# Presentation: 371592

## CIVIL AIR PATROL

- Colorado Springs Cadet Squadron
-  Lt Col M. T. McNeely

- ORBITAL MECHANICS !!

-                                                  PRESENTS
-    INTRO TO SPACE COURSE

## Why is this important?

**- Orbital mechanics is the ‘road map’ to putting anything**
**  ****in Space  (there is no Rand-McNally in the stars)**
**- Only way to find objects once they are on orbit**
**  ****(protect the Shuttle from orbiting debris)**
**- Allows the United States to fulfill its Nuclear Risk **
**  ****Reduction Treaty obligations**

## ORBITAL MECHANICSLesson Plan 1 - Part 1

- ORBITAL MECHANICSLesson Plan 1 - Part 1

- Origins
- Physical Laws
- Requirements for Injection
- Classifications of Orbits
- Coordinate Reference Systems
- Orbital Elements

## ORBITAL MECHANICSLesson Plan 1 - Part 2

- ORBITAL MECHANICSLesson Plan 1 - Part 2

- Ground Tracks
- Perturbations
- Launch Considerations
- Orbital Maneuvers
- De-orbit/Decay

## ORBITAL MECHANICSLesson Plan 1 - Part 1

- ORBITAL MECHANICSLesson Plan 1 - Part 1

- Origins
- Physical Laws
- Requirements for Injection
- Classifications of Orbits
- Coordinate Reference Systems
- Orbital Elements

## ORIGINSNicholas Copernicus

- ORIGINSNicholas Copernicus

- Revived Helio-centric model
- Believed planetary orbits were circles

## ORIGINSTycho Brahe

- Introduced precision into astronomical measurements
- Mentor to Johannes Kepler

## ORIGINSJohannes Kepler

- ORIGINSJohannes Kepler

- Derived 3 laws based upon his observations of planetary motion

## ORBITAL MECHANICS

- Origins
- Physical Laws
- Requirements for Injection
- Classifications of Orbits
- Coordinate Reference Systems
- Orbital Elements

## PHYSICAL LAWSKepler’s 1st Law:  Law of Ellipses

- The orbits of the planets are ellipses with the sun at one focus

## PHYSICAL LAWSEllipses

**Period (T)**

**Semi-Major Axis (a)**

**Semi-Minor Axis (b)**

## PHYSICAL LAWS

## PHYSICAL LAWSKepler’s 2nd Law:  Law of Equal Areas

- The line joining the planet to the center of the sun sweeps out equal areas in equal times

## PHYSICAL LAWSKepler’s 2nd Law:  Law of Equal Areas

## PHYSICAL LAWSKepler’s 2nd Law:  Law of Equal Areas

- t1-t0 = t3-t2
- Area 1 = Area 2
- Satellite travels at varying speeds

## PHYSICAL LAWSKepler’s 3rd Law:  Law of Harmonics

- The squares of the periods of two planets’ orbits are proportional to each other as the cubes of their semi-major axes:T12/T22 = a13/a23
- In English:
- Orbits with the same semi-major axis will have the same period

## PHYSICAL LAWSSir Isaac Newton

- PHYSICAL LAWSSir Isaac Newton

- Derived three laws of motion
- Derived the Law of Universal Gravitation
- Explained why Kepler’s laws worked

## PHYSICAL LAWSNewton’s 1st Law:  Law of Inertia

- Every body continues in a state of uniform motion unless it is compelled to change that state by a force imposed upon it

## PHYSICAL LAWSNewton’s 2nd Law:  Law of Momentum

- Change in momentum is proportional to and in the direction of the force applied
- Momentum equals mass x velocity
- Change in momentum gives:  F = ma

## PHYSICAL LAWSNewton’s 3rd Law:  Action - Reaction

- For every action, there is an equal and opposite reaction
- Hints at conservation of momentum

## PHYSICAL LAWSNewton’s Law of Universal Gravitation

- Between any two objects there exists a force of attraction that is proportional to the product of their masses and inversely proportional to the square of the distance between them

## ORBITAL MECHANICS

- Origins
- Physical Laws
- Requirements for Injection
- Classifications of Orbits
- Coordinate Reference Systems
- Orbital Elements

## INJECTION REQUIREMENTSSpeed

## INJECTION REQUIREMENTSSpeed

## INJECTION REQUIREMENTSSpeed

**100 miles**

**17,500 mi/hr**

## INJECTION REQUIREMENTSAltitude

- INJECTION REQUIREMENTSAltitude

- Are you moving FASTER or SLOWER the higher your altitude?

## INJECTION REQUIREMENTSAltitude

**V****C**** = **

**G(m****1****+m****2****)**

**a**

**V****C**** = 5.59 km/s**

**V****C**** = 4.56 km/s**

**2E**

**3E**

## INJECTION REQUIREMENTSAltitude

## INJECTION REQUIREMENTSDirection

## ORBITAL MECHANICS

- Origins
- Physical Laws
- Requirements for Injection
- Classifications of Orbits
- Coordinate Reference Systems
- Orbital Elements

## ORBIT CLASSIFICATION

- Size/Period
- Location
- Shape

## ORBIT CLASSIFICATIONSize/Period

- ORBIT CLASSIFICATIONSize/Period

- Defined by semi-major axis (a)
- Low Earth Orbit (LEO)
- High Earth Orbit (HEO)
- Semi-synchronous Orbit
- Geo-synchronous Orbit

## ORBIT CLASSIFICATIONLocation

- ORBIT CLASSIFICATIONLocation

- Equatorial
- Polar

## ORBIT CLASSIFICATIONShape (Conic Sections)

**Circle**
**Ellipse**

## ORBIT CLASSIFICATIONShape (Conic Sections)

**Trajectories:**
**	****Parabola**
**	****Hyperbola**

## ORBIT CLASSIFICATIONSCircular Orbits

- ORBIT CLASSIFICATIONSCircular Orbits

- Characteristics
- Constant speed
- Nearly constant altitude
- Typical Missions
- Reconnaissance/Weather (DMSP)
- Manned
- Navigational (GPS)
- Geo-synchronous (Comm sats)

## ORBIT CLASSIFICATIONSElliptical Orbits

- ORBIT CLASSIFICATIONSElliptical Orbits

- Characteristics
- Varying speed
- Varying altitude
- Asymmetric Ground Track
- Typical Missions
- Deep space surveillance (Pioneer)
- Communications (Polar comm.)
- Ballistic Missiles

## ORBIT CLASSIFICATIONSParabolic/Hyperbolic Trajectories

- ORBIT CLASSIFICATIONSParabolic/Hyperbolic Trajectories

- Characteristics
- Escaped Earth’s gravitational influence
- Heliocentric
- Typical Missions
- Interplanetary exploration (Galileo, Phobos, Magellan)

## ORBIT CLASSIFICATIONSOrbit Geometry

## ORBIT CLASSIFICATIONSEccentricity

## ORBIT CLASSIFICATIONSEccentricity

## ORBIT CLASSIFICATIONSEccentricity

**Eccentricity = c/a**

## ORBITAL MECHANICS

- Origins
- Physical Laws
- Requirements for Injection
- Classifications of Orbits
- Coordinate Reference Systems
- Orbital Elements

## COORDINATE SYSTEMS

- Defines positions and directions in a consistent manner -- allows communication
- Facilitates the description of a satellite’s position and subsequent motion
- Proper choice of reference determines the utility of a coordinate system

## COORDINATE SYSTEMSOrdinates

- COORDINATE SYSTEMSOrdinates

- Origin
- Where you’re starting from
- Fundamental Plane
- Plane which you’re measuring in
- Principle Direction
- Direction which you’re measuring from

## COORDINATE SYSTEMSClassifications

- COORDINATE SYSTEMSClassifications

- Inertial
- Non-rotating
- Time Independent
- Non-inertial
- Rotating
- Time Dependent

## COORDINATE SYSTEMSExamples

- COORDINATE SYSTEMSExamples

- Geographic
- Topocentric
- Geocentric Inertial
- Orbit Inertial

## COORDINATE SYSTEMSGeographic

- Purpose:  To locate points on the Earth’s surface

## COORDINATE SYSTEMSTopocentric

- Purpose:  To locate a satellite with respect to a specific point on the Earth

## COORDINATE SYSTEMSTopocentric

## COORDINATE SYSTEMSTopocentric

**Origin:  Antenna**
**FP:  Local Horizon**
**PD:  True North**

## COORDINATE SYSTEMSGeocentric Inertial

- Purpose:  To determine the exact orientation of an orbital plane and to locate points in space with respect to the Earth

## COORDINATE SYSTEMSGeocentric Inertial

## COORDINATE SYSTEMSGeocentric Inertial

## COORDINATE SYSTEMSOrbit Inertial

- Purpose:  To fix the satellite orbit in the orbital plane

## COORDINATE SYSTEMSReview

- COORDINATE SYSTEMSReview

- Geographic
- Locates a point on the Earth’s surface
- Requires Latitude and Longitude
- Topocentric
- Locates a satellite with respect to a site
- Requires Azimuth, Elevation, Range

## COORDINATE SYSTEMSReview

- COORDINATE SYSTEMSReview

- Geocentric Inertial
- Locates orbital plane with respect to the Earth
- Requires Right Ascension and Inclination
- Orbit Inertial
- Locate orbit within orbital plane
- Requires Argument of Perigee

## ORBITAL MECHANICS

- Origins
- Physical Laws
- Requirements for Injection
- Classifications of Orbits
- Coordinate Reference Systems
- Orbital Elements

## ORBITAL ELEMENTSDefinition

- ORBITAL ELEMENTSDefinition

- A set of mathematical parameters that enables us to accurately describe satellite motion

## ORBITAL ELEMENTSPurpose

- ORBITAL ELEMENTSPurpose

- Discriminate one satellite from other satellites
- Predict where a satellite will be in the future or has been in the past
- Determine amount and direction of maneuver or perturbation

## ORBITAL ELEMENTSKeplerian Elements

- ORBITAL ELEMENTSKeplerian Elements

- Semi-Major Axis (Size)
- Eccentricity (Shape)
- Inclination
- Right Ascension
- Argument of Perigee
- Epoch Time (Location within orbit)
- True Anomaly

**(Orientation)**

## ORBITAL ELEMENTSKeplerian Elements:  Inclination

## ORBITAL ELEMENTSKeplerian Elements:  Right Ascension

## ORBITAL ELEMENTSKeplerian Elements:  Argument of Perigee

****

**Argument of Perigee (********)**

## ORBITAL ELEMENTSKeplerian Elements:  True Anomaly

## ORBITAL ELEMENTSKeplerian Elements:  True Anomaly

## ORBITAL ELEMENTSKeplerian Elements:  Inclination

## ORBITAL MECHANICSLesson Plan 1 - Part 1   SUMMARY

- ORBITAL MECHANICSLesson Plan 1 - Part 1   SUMMARY

- Origins
- Physical Laws
- Requirements for Injection
- Classifications of Orbits
- Coordinate Reference Systems
- Orbital Elements