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| Roy writes about $\omega$ as if it is the angle from the orbiting body perpendicular the equatorial plane ... or something. Confusing. ---- |
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| Roy writes about $\omega$ as if it is the angle from the orbiting body perpendicular the equatorial plane ... or something. Confusing. | ---- === Wikipedia === A similar result from Wikipedia's [[https://en.wikipedia.org/wiki/Nodal_precession | Nodal precession ]] page. $ \omega_p ~=~ - { \Large { 3 \over 2 } ~ { { R^2 } \over { a (1-e^2) )^2 } } } ~ J_2 ~ \omega ~ \cos i $ |
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| === An example === | |
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| === An example === |
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| $ \bar{n} ~= n_0 \times 1.000171899 $ which suggests the orbital period is reduced by 0.000171869 × 86164.099 or 14.809 seconds |
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=== Wikipedia === A similar result from Wikipedia's [[https://en.wikipedia.org/wiki/Nodal_precession | Nodal precession ]] page. $ \omega_p ~=~ - { \Large { 3 \over 2 } ~ { { R^2 } \over { a (1-e^2) )^2 } } } ~ J_2 ~ \omega ~ \cos i $ |
Apsidal Precession
The Earth's equatorial bulge causes orbits (perigee and apogee) to drift westward. From AE Roy Orbital Motion 1978:
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longitude of the ascending node |
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semimajor axis |
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eccentricity |
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inclination |
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standard gravitational parameter, 398600.4418 km³/s² for Earth |
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zonal ablateness factor, 1.08262668e-3 for Earth |
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unperturbed mean motion |
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perturbed mean motion |
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Earth Equatorial Radius = 6378.137 km |
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unperturbed orbital period |
Roy writes about 
a03
T2
= n0
1+3 J2R22 p2 
1−23sin(i)2
(1−e2)1
2
n0
t
= −3 J2R22 p2 n cos(i) −23 J2R2a(1−e2)2 T2 cos(i)
Wikipedia
A similar result from Wikipedia's Nodal precession page.
p = −23 R2a(1−e2))2 J2 cosi
An example
An 8 degree inclined orbit,
So,
The apsides will precess by about the same amount per orbit.