Idstein
Flensburg
Wien
North Sea
Offenbach
  • Mean Motion (nrev):
    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)]
    Simulation of a satellite orbit (The red part shows when the satellite is in communication range seen from Denmark)

  • 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