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 R_E = 1 Earth Radius; R_E = 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 = [ 3J₂R_E² (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:

Da_W = 360^o [ -3J₂R_E²nDtcosi / 2p_o² ]

a_W(t) = a_W + Da_W

a_W(t) = 251^o.0219 + (-5^o.381875553) = 245^o.6400244

The precession of the Argument of Perigee will have the following form:

Dw = 360^o [ 3J₂R_E²nDt (5cos²i - 1) / 4p_o² ]

w(t) = w + Dw

w(t) = 33^o.8641 + 3^o.913574162 = 37^o.77767416

Special Note: 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.
 

PROCEED TO STEP #8