|
Size: 1592
Comment:
|
Size: 1707
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 8: | Line 8: |
| || $ a_0 $ || semimajor axis || | || $ a $ || semimajor axis || |
| Line 12: | Line 12: |
| || $ J_2 $ || zonal ablateness factor || | || $ J_2 $ || zonal ablateness factor, 1.08262668e-3 for Earth || |
| Line 27: | Line 27: |
| ---- |
|
| Line 29: | Line 31: |
| An 8 degree inclined orbit, $ r_p $ = 8378 km, $ r_a $ = 76000 km. So, $ a $ = 42164 km, e = 0.80189 |
Apsidal Precession
The Earth's equatorial bulge causes orbits to drift, with westward orbit perigee and apogee drifting westward. From AE Roy Orbital Motion 1978:
\Omega |
longitude of the ascending node |
a |
semimajor axis |
e |
eccentricity |
i |
inclination |
\mu |
standard gravitational parameter, 398600.4418 km³/s² for Earth |
J_2 |
zonal ablateness factor, 1.08262668e-3 for Earth |
p |
p ~=~ a ( 1 - e^2 ) = r_p r_a / a |
n_0 |
unperturbed mean motion |
\bar{n} |
perturbed mean motion |
R |
Earth Equatorial Radius = 6378.137 km |
{n_0}^2 ~=~ \mu / {a_0}^3 . . . unperturbed mean motion
\bar{n} ~=~ n_0 \left[ 1 + { \large { { 3 ~ J_2 R^2 } \over { 2 ~~~ p^2 ~ } } } \left( 1 - {\large { 3 \over 2 } } \sin( i )^2 \right) (1-e^2)^{1/2} \right]
{ \Large { { \partial \Omega } \over { \partial t } } } ~=~ -{ \large { { 3 ~ J_2 R^2 } \over { 2 ~~~ p^2 ~ } } } ~ \bar{n} ~ \cos( i )
Roy writes about \omega as if it is the angle from the orbiting body perpendicular the equatorial plane ... or something. Confusing.
An example
An 8 degree inclined orbit, r_p = 8378 km, r_a = 76000 km.
So, a = 42164 km, e = 0.80189