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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

Basic Orbital Mechanics

Dr. Andrew Ketsdever

MAE 5595

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

Kepler’s 3rd Law

classical orbital elements2
Classical Orbital Elements
  • Right Ascension of the Ascending Node (RAAN)
classical orbital elements3
Classical Orbital Elements
  • Argument of Perigee
computing coes
Computing COEs
  • From a R and V vector
    • Can compute the 6 COEs
    • Also works in reverse (given COEs compute R and V)
    • Example:
slide11
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.
slide12

Ground Tracks

Ground Track Slides Courtesy of Major David French

slide13

ΔN

15º / hr

P =

COE Determination

ΔN

Δ longitude

Semimajor axis

slide14

COE Determination

Eccentricity

slide15

i = highest latitude

COE Determination

Inclination

slide16

ω = 90º

COE Determination

Argument of Perigee

slide17

COE Determination

True Anomaly

slide22

Geosynchronous

e = 0

e = 0.4

w = 180°

e = 0

i = 0°

e = 0.6

w = 90°

orbit prediction
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 prediction1
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
  • Convert unsteady elliptical motion into unsteady circular motion into steady circular motion…
orbital prediction
Orbital Prediction
  • Given

a = 7000 km

e = 0.05

    • = 270º

Find the time of flight to final = 50º

orbital prediction1
Orbital Prediction
  • n = 0.001078 rad/sec
  • Einitial = 272.87º
  • Efuture = 47.84º
  • Minitial = 275.73º
  • Mfuture = 45.72º
  • TOF = 2104.58 sec or 35.08 min