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Basic Orbital Mechanics

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

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  1. Basic Orbital Mechanics Dr. Andrew Ketsdever MAE 5595

  2. Conic Sections

  3. Elliptical Orbit Geometry

  4. Conic Sections

  5. Classical Orbital Elements • Semi-Major Axis, a • Size • Eccentricity, e • Shape Kepler’s 3rd Law

  6. Classical Orbital Elements • Inclination • Tilt

  7. Classical Orbital Elements • Right Ascension of the Ascending Node (RAAN)

  8. Classical Orbital Elements • Argument of Perigee

  9. Classical Orbital Elements • True Anomaly

  10. Computing COEs • From a R and V vector • Can compute the 6 COEs • Also works in reverse (given COEs compute R and V) • Example:

  11. 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.

  12. Ground Tracks Ground Track Slides Courtesy of Major David French

  13. ΔN 15º / hr P = COE Determination ΔN Δ longitude Semimajor axis

  14. COE Determination Eccentricity

  15. i = highest latitude COE Determination Inclination

  16. ω = 90º COE Determination Argument of Perigee

  17. COE Determination True Anomaly

  18. Orbit Examples

  19. Molniya

  20. Geostationary

  21. Geosynchronous

  22. Geosynchronous e = 0 e = 0.4 w = 180° e = 0 i = 0° e = 0.6 w = 90°

  23. 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

  24. 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…

  25. Orbit Prediction

  26. Orbital Prediction • Given a = 7000 km e = 0.05 • = 270º Find the time of flight to final = 50º

  27. 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

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