Some orbit elements do not remain the same after the Epoch time (t0) has passed. All satellite orbits precess in a periodic fashion.
Specifically, R.A. of Ascending Node and the Argument of Perigee will precess because of the spheroid shape of the Earth. This step is more commonly known as "J2 propagation". These two orbit elements can vary quickly over the course of a few hours. Since our chosen propagation time is over 24 hours, correcting for these critical precession terms is essential.
First, several specific constants have to be determined:
Let RE = 1 Earth Radius; RE = 1.0 Earth Radii
Let a1 = a / (km/Earth Radii); a1 = 7791.787473 km / (6378.135 km/Earth Radius) = 1.221640413 Earth Radii
Let J2 = 1.0826267 x 10-3 (This is the second gravitational zonal harmonic of the Earth: i.e. J2 Propagation)
Let d1 = [ 3J2RE2 (3cos2i - 1) ] / [ 4a12 (1-e2)3/2 ]: d1 = 7.468325145 x 10-5
Let a0 = -a1 [ 134d13/81 + d12 + d1/3 - 1 ]; a0 = 1.221609994 Earth Radii
Let p0 = a0 (1-e2); p0 = 1.221609967 Earth Radii
The precession of the R.A. of Ascending Node will have the following form:
DaW = 360o [ -3J2RE2nDtcosi / 2po2 ]
aW(t) = aW + DaW
aW(t) = 251o.0219 + (-5o.381875553) = 245o.6400244
The precession of the Argument of Perigee will have the following form:
Dw = 360o [ 3J2RE2nDt (5cos2i - 1) / 4po2 ]
w(t) = w + Dw
w(t) = 33o.8641 + 3o.913574162 = 37o.77767416
The precession formulae for this
section was taken directly from "The SGP Model" section of the
NORAD SpaceTrack Report No. 3
technical paper. Many thanks to Felix R. Hoots, Ronald L. Roehrich and T.S.
Kelso who wrote and compiled this wealth of information that made this
Orbit Precession section possible.
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Step 7: Orbit Precession Was Last Modified On November 11, 2013