|
⇤ ← Revision 1 as of 2018-04-03 21:36:40
Size: 1428
Comment:
|
Size: 1592
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 24: | Line 24: |
Roy writes about $\omega$ as if it is the angle from the orbiting body perpendicular the equatorial plane ... or something. Confusing. === An example === |
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_0 |
semimajor axis |
e |
eccentricity |
i |
inclination |
\mu |
standard gravitational parameter, 398600.4418 km³/s² for Earth |
J_2 |
zonal ablateness factor |
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.