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Celestial Mechanics II

This Lecture. Derivation of Lagrange's Planetary Equations Satellite orbits around the non-spherical Earth. Why is this important?. All orbits are perturbed to some degreeLagrange's Planetary Equations describe effects on orbital elements caused by perturbationsNumerous practical applications,

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Celestial Mechanics II

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    1. Celestial Mechanics II

    2. This Lecture Derivation of Lagrange’s Planetary Equations Satellite orbits around the non-spherical Earth

    3. Why is this important? All orbits are perturbed to some degree Lagrange’s Planetary Equations describe effects on orbital elements caused by perturbations Numerous practical applications, e.g., satellite dynamics

    4. Lagrange’s Planetary Equations

    5. Osculation condition

    6. Osculation condition

    7. Lagrange brackets

    8. Lagrange brackets

    9. Lagrange brackets Total number of permutations: 36 But [a,a]=0 etc ? 30 But [a,e]=-[e,a] etc ? 15

    10. Angular elements (i,?,?)

    11. Geometry & time elements (a,e,?)

    12. Mixed terms

    13. Lagrange’s Planetary Equations

    14. The non-spherical Earth

    15. Second Harmonics J2

    16. Averaging out short-term perturbations

    17. J2 effects on a, e, i

    18. J2 effect on ? Angular momentum vector of orbit precesses about Earth’s rotational axis ISS: a=1.0527 R? e=0.0005 R?=6378 km i=52º J2=1.082·10-3 n= k?a-3/2 =0.0689 rad min-1 ? 5.1º per day

    19. J2 effect on ?

    20. Molniya and Tundra orbits

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