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Understanding Earth's Rotational Dynamics in Orbital Mechanics

Exploring concepts like inertial and moving frames, equatorial plane, nodes, apse lines, perigee, and orbits in celestial mechanics. Learn about Earth's rotation axis and orbital paths for spacecraft.

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Understanding Earth's Rotational Dynamics in Orbital Mechanics

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  1. V V a a P P C C r r Z Z r r s s O O Y Y o o X X ut un

  2. m m m Fg Fg Fg Fg Fg Fg M M M r r r

  3. V Fnet P Fg m Z Z r r m O O Y Y X X

  4. V Fnet Fg P m Z Z r r O O m Y Y X X

  5. V Fnet P m Z r O Y X r Z Z’ Moving frame O O ’ Y Y’ X X’ Inertial frame

  6. Fg m r m M M rm rM Z Z Z’ Z’ O O Y Y Y’ Y’ X X X’ X’

  7. rrel r o ro O Q P Z Z k Moving frame Moving frame j z y X X i Y Y Inertial frame Inertial frame x

  8. Earth axis of rotation z’ P rrel Z z Greenish meridian y o y’ x Y  Equator X θg Λ x’

  9. R1 Z O Y X m1 m1 m1 G F12 r r F21 RG m2 m2 m2 R2 v v vr m2 r m2 r  m1 e m1

  10. B rB b  r O f r+dr vr v v  = /2  Apse line f f ra rp

  11. S/C Perigee  f

  12. Line of nodes Perigee f  Ellipse focus Periapsis P f Latus rectum

  13. Earth’s north polar axis e Z S/C Perigee i  v h r  Earth’s equatorial plane Y Ascending node X   Node line

  14. v Semilatus rectum  v vr r Periapse f

  15. Asymptote Asymptote Vacant orbit  M  b    Apse line P F C A F’ Empty focus rp a a |ra| II I

  16. 1 b O f 2 ae a

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