinit_radius_oblate = 2575.; /* Titan */ radius [km] */

ephinit_radius_oblate = 6051.; /* Venus */

ephinit_alt_atm = 200.; /* Mars */ /* bodydetic altitude to

ephinit_alt_atm = 1000.; /* Titan */ use as atmosphere

ephinit_alt_atm = 200.; /* Venus */ interface [km] */

The "ephinit_radius_polar" for Mars is the average of two polar radii, namely the one for the 

Mars North Pole and the one for the Mars South Pole. Also, "ephinit_gm" and 

"ephinit_radius_oblate" are determined by the choice of gravitational field arrays (C and S 

matrices as well as the J array of zonals) and are specified along with these array values in 

routine "oblateness_perturbation.c" as discussed in the "Programming Interface" section of this 

document below. Any attempt to override the specified values of "ephinit_gm" and 

"ephinit_radius_oblate" will result in an error. 

The two C extern variables "ephinit_sc_area" and "ephinit_sc_mass" are spacecraft dependent. 

Despite this fact, they are currently set by default to 37.12 [m^2] and 1395 [kg], respectively, in 

the “ephinit” routine. These are the values associated with the APL Messenger spacecraft that 

was used in the development of this software. 

All other C extern variables associated with “iload” elements default to a value of zero. The two 

C extern values not associated with “iload” elements default to a value of one as indicated in the 

table at the top of this section. To override any of the default values of these C extern variables 

when using the Ephemeris Estimator as a standalone program, see the “Programming Interface” 

section of this document below. 

G.3 Subroutine Interface 

What follows is a description of each of the five routines of the subroutine interface along with 

paragraph descriptions of how those routines are to be called with respect to one another. 

(1) Initialize or re-initialize natural body ephemeris data using routine 

“ephinit”

The first call to this routine must occur before the first call to the "ephupd" routine. Arguments 

“plan_eph”, "n_plan_eph", “sat_eph”, and "n_sat_eph" are not present when executing with 

Mars or Venus as the central body since currently "plan_eph" is only needed for Saturn when 

Titan is the central body and "sat_eph" is only needed for Titan itself. The lack of need for 
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explicit planetary ephemerides for Venus and Mars is because the barycenter and real center of 

both Venus and Mars are considered to be co-located. There is a slight offset of the Mars 

barycenter from its real center due to its two moons Phobos and Deimos, but the offset is small. 

This means that the associated barycenter data with respect to the Solar System Barycenter is all 

that is needed for these central bodies. 

 /* cause initialization or re-initialization

 of natural body ephemeris data --

 output status (0 = outright success,

 <0 = outright failure and the particular

 negative value indicates where the 

failure

 occurred, see "Error Codes" section

 below) */

int ephinit(sun_eph,n_sun_eph,bary_eph,n_bary_eph,plan_eph,n_plan_eph,

 sat_eph,n_sat_eph)

double sun_eph[]; /* input Sun Chebyshevs (see "Format of the

 Chebyshev Ephemeris Arrays" section

 below) (SPK Type-2 Records) */

int n_sun_eph; /* input number of Developmental Ephemeris

 array elements of the Sun */

double bary_eph[]; /* input planetary barycenter Chebyshevs

 (see "Format of the Chebyshev Ephemeris

 Arrays" section below) (SPK Type-2 

 Records) */

int n_bary_eph; /* input number of Developmental Ephemeris

 array elements of the planetary

 barycenter */

double plan_eph[]; /* input planet Chebyshevs (if needed)

 (see "Format of the Chebyshev Ephemeris

 Arrays" section below) (SPK Type-3 

 Records) */

int n_plan_eph; /* input number of "satellite ephemeris"

 array elements of the associated

 planet */

double sat_eph[]; /* input satellite Chebyshevs (if needed)

 (see "Format of the Chebyshev Ephemeris

 Arrays" section below) (SPK Type-3 

 Records) */

int n_sat_eph; /* input number of "satellite ephemeris"

 array elements of the associated

 satellite */
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(2) Initialize or re-initialize spacecraft orbital state and epoch using routine 

“ephupd0”

The first call to this routine must occur before the first call to the "ephupd" routine. The epoch 

of the orbital state provided in any call to this routine must precede the time tag associated with 

the first acceleration datum in the first call to the "ephupd" routine that occurs thereafter, 

presuming there is any acceleration data provided in that call to "ephupd". The epoch of the 

orbital state provided in subsequent calls to this routine, where all calls other than the first call to 

this routine are the subsequent calls, must be greater than or equal to the ephemeris time of the 

end of the atmospheric pass at the end of the current orbit if there was an atmospheric pass, or 

greater than or equal to the ephemeris time of the periapsis at the end of the current orbit if there 

was no atmospheric pass. Not to be confused, this is the situation that exists after the most recent 

previous call to the "ephupd" routine. 

 /* cause initialization or re-initialization

 of spacecraft orbital state --

 output status (0 = outright success,

 <0 = outright failure and the particular

 negative value indicates where the

 failure occurred, see "Error codes"

 section below) */

int ephupd0(et_entry,rentry,et_peri,rperi,rperir,rperi_dalt,rperi_dlat,

 rperi_lat,et_exit,rexit,et0,x0)

double *et_entry; /* output ephemeris time associated with next

 atmospheric entry (seconds past J2000) 

*/

double rentry[6]; /* output orbital state vector associated

 with next atmospheric entry [m, m/s] in

 Earth mean equator and equinox of J2000

 coordinates */

double *et_peri; /* output ephemeris time of next periapsis

 (seconds past J2000) */

double rperi[6]; /* output orbital state vector of next

 periapsis [m, m/s] in Earth mean equator

 and equinox of J2000 coordinates */

double rperir[6]; /* output orbital state vector of next

 periapsis [m, m/s] in central body

 equator and prime meridian of date

 (rotating) coordinates */

double *rperi_dalt; /* output bodydetic altitude ("gdalt" in 

POST)

 of next periapsis [m] */

double *rperi_dlat; /* output bodydetic latitude ("gdlat" in 

POST)

 of next periapsis [deg] */

double *rperi_lat; /* output bodycentric latitude ("decln" in
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 POST) of next periapsis [deg] */

double *et_exit; /* output ephemeris time associated with next

 atmospheric exit (seconds past J2000) 

*/

double rexit[6]; /* output orbital state vector associated

 with next atmospheric exit [m, m/s] in

 Earth mean equator and equinox of J2000

 coordinates */

double et0; /* input epoch ephemeris time

 (seconds past J2000) */

double x0[6]; /* input spacecraft orbital state [m, m/s]

 at epoch in Earth mean equator and

 equinox of J2000 coordinates */

(3) Integrate forward one orbit with or without accelerometer data using routine 

“ephupd”

Presuming that routine "ephupd" has been previously called, then a call to routine "ephupd" will 

integrate forward one complete orbit, the so-called "current orbit", which ends at the so-called 

"current periapsis", or at the point on the orbit just beyond the "current periapsis" where the 

atmosphere is declared to have been exited. This occurs while possibly processing one or more 

time-wise contiguous sets of tabular acceleration data. Then routine "ephupd" will integrate 

beyond the end of the "current orbit" to predict the following apoapsis, the so-called "next 

apoapsis", followed by the periapsis after that, the so-called "next periapsis". If this is the first 

call to "ephupd" after a call to routine "ephupd0", then "ephupd" will treat the epoch and orbital 

state provided by the call to "ephupd0" as defining the "current orbit" no matter where the orbital 

state is on that orbit. In this situation, "ephupd" will only integrate from that epoch to the end of 

the "current orbit" before integrating to predict the following apoapsis and subsequent periapsis. 

Routine "ephupd" must be called exactly once per orbit and this call should be made as soon as 

possible after the pass through the atmosphere, with its associated gathering of accelerometer 

data, has been completed, or if there is no pass through the atmosphere, then as soon as possible 

after passing through periapsis. In other words, the orbit to be predicted begins at the end of the 

atmospheric pass at the end of the "current orbit" or at the periapsis at the end of the "current 

orbit", i.e., the "current periapsis", if there is no atmospheric pass. 

All tabular acceleration data provided to this routine must be in chronological order. If there are 

no maneuvers and no atmospheric pass, i.e., no tabular acceleration data, then simply set integer 

argument "n_data" to the literal 0 or a zero-valued integer variable and set double precision 

arguments "et" and "acc" to the literal 0, or zero-valued double precision variables. If argument 

"n_zero" is not set to zero, then the acceleration data can measure the effects for any of the 

following scenarios: maneuver(s) only, an atmospheric pass only, or maneuver(s) followed by an 

atmospheric pass. If there are both maneuver(s) and an atmospheric pass in the acceleration 

data, then the last time-wise contiguous set of tabular acceleration data provided on a given orbit 

must be the acceleration data associated with the atmospheric pass, i.e., any maneuver(s) 
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measured in the acceleration data must precede the atmospheric pass. The only acceleration data 

that can extend in time beyond this "current periapsis" is the acceleration data associated with the 

atmospheric pass. The acceleration data associated with the atmospheric pass must extend 

beyond the "current periapsis", as this is what identifies that particular set of tabular acceleration 

data as being an atmospheric pass as opposed to a maneuver. It is possible to contain a 

maneuver within an atmospheric pass, an atmospheric pass within a maneuver, or one can lead 

into the other; but a maneuver surrounding "current periapsis" that is not within an atmospheric 

pass will lead to the creation of data earmarked as being part of an atmospheric pass when it is 

not, and this will cause bookkeeping problems in other AA routines when the Ephemeris 

Estimator is used as part of the AADS. Furthermore, no time-wise contiguous set of tabular 

acceleration data is permitted to start after the "current periapsis", as that would be in the 

subsequent, i.e., "next" orbit. This routine can only handle one orbit at a time. 

 /* integrate forward one complete orbit

 the so-called "current orbit" which

 ends at the so-called "current 

periapsis"

 or at the point where the atmosphere

 is exited that is associated with the

 "current periapsis", while possibly

 processing one or more time-wise

 contiguous sets of tabular acceleration

 data and then integrate beyond that to

 predict the following apoapsis, the

 so-called "next apoapsis", and 

periapsis,

 the so-called "next periapsis" --

 output status (2 = surface intercept,

 1 = altitude intercept, 0 = outright

 success, <0 = outright failure to 

complete

 all of the integrations and the 

particular

 negative value indicates where in the

 source code that the failure occurred,

 see "Error Codes" section below) */

int ephupd(et_peri0,rperi0,rperi0_dalt,rperi0_dlat,rperi0_lat,et_apo,rapo,

 et_entry,rentry,et_peri,rperi,rperir,rperi_dalt,rperi_dlat,rperi_lat,

 et_exit,rexit,altmin,n_data,et,acc) 

double *et_peri0; /* output ephemeris time of current periapsis

 (seconds past J2000) */

double rperi0[6]; /* output orbital state vector of current

 periapsis [m, m/s] in Earth mean equator

 and equinox of J2000 coordinates */

double *rperi0_dalt; /* output bodydetic altitude ("gdalt" in 

POST)
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 of current periapsis [m] */

double *rperi0_dlat; /* output bodydetic latitude ("gdlat" in 

POST)

 of current periapsis [deg] */

double *rperi0_lat; /* output bodycentric latitude ("decln" in

 POST) of current periapsis [deg] */

double *et_apo; /* output ephemeris time of next apoapsis

 (seconds past J2000) */

double rapo[6]; /* output orbital state vector of next

 apoapsis [m, m/s] in Earth mean equator

 and equinox of J2000 coordinates */

double *et_entry; /* output ephemeris time associated with next

 atmospheric entry (seconds past J2000) 

*/

double rentry[6]; /* output orbital state vector associated

 with next atmospheric entry [m, m/s] in

 Earth mean equator and equinox of J2000

 coordinates */

double *et_peri; /* output ephemeris time of next periapsis

 (seconds past J2000) */

double rperi[6]; /* output orbital state vector of next

 periapsis [m, m/s] in Earth mean equator

 and equinox of J2000 coordinates */

double rperir[6]; /* output orbital state vector of next

 periapsis [m, m/s] in central body

 equator and prime meridian of date

 (rotating) coordinates */

double *rperi_dalt; /* output bodydetic altitude ("gdalt" in 

POST)

 of next periapsis [m] */

double *rperi_dlat; /* output bodydetic latitude ("gdlat" in 

POST)

 of next periapsis [deg] */

double *rperi_lat; /* output bodycentric latitude ("decln" in

 POST) of next periapsis [deg] */

double *et_exit; /* output ephemeris time associated with next

 atmospheric exit (seconds past J2000) */

double rexit[6]; /* output orbital state vector associated

 with next atmospheric exit [m, m/s] in

 Earth mean equator and equinox of J2000

 coordinates */

double altmin; /* input minimum acceptable bodydetic

 altitude that will cause the altitude

 intercept output status of this routine

 to be set if the periapsis of the "next

 orbit" dips below this value [m] */

int n_data; /* input number of ephemeris time tags and

 acceleration 3-vectors */

double et[]; /* input ephemeris time tag array associated

 with the tabular acceleration data
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 (seconds past J2000) */

double acc[][3]; /* input tabular acceleration data array

 [m/s^2] */

(4) Return atmospheric pass orbital states and bodydetic altitudes using 

routine “ephatm”

The first call to this routine must occur after the first call to the "ephupd" routine. The results 

from this routine are always the results associated with the most recent previous call to 

“ephupd”.

 /* return entry epoch and both the spacecraft

 orbital states and the associated

 bodydetic altitudes through the

 atmospheric pass -- output status

 (0 = outright success, <0 = outright

 failure and the particular negative 

value

 indicates where the failure occurred,

 see "Error Codes" section below) */

int ephatm(etatm0,xatm,aatm,n_atm)

double *etatm0; /* output ephemeris time associated with

 atmospheric entry (seconds past J2000) 

*/

double xatm[][6]; /* output spacecraft orbital states [m, m/s]

 in Earth mean equator and equinox of

 J2000 coordinates */

double aatm[]; /* output spacecraft bodydetic altitudes

 [m] */

int *n_atm; /* output number of spacecraft orbital states

 and associated bodydetic altitudes [] */

(5) Return number of orbital states and altitudes available in “ephatm” using 

routine “ephatm0”

 /* return number of spacecraft orbital states

 and associated bodydetic altitudes 

through 

 the atmospheric pass – output status

 (0 = success and !0 = failure) */

int ephatm0(n_atm)

int *n_atm; /* output number of spacecraft orbital states

 and associated bodydetic altitudes [] */
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G.4 Format of the Chebyshev Ephemeris Arrays 

The "sun_eph", "bary_eph", "plan_eph", and "sat_eph" arguments to routine "ephinit" are 

concatenated one-dimensional arrays with the following format. Yes, the value of array[4], 

array[4+m+1], ..., array[4+(n-1)*(m+1)] is the exact same value represented here by m (the 

number of double precision words per record) for any given body, although the value of m does 

vary between bodies. The number of contiguous records being stored is represented here by n. 

This repetitious array loading is done to make each contiguous set of m+1 array elements that 

begins with one of those duplicate elements be exactly what is expected in the input argument of 

the appropriate SPK ephemeris record evaluation routine associated with that data. The 

appropriate SPK ephemeris record evaluation routine for "sun_eph" and "bary_eph" data, which 

always comes from a Development Ephemeris (DE) file, is "spke02" which handles Chebyshev 

polynomials of position only data, and the appropriate SPK ephemeris record evaluation routine 

for "plan_eph" and "sat_eph" ephemeris data, which always comes from a so-called "satellite 

ephemeris" file, is "spke03" which handles Chebyshev polynomials of position and velocity data. 

Both evaluation routines return body orbital state at the specified ephemeris time. In the case of 

"spke03", the body orbital state is solved for directly from the 6 sets of Chebyshev coefficients 

that are present. While in the case of "spke02", the body position is solved for directly from the 

3 sets of Chebyshev coefficients that are present, and the body velocity is solved for directly as 

the derivative of those same 3 sets of Chebyshev coefficients. The ability to readily get the 

derivative of a set of Chebyshev coefficients is one of the fundamental properties of Chebyshev 

polynomials. 

array[0] = beginning ephemeris time (seconds past J2000)

array[1] = time span of each data record [s]

array[2] = number of contiguous data records present

array[3] = (unused)

array[4] = number of double precision words per record (m)

array[4+1]-array[4+m] = 1st Chebyshev record data words

array[4+m+1] = number of double precision words per record (m)

array[4+m+1+1]-array[4+2*(m+1)-1]

 = 2nd Chebyshev record data words

 . 

 . 

 . 

array[4+(n-1)*(m+1)] = number of double precision words per record (m)

array[4+(n-1)*(m+1)+1]-array[4+n*(m+1)-1]

 = nth Chebyshev record data words

G.5 Error Codes 

The following is a list of error messages which are prefixed by the associated error codes 

followed by the associated routines where the errors will have taken place. The error code will 

be returned to the highest level calling routine if C extern variable "ephdriver_error_handling" is 
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set to 0, i.e., error code -2 will be returned by "ephatm", error codes -3 through -11 will be 

returned by "ephinit", and all other error codes will be returned by "ephupd" or "ephupd0". 

Otherwise, the error message will be printed and then "exit(1)" will be executed at the point in 

the code where the error is detected. The occasional "%d" in these error messages will be 

replaced with an integer value if and when the error message is printed, and the "\n" in the error 

code -32 message will cause a new line to be generated at that location. 

 -1: addrot: bad axis = %d input

 -2: ephatm: ephupd has not yet been called

 -3: ephinit: illegal central body number

 -4: ephinit: sun ephemeris array is missing

 -5: ephinit: sun ephemeris array is too long

 -6: ephinit: barycenter ephemeris array is missing

 -7: ephinit: barycenter ephemeris array is too long

 -8: ephinit: planet ephemeris array is missing

 -9: ephinit: planet ephemeris array is too long

 -10: ephinit: satellite ephemeris array is missing

 -11: ephinit: satellite ephemeris array is too long

 -12: ephupd: ephinit has not yet been called

 -13: ephupd: ephupd0 has not yet been called

 -14: ephupd: acc and et array arguments are too long to be stored

 -15: ephupd: illegal value of specified array sizes

 -16: ephupd: integration would start before beginning of ephemeris

 -17: ephupd: unsupported central body number %d detected

 -18: ephupd: bad time tag data in acceleration data table

 -19: ephupd: acceleration data starts before current orbit

 -20: ephupd: last acceleration data set is entirely beyond current periapsis

 -21: ephupd: last acceleration single datum is beyond current periapsis

 -22: ephupd: integration attempting to go off end of ephemeris

 -23: ephupd0: ephinit has not yet been called

 -24: ephupd0: integration would start before beginning of ephemeris

 -25: ephupd0: unsupported central body number %d detected

 -26: ephupd0: new epoch is before current epoch in ephupd

 -27: ephupd0: integration attempting to go off end of ephemeris

 -28: integ: imeth = %d not supported

 -29: integ: imeth = %d should never have occurred

 -30: integ: illegal imeth = %d

 -31: integ: this should not happen (imeth = %d)

 -32: integ: integrator choked \n iflag = %d

 -33: oblateness_perturbation: could not open VENUSGRV

 -34: oblateness_perturbation: Venus MAX_J = %d exceeded

 -35: oblateness_perturbation: Venus MAX_CS = %d exceeded

 -36: oblateness_perturbation: could not open MARSGRV

 -37: oblateness_perturbation: Mars MAX_J = %d exceeded

 -38: oblateness_perturbation: Mars MAX_CS = %d exceeded

 -39: oblateness_perturbation: could not open TITANGRV

 -40: oblateness_perturbation: Titan MAX_J = %d exceeded

 -41: oblateness_perturbation: Titan MAX_CS = %d exceeded
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 -42: oblateness_perturbation: bad central body number %d

 -43: oblateness_perturbation: MAX_J = %d exceeded

 -44: oblateness_perturbation: MAX_CS = %d exceeded

 -45: oblateness_perturbation: ephinit_gm wrongly altered

 -46: oblateness_perturbation: ephinit_radius_oblate wrongly altered

 -47: plsang: bad body number

<-47: ephupd: = -int(10.*ephemeris_time_tag) to indicate apparent hole in the

 last acceleration data set

G.6 Programming Interface 

G.6.1 J array, C matrix, and S matrix data 

There are three sets of central body gravitational field arrays that are hard coded into file 

"oblateness_perturbation.c" according to the central body at hand. These are the normalized C 

and S matrices as well as the normalized J array of zonals. The arrays associated with this data 

are loaded in such a way that the degree and order can be readily truncated to any size from 2 to 

the maximum degree and maximum order available with the unused portions of the arrays being 

ignored. Each J term is immediately followed by the associated C and S matrix terms as follows. 

 J(n) 

 C(n,1) S(n,1) 

 C(n,2) S(n,2) 

 .

 .

 .

 C(n,n) S(n,n) 

The exact values of both the central body gravitation C extern variable "ephinit_gm" and the 

oblateness radius C extern variable "ephinit_radius_oblate" that were identified in the "C Extern 

Variable Interface" section are mandated by the choice of these gravitational field arrays, i.e., all 

three arrays, the central body gravitation, and the oblateness radius come as a set. So, neither 

the central body nor the oblateness radius should be superseded with alternative values, and it is 

treated as an error if they are. 

"The The latest Venus gravity field is MGNP180U, which is a 180 degree and order model based 

on the IAU 1991 Venus pole and prime meridian locations and a reference radius of 6051.0 km. 

This gravity field was developed using data collected from the Magellan mission. The file can 
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be downloaded from the following site: http://pds-geosciences.wustl.edu/geo/mgn-v-rss-5-

gravity-l2-v1/mg_5201/gravity/shgj180u.a01." 

"The most recent Mars gravity field model is MRO110B. Because the MRO110B gravity field 

model requires a new orientation model (which requires extensive software updates), the 

MGS85F2 gravity field is being used. The MGS85F2 gravity field is an 85 degree and order 

model based on the IAU 2000 [2] Mars pole and prime meridian locations and a reference radius 

of 3396.2 km. It is the last Mars gravity field model to use the IAU orientation. This gravity 

field was developed using data collected from Mariner 9, Viking 1 and 2, and MGS mapping 

through Nov. 18, 2001. The file can be downloaded from the following site: http://pdsgeosciences.wustl.edu/geo/mgs-m-rss-5-sdp-v1/mors_1024/sha/jgm85f02.sha." 

"The latest Titan gravity field is a 3 degree and order model referred to as the SOL2 approach. It 

is based on radiometric tracking and optical navigation imaging data from the Cassini mission 

combined with data from the Pioneer and Voyager missions, as well astronomical observations 

of Saturn and its satellites [3]." 

The three paragraphs of quoted text are from the "Autonomous Aerobraking Planetary Constants 

and Models" document [1]. The only alterations made thereto are the reference numbers which 

have been adjusted to be the reference numbers used in this document. 

G.6.2 Inclusion and exclusion of code by choice of central body 

The inclusion and exclusion of blocks of code based on the central body at hand is effected with 

the value assigned to macro CBOD in include file "ephest.h". The relevant values of CBOD are 

299 for Venus, 499 for Mars, and 606 for Titan. File “ephest.h” must be edited to assign the 

correct central body number to CBOD, and then all routines that cause file “ephest.h” to be 

included must be re-compiled. The largest of these blocks of code is the implementation of the C 

and S matrices as well as the J array in file "oblateness_perturbation.c". Lesser examples 

including the assignment of default values to C extern variables appear in files “aads_blkdat.h”, 

“eevardefine.c”, "ephbuild.c", “ephdriver.c”, “ephest.h”, “ephiload.c”, "ephinit.c", "ephupd.c", 

"ephupd0.c", "fauto.c", and "plsang.c". 

G.6.3 Specifying Whether to Treat code as Standalone or as part of the AADS 

The determination of whether to treat the code as a standalone or as a part of the AADS is totally 

determined by the value assigned to macro STANDALONE in include file "ephest.h". Except 

for the specification of central body in macro CBOD as described and adjustments to the main 

program when the code is treated as standalone, no other modifications to the Ephemeris 

Estimator source code are needed or should occur. The relevant values of STANDALONE are 

1 for yes and 0 for no. If the code is treated as part of the AADS, then the various C extern 

variables associated with the “iload” data structure, as specified in the first part of the 

“C Extern Variable Interface” section of this document, are updated before each orbit is 
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integrated with the contents of the “iload” data structure. The appropriate “iload” data structure 

for the central body being Mars or Venus is the first include file below. The appropriate “iload” 

data structure for the central body being Titan is obviously the second include file below. 

 aads_iloads.h 

 aads_iloads_titan.h 

The “iload” updates all take place in routine “ephiload” as called by routine “ephupd0”, or in 

routine “ephupd” if routine “ephupd0” is not called on a given orbit. If the Ephemeris Estimator 

code is treated as standalone, then these C extern variables are initially set to their built-in values, 

as specified in the second, third, and fourth parts of the “C Extern Variable Interface” section of 

this document, and are never altered after that, except explicitly by the main program. 

Manipulation of C extern variables by the main program is described next. 

G.6.4 Establishing and Possibly Overriding Default Values of C Extern 

Variables 

To override one or more of the default values described in the “C Extern Variable Interface” 

section of this document, file “ephest.h” must be included in the main program, and the values in 

question must be explicitly set before the first call to “ephinit” occurs. After that, these values 

can continue to be altered as needed. 

G.6.5 Generation of Natural Body Ephemeris Arrays using Auxiliary Routine 

“Ephbuild”

The generation of natural body ephemeris arrays is effected by calling auxiliary routine 

"ephbuild". Arguments "plan", "n_plan", "sat", and "n_sat" are not present when executing at 

Mars and Venus. The setting of macro CBOD to one of the three body numbers mentioned 

instructs routine "ephbuild" as to which natural body ephemeris arrays to generate. 

int ephbuild(sun,n_sun,bary,n_bary,plan,n_plan,sat,n_sat,et0,etf)

double sun[]; /* output Sun with respect to Solar System Barycenter

 ephemeris array */

int *n_sun; /* output number of double precision words in sun[] 

*/

double bary[]; /* output Venus, Mars system barycenter, or Saturn

 system barycenter with respect to the Solar

 System Barycenter ephemeris array */

int *n_bary; /* output number of double precision words in bary[] 

*/

double plan[]; /* output Saturn with respect to Saturn system

 barycenter ephemeris array */

int *n_plan; /* output number of double precision words in plan[] 

*/
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double sat[]; /* output Titan with respect to Saturn system

 barycenter ephemeris array */

int *n_sat; /* output number of double precision words in sat[] 

*/

double et0; /* input requested ephemeris time start of all 

natural

 body ephemeris arrays (seconds past J2000) */

double etf; /* input requested ephemeris time end of all natural

 body ephemeris arrays (seconds past J2000)

 -- not currently used */

G.6.6 Extraction of Time-tagged Acceleration Data from a File using 

Auxiliary Routine “Ephunload”

When the Ephemeris Estimator is run in standalone mode, all acceleration data is relayed to the 

Ephemeris Estimator in ASCII files. Auxiliary routine “ephunload” extracts this data from one 

of those files that is always named “ee_accel.dat”, and returns it in three variables: a time-tag 

array, a Cartesian acceleration array, and a variable that specifies the number of acceleration 

records that are present. Macro MAX_ACC, which is used to dimension the arrays, is specified 

in include file “ephest.h”. These three variables are the form in which acceleration data is to be 

delivered to routine “ephupd” either directly or via routine “ephdriver”.

void ephunload(et,acc,n_data)

double et[MAX_ACC]; /* input ephemeris time tag array associated

 with the tabular acceleration data

 (seconds past J2000) */

double acc[MAX_ACC][3]; /* input tabular acceleration data array

 [m/s^2] */. 

int *n_data; /* input number of ephemeris time tags and

 acceleration 3-vectors */

G.7 Terminology 

The word “bodydetic” is used throughout this document instead of the Earth relative word 

“geodetic” or the planet relative word “planetodetic”. Given that the Earth is not used as a 

central body in this document and given that Titan is a natural satellite of a planet but not a 

planet itself, a more generic word was needed. 

G.8 Future Work 

There needs to be additional work on the handling of acceleration tables by the integrator. There 

is a need for additional gravitating bodies, with Jupiter being included when Mars is the central 

body being a prime example. This in particular will alter the interfaces to routines “ephbuild” 

and “ephinit” as well as the code in routine “fauto.” Finally, the solar radiation pressure model 

needs to be modified to include penumbra effects. 
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G.8.1Example 1: Overall Interface Routine “Ephdriver”—a Subroutine 

Interface Example 

This routine was originally developed by the AADS to combine the five Ephemeris Estimator 

interface routines into one overall interface routine. The main program examples in the below 

example 2 and example 3 sections both make use of this routine. 

The only argument of "ephdriver" below not already described in the interfaces to the five 

routines in the “Subroutine Interface” section is the first argument "init_orb". Otherwise, the 

routine or routines named in the comment that immediately follows each of the other arguments 

of "ephdriver" below are the associated interface routines where that argument is described. 

/*

* Copyright 2011, KinetX, Inc. This software is developed as freeware and

* may be freely reproduced, distributed, and used by anyone as long as it is

* not used for profit and as long as any derivative works are also freeware.

*/

/* Written by Robert W. Maddock with occasional modifications by

* David L. Skinner */

#include <stdio.h>

#include <stdlib.h>

#include "ephest.h"

void ephdriver(

/* input: initialization control flag and state data */

init_orb, tepoch, x,

/* input: natural body ephemeris data */

sun, n_sun, bary, n_bary,

#if CBOD == 606

 plan, n_plan, sat, n_sat,

#endif

/* input: acceleration data */

et, acc, n_data,

/* output: previous "current" periapsis data */

et_peri0, rperi0_dalt,

/* output: predicted "next" apoapsis data */

et_apo, rapo,

/* output: predicted "next" periapsis and atmosphere entry/exit data */

et_entry, rentry, et_peri, rperi, rperir, rperi_dalt, et_exit, rexit,
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/* output: data for Atmosphere Estimator (AtmosEst) */

n_atm, altitudes_atm, states_atm )

int *init_orb; /* input control flag where

 0 do not call routines "ephinit" and "ephupd0"

 1 call routines "ephinit" and "ephupd0"

 output is the reset value of the flag which is 0 */

double tepoch; /* et0 in ephupd0 */

double x[6]; /* x0 in ephupd0 */

double sun[]; /* ephinit */

int n_sun; /* ephinit */

double bary[]; /* ephinit */

int n_bary; /* ephinit */

#if CBOD == 606

 double plan[]; /* ephinit */

 int n_plan; /* ephinit */

 double sat[]; /* ephinit */

 int n_sat; /* ephinit */

#endif

double et[]; /* ephupd */

double acc[][3]; /* ephupd */

int n_data; /* ephupd */

double *et_peri0; /* ephupd */

double *rperi0_dalt; /* ephupd */

double *et_apo; /* ephupd */

double rapo[6]; /* ephupd */

double *et_entry; /* ephupd */

double rentry[6]; /* ephupd0, ephupd */

double *et_peri; /* ephupd0, ephupd */

double rperi[6]; /* ephupd0, ephupd */

double rperir[6]; /* ephupd0, ephupd */

double *rperi_dalt; /* ephupd0, ephupd */

double *et_exit; /* ephupd0, ephupd */

double rexit[6]; /* ephupd0, ephupd */

double aatm[]; /* ephatm */

double xatm[][6]; /* ephatm */

int *n_atm; /* ephatm0, ephatm */

{ 

 double altmin=0;

 double etatm0;

 double rperi0[6];

 double rperi0_dlat;

 double rperi0_lat;

 double rperi_dlat;

 double rperi_lat;

 int i;

/*
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 int iflag;

*/

 int iistat;

 int init;

 int istat;

 static int first=1;

 /****** External references *******/

 extern int ephatm0();

 extern int ephatm();

 extern int ephinit();

 extern int ephupd0();

 extern int ephupd();

 init=(*init_orb);

 *init_orb=0;

 if (first || (init-10*(init/10))) {

 first=0;

 istat=ephinit(sun,n_sun,bary,n_bary

 #if CBOD == 606

 ,plan,n_plan,sat,n_sat

 #endif

 );

 if (ephdriver_print>=1)

 printf("ephinit=%d\n",istat);

 if (istat!=0)

 exit(1);

 } 

 if (init-10*(init/10)) {

 istat=ephupd0(et_entry,rentry,et_peri,rperi,rperir,rperi_dalt,

 &rperi_dlat,&rperi_lat,et_exit,rexit,tepoch,x);

 if (ephdriver_print>=1)

 printf("ephupd0=%d\n",istat);

 if (istat!=0)

 exit(1);

 if (ephdriver_print>=1) {

 printf("next atmospheric entry: %f %f %f %f %f %f %f\n",*et_entry,

 rentry[0],rentry[1],rentry[2],rentry[3],rentry[4],rentry[5]);

 printf("next periapsis: %f %f %f %f %f %f %f\n",*et_peri,

 rperi[0],rperi[1],rperi[2],rperi[3],rperi[4],rperi[5]);

 printf("next periapsis rotating: %f %f %f %f %f %f\n",

 rperir[0],rperir[1],rperir[2],rperir[3],rperir[4],rperir[5]);

 printf("next periapsis bodydetic altitude: %f\n",*rperi_dalt);

 printf("next periapsis bodydetic latitude: %f\n",rperi_dlat);

 printf("next periapsis bodycentric latitude: %f\n",rperi_lat);

 printf("next atmospheric exit: %f %f %f %f %f %f %f\n",*et_exit,
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 rexit[0],rexit[1],rexit[2],rexit[3],rexit[4],rexit[5]);

 } 

 } 

 iistat=ephupd(et_peri0,rperi0,rperi0_dalt,&rperi0_dlat,&rperi0_lat,et_apo,

 rapo,et_entry,rentry,et_peri,rperi,rperir,rperi_dalt,&rperi_dlat,

 &rperi_lat,et_exit,rexit,altmin,n_data,et,acc);

 if (ephdriver_print>=1)

 printf("ephupd=%d\n",iistat);

 if (iistat!=0)

 exit(1);

 if (ephdriver_print>=1) {

 printf("current periapsis: %f %f %f %f %f %f %f\n",*et_peri0,

 rperi0[0],rperi0[1],rperi0[2],rperi0[3],rperi0[4],rperi0[5]);

 printf("current periapsis bodydetic altitude: %f\n",*rperi0_dalt);

 printf("current periapsis bodydetic latitude: %f\n",rperi0_dlat);

 printf("current periapsis bodycentric latitude: %f\n",rperi0_lat);

 printf("next apoapsis: %f %f %f %f %f %f %f\n",*et_apo,

 rapo[0],rapo[1],rapo[2],rapo[3],rapo[4],rapo[5]);

 if (iistat==0) {

 printf("next atmospheric entry: %f %f %f %f %f %f %f\n",*et_entry,

 rentry[0],rentry[1],rentry[2],rentry[3],rentry[4],rentry[5]);

 printf("next periapsis: %f %f %f %f %f %f %f\n",*et_peri,

 rperi[0],rperi[1],rperi[2],rperi[3],rperi[4],rperi[5]);

 printf("next periapsis rotating: %f %f %f %f %f %f\n",

 rperir[0],rperir[1],rperir[2],rperir[3],rperir[4],rperir[5]);

 printf("next periapsis bodydetic altitude: %f\n",*rperi_dalt);

 printf("next periapsis bodydetic latitude: %f\n",rperi_dlat);

 printf("next periapsis bodycentric latitude: %f\n",rperi_lat);

 printf("next atmospheric exit: %f %f %f %f %f %f %f\n",*et_exit,

 rexit[0],rexit[1],rexit[2],rexit[3],rexit[4],rexit[5]);

 } 

 } 

 istat=ephatm0(n_atm);

 if (ephdriver_print>=1)

 printf("ephatm0=%d n_atm=%d\n",istat,*n_atm);

 if (istat!=0)

 exit(1);

 if (*n_atm>MAX_STT) {

 printf("ephdriver: MAX_STT = %d exceeded\n",MAX_STT);

 exit(1);

 } 

 istat=ephatm(&etatm0,xatm,aatm,n_atm);

 if (ephdriver_print>=1)

 printf("ephatm=%d\n",istat);

 if (istat!=0)

 exit(1);
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 if (ephdriver_print>=1)

 printf("n_atm=%d etatm0=%f\n",*n_atm,etatm0);

 if (ephdriver_print>1) {

 for (i=0; i<*n_atm; i++) {

 printf("atmosphere: %f %e %e %e %e %e %e\n",etatm0+(double)(i),

 xatm[i][0],xatm[i][1],xatm[i][2],xatm[i][3],xatm[i][4],xatm[i][5]);

 printf("atmosphere bodydetic altitude: %f\n",aatm[i]);

 } 

 } 

 /* SAVE DATA FILES FOR TROUBLESHOOTING */

 FILE *fp;

 fp = fopen("ee_per.csv","a");

 fprintf(fp, "%f %f %f %f %f %f %f\n",*et_peri0,

 rperi0[0],rperi0[1],rperi0[2],rperi0[3],rperi0[4],rperi0[5]);

 fclose(fp);

 fp = fopen("ee_per_a.csv","a");

 fprintf(fp, "%f\n",*rperi0_dalt);

 fclose(fp);

 fp = fopen("ee_apo.csv","a");

 fprintf(fp, "%f %f %f %f %f %f %f\n",*et_apo,

 rapo[0],rapo[1],rapo[2],rapo[3],rapo[4],rapo[5]);

 fclose(fp);

/*

 fp = fopen("alt.csv","a");

 for (i=0; i<*n_atm; i++) fprintf(fp, "%.23e %.23e\n",

 etatm0+(double)(i),altitudes_atm[i]);

 fclose(fp);

 fp = fopen("scpos.csv","a");

 for (i=0; i<*n_atm; i++) fprintf(fp, "%.23e %.23e %.23e %.23e\n",

 etatm0+(double)(i),states_atm[i][0],states_atm[i][1],states_atm[i][2]);

 fclose(fp);

 fp = fopen("scvel.csv","a");

 for (i=0; i<*n_atm; i++) fprintf(fp, "%.23e %.23e %.23e %.23e\n",

 etatm0+(double)(i),states_atm[i][3],states_atm[i][4],states_atm[i][5]);

 fclose(fp);

*/

 } 

G.8.2 Example 2: Titan Non-atmospheric Run-out—a Main Program 

Example 

There are nine orbits in this Titan non-atmospheric run-out, which corresponds to the Titan runout. Only two arguments to "ephdriver" have name changes in this main program, and these are 

the second argument which is "tepoch" instead of "et0" and the third argument which is "x" 
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instead of "x0". Before the first call to "ephdriver", the epoch in variable "tepoch" and the 

orbital state in array "x" are initialized. This is indicated to "ephdriver" by setting its first 

argument "init_orb" to 1 which indicates to call routines "ephinit" and "ephupd0". After that, the 

other 8 calls to "ephdriver" are preceded by "init_orb" being set to 0 which indicates to not call 

either "ephinit" or "ephupd0". (This is an optional setting given that “ephdriver” always resets 

“init_orb” to 0.) Finally, note that run-outs like this have no maneuvers or atmospheric passes 

and therefore no accelerometer data (n_data = 0). 

/*

* Copyright 2011, KinetX, Inc. This software is developed as freeware and

* may be freely reproduced, distributed, and used by anyone as long as it is

* not used for profit and as long as any derivative works are also freeware.

*/

/* Written by David L. Skinner */

#include <stdio.h>

#include <stdlib.h>

#include "ephest.h"

main()

{ 

 double aatm[MAX_STT];

 double bary[4+NRECS*(NR+1)];

 double et[MAX_ACC]={0};

 double et_apo;

 double et_entry;

 double et_exit;

 double et_peri;

 double et_peri0;

 double plan[4+NRECS*(NR_699+1)];

 double rapo[6];

 double rentry[6];

 double rexit[6];

 double rperi[6];

 double rperi0[6];

 double rperi0_dalt;

 double rperi_dalt;

 double rperir[6];

 double sat[4+NRECS*(NR_606+1)];

 double sun[4+NRECS*(NR_10+1)];

 double tepoch;

 double x[6];

 double xatm[MAX_STT][6];

 int init_orb;

 int istat;
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 int n_atm;

 int n_bary;

 int n_plan;

 int n_sat;

 int n_sun;

 /****** External references *******/

 extern int ephbuild();

 extern void ephdriver();

 extern void ephunload();

 ephdriver_error_handling=1;

 ephdriver_print=1;

 tepoch = 292507200.0000000;

 x[0] = 1.101775903953336e+06;

 x[1] = 4.532982772796417e+06;

 x[2] = 1.694457972447233e+07;

 x[3] = -1.306418564602341e+02;

 x[4] = -3.646815435373888e+02;

 x[5] = 1.060535718871817e+02;

 n_data = 0;

 istat=ephbuild(sun,&n_sun,bary,&n_bary,plan,&n_plan,sat,&n_sat,tepoch,0.);

 if (istat!=0) {

 printf("istat = %d after call to ephbuild\n",istat);

 exit(1);

 } 

 init_orb = 1; /* integrate orbit 1 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 init_flag = 0; /* integrate orbit 2 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 init_flag = 0; /* integrate orbit 3 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,
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 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 init_flag = 0; /* integrate orbit 4 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 init_flag = 0; /* integrate orbit 5 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 init_flag = 0; /* integrate orbit 6 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 init_flag = 0; /* integrate orbit 7 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 init_flag = 0; /* integrate orbit 8 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 init_flag = 0; /* integrate orbit 9 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm); 

 } 

G.8.3 Example 3: Mars Aerobraking with Orbital State Updates 

—a Main Program Example 

There are 20 orbits in this Mars example, which is the example that was used to compare the 

Ephemeris Estimator to DPTRAJ/MIRAGE. Only two arguments to "ephdriver" have name 

changes in this main program, and these are the second argument which is "tepoch" instead of 

"et0" and the third argument which is "x" instead of "x0". Before the first call to "ephdriver", the 
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epoch in variable "tepoch" and the orbital state in array "x" are initialized. Before the eighth and 

fifteenth calls to "ephdriver", the epoch in variable "tepoch" and the orbital state in array "x" are 

updated. In all three cases, this is indicated to "ephdriver" by setting its first argument "init_orb" 

to 1 which indicates to call routines "ephinit" and "ephupd0". The rest of the calls to "ephdriver" 

are preceded by "init_orb" being set to 0, which indicates to not call either "ephinit" or 

"ephupd0". (This is an optional setting given that “ephdriver” always resets “init_orb” to 0.) 

Note that all 20 calls to “ephdriver” are preceded by eight lines beginning with the line “if 

(init_acc) {“. In this example, variable “init_acc” has previously been set to 1. So, this “if” 

clause will test true. The lines that will be executed consist of a "system" call, a test to see if the 

“system” call was successful with error termination if it was not, and a call to “ephunload”. This 

call to “ephunload” reads the file "ee_accel.dat" created by the “system” call, unloads its timetagged acceleration data contents into arrays “et” and “acc”, and sets variable “n_data” to the 

number of acceleration records that are present. Notice how the call to “ephbuild” in this 

example only has six arguments, i.e., arguments “plan,” “n_plan,” “sat,” and “n_sat” are missing. 

This is because the central body is not Titan. 

/*

* Copyright 2011, KinetX, Inc. This software is developed as freeware and

* may be freely reproduced, distributed, and used by anyone as long as it is

* not used for profit and as long as any derivative works are also freeware.

*/

/* Written by David L. Skinner */

#include <stdio.h>

#include <stdlib.h>

#include "ephest.h"

main()

{ 

 double aatm[MAX_STT];

 double acc[MAX_ACC][3]={0};

 double bary[4+NRECS*(NR+1)];

 double et[MAX_ACC]={0};

 double et_apo;

 double et_entry;

 double et_exit;

 double et_peri;

 double et_peri0;

 double rapo[6];

 double rentry[6];

 double rexit[6];

 double rperi[6];

 double rperi0_dalt;

 double rperi_dalt;

 double rperir[6];
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 double sun[4+NRECS*(NR_10+1)];

 double tepoch;

 double x[6];

 double xatm[MAX_STT][6];

 int init_acc;

 int init_orb;

 int istat;

 int n_atm;

 int n_bary;

 int n_sun;

 /****** External references *******/

 extern int ephbuild();

 extern void ephdriver();

 extern void ephunload();

 ephdriver_error_handling=1;

 ephdriver_print=1;

 tepoch = 2.93329038208989500999451e+08;

 x[0] = 1.72760675314441435039043e+07;

 x[1] = -4.52485670035811886191368e+06;

 x[2] = 4.07681638074280992150307e+07;

 x[3] = -2.70857367232199344186938e+01;

 x[4] = 3.69688306831999113910570e+02;

 x[5] = 5.25096242285018348638914e+01;

 init_acc = 1;

 istat=ephbuild(sun,&n_sun,bary,&n_bary,tepoch,0.);

 if (istat!=0) {

 printf("istat = %d after call to ephbuild\n",istat);

 exit(1);

 } 

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit017.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 1; /* integrate orbit 1 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,
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 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit018.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 2 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit019.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 3 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit020.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 4 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);
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 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit021.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 5 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit022.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 6 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit023.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat); 

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 7 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 tepoch = 2.94028400000000000000000e+08;

 x[0] = -9.31159024916070397011936e+05;

 x[1] = -2.42423837009716685861349e+06;

 x[2] = -3.07023892755041271448135e+06;

 x[3] = 9.67849587909739511815133e+02;

 x[4] = -4.17531521449173487781081e+03;
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 x[5] = 1.01175500943769566219999e+03;

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit024.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 1; /* integrate orbit 8 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit025.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 9 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit026.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 10 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit027.dat ee_accel.dat");

 if (istat!=0) {
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 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 11 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit028.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 12 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit029.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 13 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit030.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 
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 init_orb = 0; /* integrate orbit 14 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 tepoch = 2.94709700000000000000000e+08;

 x[0] = -9.96845590627893456257880e+05;

 x[1] = -2.14550716982444468885660e+06;

 x[2] = -3.15225289098504697903991e+06;

 x[3] = 9.13219270463832799578086e+02;

 x[4] = -4.26052627359854159294628e+03;

 x[5] = 8.33728815678350883899839e+02;

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit031.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 1; /* integrate orbit 15 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit032.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 16 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit033.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 
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 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 17 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit034.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data); 

 } 

 init_orb = 0; /* integrate orbit 18 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit035.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 19 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);

 if (init_acc) {

 istat=system("cp mars_roc.ee_accel_orbit036.dat ee_accel.dat");

 if (istat!=0) {

 printf("istat = %d after 1st call to system\n",istat);

 exit(1);

 } 

 ephunload(et,acc,&n_data);

 } 

 init_orb = 0; /* integrate orbit 20 */

 ephdriver(&init_orb,tepoch,x,sun,n_sun,bary,n_bary,et,acc,n_data,

 &et_peri0,&rperi0_dalt,&et_apo,rapo,

 &et_entry,rentry,&et_peri,rperi,rperir,&rperi_dalt,

 &et_exit,rexit,&n_atm,aatm,xatm);
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G.9 References 

1. PRELIMINARY Autonomous Aerobraking Planetary Constants and Models,

Version 0.06, June 9, 2011. 

2. Seidelmann, P.K., et al., “Report of the IAU/IAG Working Group on Cartographic 

Coordinates and Rotational Elements of the Planets and Satellites: 2000,” Celestial 

Mechanics and Dynamical Astronomy, in press, 2002.

3. Luciano less, et al., “Gravity Field, Shape, and Moment of Inertia of Titan,” Science 327, 

1367 (2010), March 12, 2010. 
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Appendix H. AADS (Supplement to Section 7.5.1) 

The spacecraft interfaces to the AADS flight software through the use of data structures, as 

shown in Figure H.1. The required AADS input data is passed into AADS through two data 

structures. The first input structure includes parameters and/or data which are likely to change 

between AADS calls, such as the following: 

 Ephemeris Estimator initialization: flag which triggers use of provided state and epoch 

as initial state for integration. 

 Ephemeris Estimator ephemerides data: including Sun, and central body barycenter for 

operation at Mars and Venus; includes Saturn and Titan information for operation at 

Titan. 

 Ephemeris Estimator time-tagged acceleration data: 10 Hz data (provided by the IMU) 

during both the maneuver (if executed) and the atmospheric pass. 

 Atmosphere Estimator acceleration data: 1 Hz data (provided by the IMU) during the 

atmospheric pass; provided epoch at start of data collection. 

 Atmosphere Estimator attitude quaternion data: used to estimate aerodynamics, which, 

along with acceleration data, can be used to estimate atmospheric density and scale 

height. 

The second input data structure to AADS contains data not likely to change between AADS 

calls, but which may be changed and uploaded to the spacecraft during the weekly update cycle. 

This AADS iLOAD structure includes data such as: 

 Planetary constants: GM for Sun, central body, as well as Saturn and Titan if 

applicable, central body radii (equatorial and polar), central body pole definition. 

 Ephemeris Estimator setup parameters: integration stepsize initial guess and 

tolerances, time offset from periapsis to estimate atmospheric entry and exit. 

 Spacecraft parameters: mass, aerodynamic reference area, central body to 

aerodynamic coordinate frame transformation. 

 Corridor settings: operational corridor lower and upper limit as well as desired target 

(as a percentage of the corridor width). 

All outputs from AADS to the spacecraft are provided in a single output data structure. This 

AADS output structure includes data such as: 

 Ephemeris Estimator atmospheric entry and exit predictions: both epoch and state used 

by spacecraft to command slew to and from AB configuration. 

 Maneuver command: magnitude, direction and epoch; current model places maneuver 

epoch at the Ephemeris Estimator predicted apoapsis time, with the maneuver 

assumed to be in the direction of the estimated orbital velocity at apoapsis. 
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In addition to this interface with the spacecraft, an additional data structure is created within 

AADS to pass information between the Atmosphere Estimator, Ephemeris Estimator, and the 

Maneuver Estimator. This AADS internal data structure includes: 

 Ephemeris Estimator prediction of the next apopasis state. 

 Ephemeris Estimator prediction of the next periapsis state (including altitude). 

 Ephemeris Estimator estimate of the current (previous) periapsis state (including 

altitude). 

 Current (previous) atmospheric pass information: provided by Ephemeris Estimator to 

the Atmosphere Estimator and includes both state and altitude estimates. 

 Atmosphere Estimator prediction of the next periapsis density and scale height 

(includes 1-sigma errors as well as correlation between the two predictions). 
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Figure H.1. AADS Interfaces with the Spacecraft using Data Structures: (1a) Spacecraft inputs to 

AADS which will or may change each AADS call, (1b) Spacecraft inputs to AADS which are not likely 

to change during the AB mission, (2) AADS outputs to the spacecraft, and (3) Intra-AADS. 

H.1 A Cycle in the Life of AADS 

With the interfaces now defined, it is possible to step through the AADS operation, at a high 

level, to better understand how the various models work together to successfully execute an AA 

mission while ensuring spacecraft safety. The AADS is called just once during each orbit, at 

some time after atmospheric exit and prior to the next apopasis, giving the spacecraft sufficient 

time to complete any onboard tasks, including execution of the AADS software and preparations 

for any maneuver commanded by AADS. 

The first processes executed during AADS operation involve the Ephemeris Estimator. This 

module is responsible for integrating the estimated spacecraft state up. This integration begins at 

either the state provided for initialization, or from the last state propagated to and stored in 
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memory. Included in this state integration are all applicable models (central body gravity field, 

3

rd body gravitational effects and solar radiation pressure). The Ephemeris Estimator is provided 

IMU acceleration data during both burns and atmospheric passes. When the Ephemeris 

Estimator integration reaches the epoch of this data, it processes the data, including it in its 

integration estimate. So, with this the Ephemeris Estimator can effectively integrate a spacecraft 

state estimate from the last AADS call, through the provided maneuver and atmosphere 

acceleration data, up to the current mission time. This is the state the Ephemeris Estimator then 

stores away to use as its initial state during the next AADS call, if a new initialization state is not 

provided. However, the Ephemeris Estimator does not stop here. The spacecraft state continues 

to be integrated through the next apoapsis (assuming no maneuver), up to and through the next 

atmospheric pass, however the atmosphere itself is not modeled. This is done to first, provide 

predicted apoapsis conditions for execution of a maneuver, if needed, and second, to provide 

state and altitude information for the current/previous atmosphere pass to the Atmosphere 

Estimator. 

At this point, the AADS calls the Atmosphere Estimator. The Atmosphere Estimator takes the 

atmospheric pass acceleration data provided by the spacecraft, along with the atmospheric pass 

state and altitude information provided by the Ephemeris Estimator, to estimate the atmospheric 

conditions (density and scale height) during the current/previous pass. This information is then 

added to an archive where atmospheric condition estimates are stored for each pass. This archive 

data is then used to predict both the density and scale height of the next periapsis, along with 

dispersion and correlation predictions. 

Once the Ephemeris and Atmosphere Estimators have calculated their prediction for the 

conditions at the spacecraft’s next periapsis, the Maneuver Estimator can now determine whether 

or not a maneuver is required, and if so, what that maneuver should be. Figure H.2 illustrates 

this process through the following steps: 

1. Calculate the predicted operational corridor location (e.g., heat rate, temperature, 

altitude, etc.) based on the information provided by the Ephemeris and Atmosphere 

Estimators. 

2. If the predicted location is within the corridor, do nothing. Note that this does not 

guarantee that the true corridor location will be within the corridor. If the AADS has 

not diverged significantly, then the difference between the predicted and true corridor 

location should be small, certainly close enough not to trigger any immediate action. 

3. If the predicted location is outside of the corridor, a change in altitude is determined to 

place the spacecraft at the desired corridor target. 

4. This change in altitude is added to the current estimated periapsis altitude, which is 

then added to the estimated apoapsis altitude to determine a new orbit semi-major 

axis, from which a new velocity at apoapsis is determined. The difference between 

this new apoapsis velocity and the current estimate of the apoapsis velocity provided 

by the Ephemeris Estimator is the required maneuver magnitude. This value is 
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positive for a periapsis raise (decrease freestream heating rate) and negative for a 

periapsis lowering (increase freestream heating rate). The maneuver direction is 

estimated to be that of the pre-maneuver velocity vector at apoapsis. Since these 

maneuvers are typically small (< 0.5 m/s), this assumption works well, even when 

considering a finite burn. 

At this time, the AADS software can be placed in stand-by mode or terminated until the next 

AADS function call to free spacecraft resources for other activities. Onboard a spacecraft, the 

AADS software will not always running, but instead is called once per orbit, typically at some 

time after an atmospheric pass ends and prior to the next apoapsis. Some AADS data does 

need to be preserved between AADS calls (e.g., Ephemeris Estimator current state prediction 

and Atmosphere Estimator atmosphere archive data), so at least a portion of the memory will 

be allocated and preserved while AADS is not running. If a maneuver is executed, the 

associated acceleration data is collected and stored, along with the subsequent atmospheric 

pass acceleration data, and provided to the AADS at the next call. This process is then 

repeated each orbit. Ideally, this would be done completely autonomously, with interactions 

from the ground no more frequent that once per week. At those times, any changes in the 

AADS parameters (e.g., corridor and/or target) could be made, along with an Ephemeris 

Estimator initialization state update. 

Figure H.2. AADS Execution Process with Respect to the Operational Corridor
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Appendix I. AAHFS (Supplement to Section 7.5.2) 

I.1 AAHFS Truth Model 

The AAHFS truth model software replicates the true behavior of the spacecraft in its 

environment. The environment and spacecraft characteristics of a typical AB mission are similar 

to many other deep-space missions. This makes the MESSENGER truth model a good initial 

starting point for developing a test environment for AA. The MESSENGER 6-DOF truth model 

includes the spacecraft dynamics, sensors, actuators and environmental disturbances. Although 

these actuator models were developed to emulate the characteristics of the MESSENGER flight 

hardware, they provide a convincing, validated environment for testing the AA approach since 

these sensors are typical of an AB spacecraft as well. The environment models approximate all 

known disturbances sources external to the vehicle. These disturbances affect both the trajectory 

and the attitude dynamics, so it is natural to encapsulate these effects in a full 6-DOF simulation. 

A key addition is that AA modeling requires detailed atmospheric and aerodynamic models to 

determine the forces and torques due to atmospheric drag. These models were not a part of the 

original MESSENGER truth models, but are easily incorporated into the code by adopting the 

architecture shown in Figure I.1-1. This figure highlights the high-level interface between the 

MESSENGER heritage software, depicted in red, and the new development to support AA, 

depicted in purple. Minimizing the interaction between the heritage code and the AB models 

reduces the complexity of the model and ensures the MESSENGER-based software is 

unperturbed. The new AB models have their own rich flight heritage as well, as they are based 

on software used for testing and operations of prior NASA AB missions. The forces and torques 

that result from these models are integrated by the full equations of motion to predict the vehicle 

state. Sensor models are used to emulate the data inputs to the GN&C system. These models 

make use of the MESSENGER flight heritage to include flight performance characteristics, 

further enhancing the fidelity of the simulation environment. 
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Figure I.1-1. AAHFS Truth Model Block Diagram 

I.1.1 MESSENGER Heritage Truth Models in AAHFS 

The MESSENGER heritage software contains complete actuator models that are sufficient for 

the AAHFS demonstration. These models include both thruster and reaction wheel models, 

which operate at 200 Hz to ensure that transient characteristics are correctly modeled. Although 

the MESSENGER reaction wheels are undersized for a typical AB mission (as the AB mission 

inertias are 3–5 times the MESSENGER values), the model can be scaled appropriately to ensure 

the torque and momentum characteristics are consistent with the simulated vehicle inertias. 

There is significant flexibility built into these models, as modifications can easily be made to 

static and running friction, wheel alignments and inertia variability, allowing for trade study and 

(if desired) Monte Carlo analysis. The MESSENGER propulsion system is perhaps overly 

complex for the AA studies, but this model has simplified modes that are consistent with 

propulsive maneuver operations during prime AB missions. Thruster capabilities allow corridor 

control maneuvers to be simulated with appropriate fidelity. The propellant supply mechanism 

can run in a fixed pressure mode or simulate tank blowdown for producing realistic thrust and 

specific impulse, as well as ensuring mass changes are modeled realistically. Thrust transients 

due to valve/thruster/thermal effects are modeled to accurately mimic system performance. 

Additional performance variation is easily accomplished including variable thruster plume 

impingement model included for Monte Carlo study. These models have undergone an extensive 

correlation with flight data, ensuring that they mimic the real hardware performance, thereby 

ensuring a high-fidelity test environment for AAHFS. 
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The MESSENGER heritage software includes high-fidelity sensor models running at rates that 

are consistent with the device operation. This includes multiple star trackers for attitude 

determination running at 10 Hz. These star tracker models have easily adjusted alignments and 

noise characteristics for sensitivity studies. The 100-Hz IMU model is critical for AAHFS 

simulation and study, since AADS algorithms heavily rely on acceleration data from IMU. A 

variety of trade studies may be useful involving this model, as it is of interest to determine the 

accuracy required of the IMU data (in particular, the accelerometer readings through the drag 

pass) to ensure the proposed AA approach meets performance goals. The IMU model includes a 

convenient environment for studying AADS sensitivity to accelerometer (and gyro) 

misalignments, scale factor errors, biases, noise (white and readout), IMU clock walk, data 

collection frequency and sensor latencies. 

The environment models in the AAHFS simulation model all of the salient perturbations that the 

spacecraft would experience when in orbit about the central body. This simulation can extract 

ephemeris information for any solar system body of interest from a SPICE SPK file. The bodies 

of interest are easily changed, allowing the simulation to be quickly adapted to different central 

bodies of interest (as well as modifying the desired gravitational perturbative bodies). The 

central body uses an optional harmonic gravity model, which can be of arbitrary degree and 

order; this provides the highest possible fidelity in integrating the translational equations of 

motion. Disturbance forces include the effects of solar radiation pressure (SRP) with a full 

umbra/penumbra eclipse model. This SRP model is specific to the MESSENGER spacecraft, but 

is scaled to get the effect to be consistent with an AB mission (based on the ratio of the Sunfacing areas between a notional AB mission and MESSENGER). For missions where this force 

is negligible (at Titan, for instance), this effect can be disabled. Additionally, disturbance torque 

models include those due to SRP as well as the gravity gradient. In general, most of these 

environment models are run at 1 Hz as the resulting disturbance forces and torques are slowly 

varying and don’t require higher execution rates. The exception is the ephemeris models, since 

the planetary states are used to calculate the right-hand side of the translational equations of 

motion. In this case, the SPICE file extractions are done at 1 Hz, but the planet states are 

interpolated up to the model integration rate of 200 Hz. 

The AAHFS dynamics models integrate the translational and rotational dynamics at 200 Hz. 

This rate is selected to capture thrust transients for thrusters pulsed at 50 Hz. A smaller step size 

would be possible; testing reveals that it does not provide additional fidelity but it does reduce 

the simulation speed. Simulation speed is of critical importance, as the goal of the project is to 

demonstrate AA is plausible for durations on the order of a week, so the AAHFS code must be 

capable of running in excess of seven days. Additionally, the AAHFS truth models include 

propellant slosh dynamics and a structural model, which are optional models for the purposes of 

this study. While these models do enhance the fidelity of the truth model software, they are 

spacecraft specific, and would need to be updated to be consistent with the vehicle of interest for 

a real AB flight program. Further, this model does not respond or get excited by the atmosphere, 

limiting its utility. It does provide some mechanism to conduct simulations on a non-rigid body, 
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particularly to model the IMU response to a flexible environment, so it is retained for future 

study purposes. Both the slosh and the structural model are easily disabled for the initial 

AAHFS testing. 

I.1.2 AAHFS Truth Model New Development 

Figure I.1-2 shows a detailed block diagram for the new AAHFS truth model development. Of 

particular interest for this discussion are the heritage elements provided by the LaRC team 

members, the atmosphere model and the aerodynamic models. These new models have been 

added to support AB specific capabilities these models have been calibrated using AB flight data 

from prior NASA AB missions. This produces a convincing environment for testing the 6-DOF 

behavior of an AB spacecraft. 

Figure I.1-2. Block Diagram for New AAHFS Truth Models 

The fidelity of the atmosphere model is of particular importance to the demonstration of an endto-end AA simulation. Additionally, flexibility of this model is of paramount importance, as this 

study aims to use atmospheric variability as one means of investigating the robustness of the 

proposed AADS algorithms. The Mars-GRAM is an engineering-level atmospheric model 

widely used for prior Mars AB study and mission analyses [refs. 1, 2].In addition to providing 

high-fidelity predictions of the mean density, temperature, pressure, and wind components at any 

planet position and altitude, Mars-GRAM allows for the simulation of perturbed profiles about 

the mean conditions, thereby offering great flexibility for testing the AA approach. The most 

recent version of Mars-GRAM (2010) has updates to reconcile the models with the AB data of 

MRO, Mars Odyssey, and MGS, making it a highly useful model for an AB study. For the two 

other central bodies in this study a Titan-GRAM model and Venus-GRAM model were utilized. 

C versions of these GRAM models have been provided, and through the use of the Simulink 

Legacy Code Tool, these models have been directly integrated into the AAHFS truth model 

software. It is of minor consequence that this code was originally conceived in FORTRAN, and 

relies on namelist files for parametric modification. Prior to running the Simulink simulation, 
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these namelist files are easily modified by MATLAB scripts. The significant capability that the 

GRAM code provides does come at the price of execution speed. For this reason, the AAHFS 

only executes the GRAM model at 1 Hz. The output atmospheric densities are generally quite 

smooth and slowly varying, so interpolation up to the 200-Hz integration time step is easily 

accomplished. This allows use of the high-fidelity GRAM models without sacrificing simulation 

speed. The AAHFS atmosphere modeling strategy allows a wide variety of studies of missions 

to Mars, Venus, and Titan with a single simulation. 

An aerodynamic model has been added to allow conversion of the atmospheric data generated by 

the GRAM software into the forces and torques operating on the vehicle. This model uses an 

underlying database of aerodynamic coefficients that are interpolated based on the spacecraft 

attitude and atmospheric density. This database is spacecraft specific (the current one in use is 

based on MRO data), and although this step in the process is mission dependent, the data 

currently in use is consistent with a typical AB spacecraft. If an aerodynamic data set was 

available for a proposed spacecraft, it is trivial to modify the software to adopt an alternate 

database. Any future flight program that uses the AA approach would substitute their vehicle 

model in for the MRO model when that data became available. As such, the use of MRO data 

for the vehicle aerodynamic properties is notional for this study. However, this database has 

been validated against an AB flight mission, thereby serving to produce more convincing test 

results. Once this model produces the necessary aerodynamic coefficients, the forces and 

torques are produced via standard aerodynamic equations [ref. 3]. It is important that these 

dynamic quantities are calculated at a high rate, as the attitude can be active during a drag pass. 

The AAHFS software computes these forces and torques at the integration rate of 200 Hz to 

ensure faithful modeling of the aerodynamics during a drag pass. 

I.1.3 AAHFS FLIGHT Software 

The flight software portion of the AAHFS model represents all of the guidance and control 

functions and algorithms necessary to ensure control of the spacecraft. As with the AAHFS truth 

model algorithms, the framework for this software was the MESSENGER guidance and control 

flight software. Where appropriate, AAHFS uses the same control code for the demonstration of 

the AA capability. This heritage software includes a typical set of attitude and maneuver 

guidance, estimation and control algorithms. The primary responsibility of this code is to ensure 

the attitude follows the desired pointing profiles, that angular momentum remains within desired 

limits, and that the propulsive maneuvers are executed successfully. One major advantage of this 

architecture is that the portion of the flight software that is inherited from MESSENGER is the 

onboard software used for the flight mission. The only significant differences are that the 

simulation runs in a workstation much faster than real time and responds to simulated 

environmental data, whereas the onboard guidance and control software runs in real time as an 

embedded application on the flight processor and is experiencing the true flight environment. 

The MESSENGER heritage code alone is insufficient to demonstrate AA. The AADS is a new 

block of software developed to handle the additional functions necessary to implement the AB
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corridor control onboard. While this set of algorithms represents a small part of the AAHFS 

software, the development of these algorithms is the primary focus of the demonstration of the 

AA capability. The remainder of the AAHFS acts as a test bed for these algorithms. 

I.1.4 Heritage Flight Software Algorithms 

Much of the AAHFS flight software block depicted in Figure I.1-3 is heritage code from the 

MESSENGER mission. A standard set of algorithms is used to ensure the necessary control 

goals are achieved. The addition of the AADS software as well as the additional drag pass 

operations of an AB spacecraft levy additional requirements on the standard MESSENGER 

software. This required modification to all elements of the software functionality to enhance the 

autonomy of the system and to ensure control is maintained through the drag pass. 

Figure I.1-3. AAHFS Guidance and Control Flight Software Block Diagram 

The MESSENGER heritage software contains a complete set of guidance algorithms. These 

algorithms maintain knowledge of all relevant solar system bodies to allow construction of a 

variety of pointing commands [ref. 4], as well as to ensure satisfactory execution of planned ΔV 

maneuvers. Transitions and parameterization of these pointing scenarios are typically handled 

with ground commands, but in the case of AA, these mode transitions need to happen 

autonomously. In the case of the pointing scenarios, the spacecraft must determine when and 

how to configure itself for an AB drag pass as well as handle the appropriate configuration for 

executing a corridor control maneuver. These events cannot be triggered via ground command, 
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as their timing is not known in advance. This forces these events to be orbit-event driven. As an 

example, the spacecraft guidance system must know the expected time of the ensuing periapsis 

passage. Based on this periapsis timing, the spacecraft must determine the duration of the AB

drag pass, and ensure that the proper reconfiguration is handled to orient a preferred axis into the 

wind prior to entering the atmosphere to ensure the necessary aerodynamic stability. As the orbit 

evolves over time due to the varied pass drag environment, the spacecraft must respond 

accordingly. As a result, the MESSENGER guidance algorithms have been modified to ensure 

these pointing transitions occur autonomously based on timing information about the orbit. 

Likewise, to ensure maneuvers are executed correctly, the spacecraft must be able to determine 

its own attitude command and maneuver timing to ensure the desired corridor control maneuver 

executes properly. The AADS function computes the desired corridor control ΔV and maneuver 

epoch, and the guidance system must use this information to autonomously implement the 

maneuver. So while much of the functionality of the onboard guidance system is unchanged, the 

level of autonomy is increased significantly. 

The estimation tasks provided by the MESSENGER flight software are reused directly for 

AAHFS. This software runs a model replacement Kalman Filter to estimate the spacecraft 

attitude from the gyro and star tracker data. Although fault scenarios are not a planned part of 

the AAHFS test program, the attitude estimation is robust to missing or incomplete sensor data, 

as is typical for flight software. The filter executes at 1 Hz, and attitude estimates are propagated 

with high-rate gyro data up to the control task rate of 50 Hz. The MESSENGER software 

supports a high-rate (50 Hz) estimation of accumulated ΔV based on the accelerometer data. 

This includes the onboard estimation of accelerometer biases prior to the maneuver. This 

process has been modified to execute autonomously, as for the MESSENGER flight program, 

the bias estimation and maneuver estimation are all accomplished with command sequences 

carefully planned by ground operators. An identical process to maneuver estimation is proposed 

for estimating the accelerations (or alternately, ΔV) from the AB drag pass. This estimation 

must happen autonomously, so the software has been configured to execute the necessary 

commands autonomously to perform the accelerometer bias estimation as well as to estimate and 

buffer the accelerations from the drag pass. This buffer of accelerations will be used in the 

AADS software, discussed in the next subsection. 

Much of the control functionality required for an AB mission is a part of the MESSENGER 

heritage flight software. This software contains algorithms for attitude control on reaction 

wheels and thrusters. The wheel control law is a hybrid law that performs an eigenaxis slew for 

large angle maneuvers with a bang-bang control law and is reduced to a PID law when the angle 

errors are small. The thruster control law uses a phase plane to control each thruster 

individually, and is typically only employed during maneuvers and momentum dumps. 

Momentum control is generally accomplished via ground command, but autonomous momentum 

control is a part of the MESSENGER heritage code, and is used for AAHFS as necessary. The 

only significant modification to the MESSENGER code to support AAHFS simulations is to 

develop a control mode for the AB drag pass. Much of the attitude control during AB is 
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accomplished by the aerodynamic stability of the vehicle. It is assumed that the vehicle is stable 

in pitch and yaw, so the roll is the only element that requires control, and this torque is assumed 

to be reasonably small. The control concept adopted for AAHFS simulations is to enter the drag 

pass on wheel control, ensuring that a pre-defined vehicle axis (the “nose”) is pointed into the 

wind. Once in the drag pass and the aerodynamics take over, the wheels spin down (off-loading 

momentum), and pitch and yaw are controlled by the aerodynamic stability. The rolling motion 

is controlled with thrusters, although few thruster pulses are required, due to the small roll torque 

and the large thruster deadbands. This strategy maintains vehicle and momentum control with 

minimal propellant usage. This ensures that the thruster pulses are captured by the buffered 

acceleration data to allow accurate orbit determination by the AADS software. 

The algorithms and data flow used for the AADS software are described in detail in Section 7.2.1

of this report. 

Reference 1: C.G. Justus, “A Mars Global Reference Atmospheric Model (MARS-GRAM) for Mission Planning and 

Analysis.” AIAA-1990-4 28th Aerospace Sciences Meeting, Reno, NV. Jan 8-11, 1990. 

Reference 2: H.L. Justh et al., “The Next Generation of Mars-GRAM and Its Role in the Autonomous Aerobraking Development 

Plan.” AAS 11-478, AAS/AIAA Astrodynamics Specialist Conference, Girdwood, AK, 2011. 

Reference 3: B.L. Stevens and F.L. Lewis, Aircraft Control and Simulation, John Wiley and Sons, Inc., Hoboken, New Jersey, 

p100-106, 2003. 

Reference 4: D.J. O’Shaughnessy and R.M. Vaughan, “MESSENGER Spacecraft Pointing Options,” AAS 03-149, AAS/AIAA 

Spaceflight Mechanics Meeting, Ponce, Puerto Rico, Feb, 2003. 
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Appendix J. AA Interface Control Document 

Autonomous Aerobraking Development Software 

Interface Control Document 

Document No.: AA-001

Document Availability Authorization: NF 1676L ID 11031

Date of Issue: 20 October 2010 

Modified: 17 November 2011 

DRAFT
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Interface Control Document 

_________________________________________ ________________ 

Project Manager Date 

_________________________________________ ________________ 

Program Executive Date 
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Table of Contents 

1 Introduction .......................................................................................................... 266

1.1 Purpose ............................................................................................................................ 266

1.2 Background ..................................................................................................................... 266

2 Documents ............................................................................................................ 267

2.1 Applicable Documents .................................................................................................... 267

2.2 Reference Documents ..................................................................................................... 267

3 Interface Design ................................................................................................... 267

3.1 Interface Identification .................................................................................................... 268

3.2 Interface Diagram ........................................................................................................... 268

3.3 Individual Interface Characteristics ................................................................................ 269

3.3.1 AAI_01: Spacecraft to Ephemeris Estimator ........................................................ 269

3.3.2 AAI_02: Spacecraft to Atmosphere Estimator ..................................................... 270

3.3.3 AAI_03: Spacecraft to Thermal Model ................................................................ 270

3.3.4 AAI_04: Spacecraft to Maneuver Estimator ......................................................... 270

3.3.5 AAI_05: Ephemeris Estimator to Atmosphere Estimator .................................... 270

3.3.6 AAI_06: Ephemeris Estimator to Maneuver Estimator ........................................ 270

3.3.7 AAI_07: Atmosphere Estimator to Maneuver Estimator ..................................... 271

3.3.8 AAI_08: Maneuver Estimator and Thermal Model .............................................. 271

3.3.9 AAI_09: Ephemeris Estimator to Spacecraft ........................................................ 271

3.3.10 AAI_010: Maneuver Estimator to Spacecraft..................................................... 271

3.4 Detailed Interface Data Description................................................................................ 271

3.4.1 Spacecraft iLOADS Interface Data Structure Element Descriptions ................... 272

3.4.2 Spacecraft Input Data Structure Element Descriptions ........................................ 277

3.4.3 AADS Internal Data Structure Element Descriptions .......................................... 281

3.4.4 AADS Output Interface Structure Element Descriptions ..................................... 284
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1.0 Introduction 

This document describes the Software Interface assumptions for the AADS. This study is led by

the NESC and is tasked with developing and testing the algorithms necessary to safely perform 

an AB operations mission autonomously on board a spacecraft. 

The AADS is a suite of models and algorithms intended to test the feasibility of an AA system. 

Three separate AADS packages are being developed for this NESC study, one each for Mars, 

Venus, and Titan. AADS for application at Mars and Titan consists of three distinct modules: 

(1) the Ephemeris Estimator, developed by KinetX, which processes spacecraft IMU acceleration 

data to estimate current and future spacecraft states, (2) the Atmosphere Estimator, developed by 

LaRC in conjunction with the National Institute of Aerospace (NIA), which processes spacecraft 

acceleration data along with Ephemeris Estimator state data to estimate the atmosphere’s density 

and scale height, and (3) the Maneuver Estimator, developed by LaRC, which processes data 

from both the Ephemeris and Atmosphere Estimators to determine whether or not a maneuver is 

required to keep the spacecraft within the desired operational corridor. The AADS for Venus 

will also include a fourth module containing temperature models, also developed at LaRC, to 

predict the maximum temperature the spacecraft will encounter during the next atmospheric 

pass. 

The AADS modules are integrated into two separate simulation environments for detailed 

performance analyses. The first is The Program to Optimize Simulated Trajectories (POST2) at 

LaRC [refs. 1, 2]. The second is a high-fidelity, software and hardware-in-the-loop simulation 

(AAHFS) based on the MESSENGER spacecraft testbed, developed at the JHU/APL. 

1.1 Purpose 

The key interfaces between spacecraft (or spacecraft simulator) and the AADS must be defined, 

understood and accepted for the efficient conduct of the development task and for its results to be 

credible. 

The primary purpose of this document is to describe the agreed upon interface definitions 

between not only the spacecraft (or spacecraft simulator) and the AADS, but between the various 

modules internal to AADS. 

1.2 Background 

Several past NASA missions have used the AB technique to reduce the fuel required to deliver a 

spacecraft into a desired orbit around a target planet or Moon with an appreciable atmosphere. 

AB was first demonstrated at Venus with Magellan in 1993 and then was used to achieve the 

science orbit of three Mars spacecraft: MGS in 1997, Mars Odyssey in 2001, and MRO in 2006. 

Instead of using only the propulsion system to decelerate the spacecraft, AB is used after the 

initial orbit insertion to further decelerate the spacecraft using aerodynamic drag. The spacecraft 

traverses the upper atmosphere of the planet or moon multiple times while controlling periapsis 
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altitude using small propulsive maneuvers at apoapsis to hold the spacecraft within a specified 

corridor. This corridor is designed to keep the spacecraft safely within required structural and/or 

thermal design limits until the desired orbit is achieved. 

Although AB itself reduces the propellant required to reach the final orbit, this reduction comes 

at the expense of additional mission time (typically 3–6 months), a large mission operations staff, 

and significant DSN coverage. This combination of critical resources results in an expensive 

operational phase of a mission. Aerobraking missions typically require daily monitoring and 

weekly support to determine the maneuvers required to maintain the spacecraft on the predefined 

mission glideslope. Significant operational cost could be saved by enabling a spacecraft to 

calculate the maneuvers required on-board, based on measurement data collected during each 

atmospheric pass and any executed maneuvers, and execute the same glideslope maintenance 

maneuvers autonomously. This capability would be enabling for some orbiter missions, where 

due to the environment and its impact on the required maneuver frequency, or simply due to 

light-time delay, successful AB mission operations from the ground alone would not be possible. 

2 Documents 

2.1 Applicable Documents 

2.2 Reference Documents 

1. Autonomous Aerobraking Planetary Constants and Models Document 

2. Detailed Documentation of the Ephemeris Estimator (users guide) 

3. Detailed Documentation of the Atmosphere Estimator 

4. Detailed Documentation of the Maneuver Estimator 

5. Detailed Documentation of the Thermal Response Surface Model 

6. Detailed Documentation of the APL High Fidelity Simulation 

7. Detailed Documentation of the assumed spacecraft sensor, actuator, etc., models 

3 Interface Design 

Only the software interfaces between the spacecraft (or spacecraft simulator) and the AADS, as 

well as those between the individual AADS modules, are included within the scope of this 

document. For a more detailed description of the AADS and its individual modules, as well as 

other simulation and environment models, see the references provided in Section 2.2. 
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3.1 Interface Identification 

This document outlines the interface between the instruments, models and simulations. The 

interfaces are provided unique identifiers for use throughout the document (i.e., AAI## - 

Autonomous Aerobraking Interface ##). The cases are ordered in the general direction of data 

flow.

a. AAI_01 - Spacecraft to Ephemeris Estimator 

b. AAI_02 - Spacecraft to Atmosphere Estimator 

c. AAI_03 - Spacecraft to Thermal Model 

d. AAI_04 - Spacecraft to Maneuver Estimator 

e. AAI_05 - Ephemeris Estimator to Atmosphere Estimator 

f. AAI_06 - Ephemeris Estimator to Maneuver Estimator 

g. AAI_07 - Atmosphere Estimator to Maneuver Estimator 

h. AAI_08 - Maneuver Estimator and Thermal Model 

i. AAI_09 - Ephemeris Estimator to Spacecraft 

j. AAI_10 - Maneuver Estimator to Spacecraft 

Each of these interfaces will be described in detail in Section 3.3. It is important to note that 

some inputs/parameters may appear in more than one interface. 

3.2 Interface Diagram 

The spacecraft interfaces to the AADS flight software through the use of data structures, as 

shown in Figure 3.2-1 (in this appendix). The required AADS input data is passed into AADS 

through two data structures. The first input data structure to AADS contains data not likely to 

change between AADS calls, but which may be changed and uploaded to the spacecraft during 

the weekly update cycle (to be referred to as spacecraft iLOADS). The second input structure 

includes parameters and/or data which are likely to change between AADS calls. All outputs 

from AADS to the spacecraft are provided in a single output data structure. In addition to this 

interface with the spacecraft, an additional data structure is created within AADS to pass 

information between the Atmosphere Estimator, Ephemeris Estimator, and the Maneuver 

Estimator. 
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Figure 3.2-1. Spacecraft and AADS Interface Diagram; (1a) Spacecraft Inputs to AADS which will or 

may change each AADS Call, (1b) Spacecraft Inputs to AADS which are not likely to Change during 

the AB Mission, (2) AADS Outputs to the Spacecraft, and (3) Intra-AADS

3.3 Individual Interface Characteristics 

This section describes the data passed through the various interfaces defined in this document. 

More detailed information regarding the individual parameters, data type, size, etc. will be 

provided in Section 3.4 of this appendix. 

3.3.1 AAI_01: Spacecraft to Ephemeris Estimator 

The spacecraft (or spacecraft simulator) provides the Ephemeris Estimator the following data: 

1. Planetary constants 

2. Spacecraft mass and geometry 

3. Integrator settings 
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4. Atmospheric entry/exit specification 

5. Spacecraft state initialization 

6. Planetary ephemerides 

7. Processed spacecraft accelerations 

3.3.2 AAI_02: Spacecraft to Atmosphere Estimator 

The spacecraft (or spacecraft simulator) provides the Atmosphere Estimator the following data: 

1. Planetary constants 

2. Spacecraft mass and geometry 

3. Atmosphere archive index 

4. Coordinate transformation 

5. Processed spacecraft accelerations 

6. Processed spacecraft quaternions 

3.3.3 AAI_03: Spacecraft to Thermal Model 

This interface is not implemented. 

The spacecraft (or spacecraft simulator) provides the Thermal Model the following data: 

1. Thermocouple 

3.3.4 AAI_04: Spacecraft to Maneuver Estimator 

The spacecraft provides the Maneuver Estimator the following: 

1. Corridor type 

2. Corridor limits 

3. Corridor target 

3.3.5 AAI_05: Ephemeris Estimator to Atmosphere Estimator 

The Ephemeris Estimator provides the Atmosphere Estimator estimated data for the following: 

1. Previous periapsis 

2. Spacecraft altitudes during previous atmospheric pass 

3. Spacecraft state estimates during previous atmospheric pass 

4. Next periapsis altitude 

3.3.6 AAI_06: Ephemeris Estimator to Maneuver Estimator 

The Ephemeris Estimator provides the Maneuver Estimator estimated data for the following: 

1. Next apoapsis 

2. Next periapsis 
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3.3.7 AAI_07: Atmosphere Estimator to Maneuver Estimator 

The Atmosphere Estimator provides the Maneuver Estimator estimated data at the next periapsis 

for the following: 

1. Density 

2. Scale height 

3. Variance 

4. Correlation 

3.3.8 AAI_08: Maneuver Estimator and Thermal Model 

The Thermal Model is called as a function from the Maneuver Estimator. Because of this, the 

interface between the two modules is simply through a standard function argument list. 

Although not included in the data structures previously described, the data exchanged between 

the Maneuver Estimator and the Thermal model includes the estimated: 

1. Density (input) 

2. Atmospheric pass duration (input) 

3. Periapsis speed (input) 

4. Orbit period (input) 

5. Max spacecraft (solar panel) temperature (output) 

The Thermal Model can be used to output the estimated density for a desired spacecraft 

temperature. In this mode, all other inputs are unchanged. 

3.3.9 AAI_09: Ephemeris Estimator to Spacecraft 

The Ephemeris Estimator provides the spacecraft the following estimated data: 

1. Atmospheric entry 

2. Atmospheric exit 

3.3.10 AAI_010: Maneuver Estimator to Spacecraft 

The Maneuver Estimator provides the spacecraft the following estimated data: 

1. Maneuver (magnitude and direction) 

2. Maneuver epoch 

3.4 Detailed Interface Data Description 

This section provides more detailed descriptions of the data parameters which reside within the 

spacecraft (or spacecraft simulator) to AADS interfaces, as well as intra-AADS interface. The 

names provided here are the same as used in the software header files to define the interface data 

structures. 
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3.4.1 Spacecraft iLOADS Interface Data Structure Element Descriptions 

ee_sun_mu gravitational constant for the Sun 

Interface Identification AAI_01

Type double

Dimension [1]

Units km3/s2

ee_saturn_mu gravitational constant for Saturn 

Interface Identification AAI_01

used for application at Titan only

Type double

Dimension [1]

Units km3/s2

cb_mu gravitational constant for the central body 

Interface Identification AAI_01, AAI_02

Type double

Dimension [1]

Units km3/s2

ee_ae_pole_ra right ascension of central body rotational pole 

Interface Identification AAI_01, AAI_02

Type double

Dimension [1]

Units deg
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ee_ae_pole_dec declination of central body rotational pole 

Interface Identification AAI_01, AAI_02

Type double

Dimension [1]

Units deg

ee_IAU_pm prime meridian with respect to central body IAU vector at epoch 

Interface Identification AAI_01

Type double

Dimension [1]

Units deg

ee_ae_omega central body rotation rate 

Interface Identification AAI_01, AAI_02

Type double

Dimension [1]

Units deg/day

ee_ae_re central body equatorial radius 

Interface Identification AAI_01, AAI_02

Type double

Dimension [1]

Units km

ee_ae_rp central body polar radius 

Interface Identification AAI_01, AAI_02

Type double

Dimension [1]

Units km

ee_oblate_radius central body oblateness radius 

(used in gravity field calculations) 

Interface Identification AAI_01

Type double

Dimension [1]

Units km
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ee_alt_atm altitude at which atmospheric interface is assumed to occur 

Interface Identification AAI_01

Type double

Dimension [1]

Units km

ee_deltat_atm time offset from atmospheric interface to specify atmospheric entry 

and exit 

Interface Identification AAI_01

Type double

Dimension [1]

Units sec

ee_stepsize variable stepsize integrator stepsize initial guess 

Interface Identification AAI_01

Type double

Dimension [1]

Units sec

Allowable values unconstrained; ignored if/when using fixed stepsize

ee_relative_error variable stepsize integrator relative error constraint 

Interface Identification AAI_01

Type double

Dimension [1]

Units n/a

Allowable values unconstrained; ignored if/when using fixed stepsize

ee_absolute_error variable stepsize integrator absolute error constraint 

Interface Identification AAI_01

Type double

Dimension [1]

Units n/a

Allowable values unconstrained; ignored if/when using fixed stepsize
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ee_mnvr_step fixed stepsize to use while integrating through maneuver 

acceleration data 

Interface Identification AAI_01

Type double

Dimension [1]

Units sec

Allowable values unconstrained; variable stepsize used if = 0

ee_atmos_step fixed stepsize to use while integrating through atmospheric pass 

acceleration data 

Interface Identification AAI_01

Type double

Dimension [1]

Units sec

Allowable values unconstrained; variable stepsize used if = 0

ae_start_orbit orbit number at the start of AADS AB;

sets index within the atmosphere archive to begin data retrieval and 

write output 

Interface Identification AAI_02

Type integer

Dimension [1]

Units n/a

ae_first_orbit_data first orbit index within the atmosphere archive which contains data 

acceptable for use by the Atmosphere Estimator 

Interface Identification AAI_02

Type integer

Dimension [1]

Units n/a

sc_area spacecraft aerodynamic / wetted reference area 

Interface Identification AAI_01, AAI_02

Type double

Dimension [1]

Units m

2
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sc_mass spacecraft mass 

Interface Identification AAI_01, AAI_02

Type double

Dimension [1]

Units km

ae_phib2a spacecraft body to aerodynamic Direction Cosine Matrix

Interface Identification AAI_02

Type double

Dimension [9]

vector is created by appending rows from matrix:

[(1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (3,1) (3,2) (3,3)]

Units n/a

me_corr_type operational corridor type 

Interface Identification AAI_04

Type integer

Dimension [1]

Units n/a

Allowable values 1 = temperature

2 = density

3 = heatrate

4 = dynamic pressure

5 = altitude

me_corr_up operational corridor upper limit 

Interface Identification AAI_04

Type double

Dimension [1]

Units if:

me_corr_type = 1, deg C

me_corr_type = 2, kg/m3

me_corr_type = 3, W/cm2

me_corr_type = 4, Pa

me_corr_type = 5, m
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me_corr_low operational corridor lower limit 

Interface Identification AAI_04

Type double

Dimension [1]

Units if:

me_corr_type = 1, deg C

me_corr_type = 2, kg/m3

me_corr_type = 3, W/cm2

me_corr_type = 4, Pa

me_corr_type = 5, m

me_targ_fac operational corridor target 

(expressed and a percentage of the total corridor width)

Interface Identification AAI_04

Type double

Dimension [1]

Units n/a

3.4.2 Spacecraft Input Data Structure Element Descriptions 

sc2ee_init_flag flag which indicates whether a new state is available for reinitialization of the AADS integrator 

Interface Identification AAI_01

Type integer

Dimension [1]

Units none

Allowable values 0 = no update available

!0 = update available

sc2ee_et_init epoch associated with new AADS integrator initialization state

Interface Identification AAI_01

Type double

Dimension [1]

Units sec (past J2000)

Allowable values unconstrained; ignored if sc2ee_init_flag = 0
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sc2ee_init_state AADS integration initialization state

Interface Identification AAI_01

Type double

Dimension [6]

Element order position = [1-3] 

velocity = [4-6]

Units position, km

velocity, km/s

Coordinate system central body, EME2000

Allowable values unconstrained; ignored if sc2ee_init_flag = 0

sc2ee_sun Sun ephemeris / Chebyshev coefficients 

Interface Identification AAI_01

Type double

Dimension [4+NRECS*(NR+1)], where

NRECS = 20

NR = 35

(sized to accommodate maximum required)

Units n/a

sc2ee_n_sun number of (usable) elements in sc2ee_sun

Interface Identification AAI_01

Type integer

Dimension [1]

Units n/a

sc2ee_bary system barycenter ephemeris / Chebyshev coefficients 

Interface Identification AAI_01

Type double

Dimension [4+NRECS*(NR+1)], where

NRECS = 20

NR = 32 for application at Venus

NR = 35 for application at Mars

NR = 23 for application at Titan

(sized to accommodate maximum required)

Units n/a
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sc2ee_n_bary number of (usable) elements in sc2ee_bary

Interface Identification AAI_01

Type integer

Dimension [1]

Units n/a

sc2ee_plan third body planetary ephemeris / Chebyshev coefficients 

Interface Identification AAI_01 - used for application at Titan only

Type double

Dimension [4+NRECS*(NR+1)], where

NRECS = 20

NR = 68

(sized to accommodate maximum possible)

Units n/a

sc2ee_n_plan number of (usable) elements in sc2ee_plan

Interface Identification AAI_01 - used for application at Titan only

Type integer

Dimension [1]

Units n/a

sc2ee_sat satellite ephemeris / Chebyshev coefficients 

Interface Identification AAI_01 - used for application at Titan only

Type double

Dimension [4+NRECS*(NR+1)], where

NRECS = 20

NR = 80

(sized to accommodate maximum possible)

Units n/a

sc2ee_n_sat number of (usable) elements in sc2ee_sat

Interface Identification AAI_01 - used for application at Titan only

Type integer

Dimension [1]

Units n/a
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sc2ee_accel spacecraft acceleration vector

Interface Identification AAI_01

Type double

Dimension POST2 = [MAX_ACC][3]

HFS = [3*MAX_ACC]

where MAX_ACC is sized to accommodate maximum duration 

drag pass with data provided at 10 Hz

Units m/s3

Coordinate system central body EME2000

sc2ee_et_accel spacecraft acceleration vector time tag

Interface Identification AAI_01

Type double

Dimension [MAX_ACC]

where MAX_ACC is sized to accommodate maximum duration 

drag pass with data provided at 10 Hz

Units sec (past J2000)

sc2ee_n_data number of (usable) acceleration data elements in sc2ee_et_accel 

and sc2ee_ee_accel

Interface Identification AAI_01

Type integer

Dimension [1]

Units n/a

sc2ae_accel spacecraft acceleration vector array 

Interface Identification AAI_02

Type double

Dimension POST2 = [MAX_STT][3]

HFS = [3*MAX_STT]

where MAX_STT is sized to accommodate maximum duration 

drag pass with data provided at 1 Hz

Units m/s3

Coordinate system central body EME2000
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sc2ae_quats central body EME2000 to spacecraft body frame quaternion

Interface Identification AAI_02

Type double

Dimension POST2 = [MAX_STT][4]

HFS = [4*MAX_STT]

where MAX_STT is sized to accommodate maximum duration 

drag pass with data provided at 1 Hz

Units n/a, scalar last

sc2ae_et_atm_pass epoch corresponding to start of sc2ae_accel and sc2ae_quats

Interface Identification AAI_02

Type double

Dimension [1]

Units sec (past J2000)

sc2ae_num_pts number of (usable) data elements in sc2ae_accel and sc2ae_quats

Interface Identification AAI_02

Type integer

Dimension [1]

Units n/a

3.4.3 AADS Internal Data Structure Element Descriptions 

ee2me_et_apo estimated time of next apoapsis

Interface Identification AAI_06

Type double

Dimension [1]

Units sec (past J2000)

ee2me_apo_state estimated next apoapsis state

Interface Identification AAI_06

Type double

Dimension [6]

Element order position = [1-3] 

velocity = [4-6]

Units position, km

velocity, km/s

Coordinate system central body, EME2000
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NESC Request No.: 09-00605 (Phase 1)

ee2me_et_peri estimated time of next periapsis

Interface Identification AAI_06

Type double

Dimension [1]

Units sec (past J2000)

ee2me_peri_state estimated next periapsis state

Interface Identification AAI_06

Type double

Dimension [6]

Element order position = [1-3] 

velocity = [4-6]

Units position, km

velocity, km/s

Coordinate system central body, EME2000

ee2me_peri_rstate estimated next periapsis state

Interface Identification AAI_06

Type double

Dimension [6]

Element order position = [1-3] 

velocity = [4-6]

Units position, km

velocity, km/s

Coordinate system central body rotating

ee2ae_alt_peri estimated altitude of next periapsis

Interface Identification AAI_05

Type double

Dimension [1]

Units m

ee2ae_et_peri_prev estimated time of previous periapsis

Interface Identification AAI_05

Type double

Dimension [1]

Units sec (past J2000)
NASA Engineering and Safety Center

Technical Assessment Report

Document #:

NESC-RP09-00605

Version:

1.0

Title:

Autonomous Aerobraking (Phase 1)

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283 of 286

NESC Request No.: 09-00605 (Phase 1)

ee2ae_et_alt_prev estimated altitude of previous periapsis

Interface Identification AAI_05

Type double

Dimension [1]

Units m

ee2ae_alt_atm estimated altitude profile during previous atmospheric pass

Interface Identification AAI_05

Type double

Dimension [MAX_STT], where MAX_STT is sized to accommodate 

maximum duration drag pass with data provided at 1 Hz

Units m

ee2ae_state_atm estimated spacecraft states during previous atmospheric pass

Interface Identification AAI_05

Type double

Dimension [MAX_STT][6], where MAX_STT is sized to accommodate 

maximum duration drag pass with data provided at 1 Hz

Element order position = [1-3] 

velocity = [4-6]

Units position, km

velocity, km/s

Coordinate system central body, EME2000

ee2ae_num_pts number of (usable) data elements in ee2ae_alt_atm and 

ee2ae_state_atm arrays

Interface Identification AAI_05

Type integer

Dimension [1]

Units n/a

ae2me_rho_plus estimated atmospheric density at next periapsis

Interface Identification AAI_07

Type double

Dimension [1]

Units kg/m3
NASA Engineering and Safety Center

Technical Assessment Report

Document #:

NESC-RP09-00605

Version:

1.0

Title:

Autonomous Aerobraking (Phase 1)

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284 of 286

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ae2me_hs_plus estimated atmospheric scale height at next periapsis

Interface Identification AAI_07

Type double

Dimension [1]

Units m

ae2me_sigma_rho_plus estimated 1 variance in ae2me_rho_plus

Interface Identification AAI_07

Type double

Dimension [1]

Units kg/m3

ae2me_sigma_hs_plus estimated 1 variance in ae2me_hs_plus

Interface Identification AAI_07

Type double

Dimension [1]

Units m

ae2me_corr_rho_hs_plus correlation between ae2me_rho_plus and ae2me_hs_plus

Interface Identification AAI_07

Type double

Dimension [1]

Units n/a

3.4.4 AADS Output Interface Structure Element Descriptions 

ee2sc_et_entry estimated epoch of next atmospheric entry

Interface Identification AAI_09

Type double

Dimension [1]

Units sec (past J2000)
NASA Engineering and Safety Center

Technical Assessment Report

Document #:

NESC-RP09-00605

Version:

1.0

Title:

Autonomous Aerobraking (Phase 1)

Page #:

285 of 286

NESC Request No.: 09-00605 (Phase 1)

ee2sc_entry_state estimated spacecraft state at next atmospheric entry

Interface Identification AAI_09

Type double

Dimension [6]

Element order position = [1-3] 

velocity = [4-6]

Units position, km

velocity, km/s

Coordinate system central body, EME2000

ee2sc_et_exit estimated epoch of next atmospheric exit

Interface Identification AAI_09

Type double

Dimension [1]

Units sec (past J2000)

ee2sc_exit_state estimated spacecraft state at next atmospheric exit

Interface Identification AAI_09

Type double

Dimension [6]

Element order position = [1-3] 

velocity = [4-6]

Units position, km

velocity, km/s

Coordinate system central body, EME2000

me2sc_et_burn epoch of next corridor control maneuver

Interface Identification AAI_10

Type double

Dimension [1]

Units sec (past J2000)

me2sc_dv_to_burn delta-v required for next corridor control maneuver

Interface Identification AAI_10

Type double

Dimension [1]

Units m/s
NASA Engineering and Safety Center

Technical Assessment Report

Document #:

NESC-RP09-00605

Version:

1.0

Title:

Autonomous Aerobraking (Phase 1)

Page #:

286 of 286

NESC Request No.: 09-00605 (Phase 1)

me2sc_dvi_vec direction / unit vector of next corridor control maneuver

Interface Identification AAI_10

Type double

Dimension [3]

Units n/a

Coordinate system central body EME2000

4 References 

1. S.A. Striepe et al., “Program To Optimize Simulated Trajectories (POST II): Volume 2, 

Utilization Manual.” Martin Marietta Corporation, 2004. 

2. G.L. Brauer et al., “Program To Optimize Simulated Trajectories (POST): Volume 1, 

Formulation Manual.” Martin Marietta Corporation, 1990.

 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Development of Autonomous Aerobraking (Phase 1)

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Murri, Daniel G.; Powell, Richard W.; Prince, Jill L.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-20114 NESC-RP-09-00605

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 20 Spacecraft Propulsion and Power

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

The NASA Engineering and Safety Center received a request from Mr. Daniel Murri (NASA Technical Fellow for Flight 

Mechanics) to develop an autonomous aerobraking capability. An initial evaluation for all phases of this assessment was 

approved to proceed at the NESC Review Board meeting. The purpose of phase 1 of this study was to provide an assessment 

of the feasibility of autonomous aerobraking. During this phase, atmospheric, aerodynamic, and thermal models for a 

representative spacecraft were developed for both the onboard algorithm known as Autonomous Aerobraking Development 

Software, and a ground-based "truth" simulation developed for testing purposes. The results of the phase 1 assessment are 

included in this report.

15. SUBJECT TERMS

autonomous aerobraking; Autonomous Aerobraking Development Software; NASA Engineering ans Safety Center; Deep 

Space Network

18. NUMBER

 OF 

 PAGES

291

19b. TELEPHONE NUMBER (Include area code)

(443) 757-5802

a. REPORT

U

c. THIS PAGE

U

b. ABSTRACT

U

17. LIMITATION OF 

 ABSTRACT

UU

Prescribed by ANSI Std. Z39.18

Standard Form 298 (Rev. 8-98)

3. DATES COVERED (From - To)

February 2010 - November 2011

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

869021.05.07.01.14

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

NASA/TM-2012-217328

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1. REPORT DATE (DD-MM-YYYY)

01- 01 - 2012