Basic Orbital Mechanics

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# Basic Orbital Mechanics - PowerPoint PPT Presentation

Basic Orbital Mechanics. Dr. Andrew Ketsdever MAE 5595. Conic Sections. Elliptical Orbit Geometry. Conic Sections. Classical Orbital Elements. Semi-Major Axis, a Size Eccentricity, e Shape. Kepler’s 3 rd Law. Classical Orbital Elements. Inclination Tilt. Classical Orbital Elements.

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### Basic Orbital Mechanics

Dr. Andrew Ketsdever

MAE 5595

Classical Orbital Elements
• Semi-Major Axis, a
• Size
• Eccentricity, e
• Shape

Kepler’s 3rd Law

Classical Orbital Elements
• Right Ascension of the Ascending Node (RAAN)
Classical Orbital Elements
• Argument of Perigee
Computing COEs
• From a R and V vector
• Can compute the 6 COEs
• Also works in reverse (given COEs compute R and V)
• Example:
COEs
• a = 7965.1 km
• e = 0.0584
• i = 90º
•  = 270º
•  = 90º
•  = 0º
• Mission: Probably remote sensing or a spy satellite because it’s in a low, polar orbit.

Ground Tracks

Ground Track Slides Courtesy of Major David French

ΔN

15º / hr

P =

COE Determination

ΔN

Δ longitude

Semimajor axis

COE Determination

Eccentricity

i = highest latitude

COE Determination

Inclination

ω = 90º

COE Determination

Argument of Perigee

COE Determination

True Anomaly

Geosynchronous

e = 0

e = 0.4

w = 180°

e = 0

i = 0°

e = 0.6

w = 90°

Orbit Prediction
• Kepler’s Problem
• If we know where a satellite (or planet) is today, where in its orbit will it be tomorrow?
• Kepler devised a series of mathematical expressions to solve this particular problem
• Eccentric Anomaly
• Mean Anomaly
• True Anomaly
Orbit Prediction
• Kepler defined the Eccentric Anomaly to relate elliptical motion to circular motion
• He also defined Mean Anomaly to make the circular motion constant
Orbital Prediction
• Given

a = 7000 km

e = 0.05

• = 270º

Find the time of flight to final = 50º

Orbital Prediction