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Two calculate the actual mean motion of the satellite measured in revolutions per day, three values are required. The first two values, the Mean Motion at Epoch nE and the First Derivative of the Mean Motion
MMdot, are given by the Two Line Elements, while the last value is the Time Since Epoch tsE.
nrev = nE + 2MMdottsE
This current Mean Motion nrev is calculated to take the drag on the satellite into account.
Mean Anomaly (Mt):
The next step is to determine the current Mean Anomaly Mt of the
satellites orbital position in degrees. The Mean Anomaly is calculated by using the time since
epoch tsE, the mean anomaly at epoch ME and the mean
motion nrev at Epoch, both given by the Two Line Elements:
Mt = ME + 360nrevtsE
Semi Major Axis (Akm):
The Semi Major Axis Akm, representing the largest radius of an eccentric
orbit (in km) as shown earlier, is given by the following equation:
Akm = 331.25e[(2/3)log(1440/nrev)]
Argument of Perigee (ω) and Right Ascension of Ascending Node (RAAN, Ω):
The Argument of Perigee ω and the Right Ascension of the
Ascending Node RAAN are both wandering with a constant speed
relative to the ECI coordinate frame. To compensate for this effect in the orbit
model, the daily change is determined as ωdot and
RAANdot (Both in degrees) in the following two equations. The
parameters used here are the orbital Inclination Inc, the orbital
Eccentricity ecc (Both found in the Two Line Elements), the Semi Major Axis of the orbit Akm and the
Earth's Equatorial Radius rEarthEq, which is equal to 6378.140km.
ωdot = [4.98204(rEarthEq/Akm)3.5 (5cos(Inc)2 - 1)]/[(1-ecc2)2]
RAANdot = [9.9641(rEarthEq/Akm)3.5 cos(Inc)]/[(1-ecc2)2]
Accordingly the Argument of Perigee ω and
Right Ascension of the Ascending Node RAAN are calculated in the following two equations by updating
the Argument of Perigee and Right Ascension of the Ascending Node given in the Two Line Elements
(ωTLE and RAANTLE).
ω = ωTLE + ωdottsE
RAAN = RAANTLE - RAANdottsE

