Hello Mariusz,

above all, I assume that you only want to calculate approximate positions. This is because with TLE data you only have a limited resolution of the values. But also, because you mix the underlying orbit propagation model of TLE with that of GPS. This should generally be avoided. TLE can be used with e.g. the SGP4 model. The instructions for orbit propagation of SGP4 can be found on the internet, but it’s a lengthy calculation process.

To your question regarding OMEGA dot. There I see two simple approaches to calculate it. Both are limited in accuracy, but reasonable for your approach:

1. read out the RAAN from two subsequent TLE parameter sets, calculate the difference and divide this by the time difference of the two TLE parameter sets.

2. Assuming that the earth can be approached by a rotation ellipsoid, one can use the following equation (the flattening of the earth at the poles is the main reason for OMEGA dot not being zero)

OMEGA dot = -1.5 * n * J_2 * (R_E / a) ^ 2 * (cos i / (1-e ^ 2) ^ 2)

- n: mean motion -> n = 2 * pi / T, where T = orbit period or n = sqrt (G * M / a ^ 3) with G = Gravitational Constant, M = Earth Mass

- a = semimajor axis

- R_E mean earth radius, e.g.

- J_2 = 0.00108263

- i = inclination

- e = eccentricity

Use SI units, e.g. m, kg, m etc. as well as radians for any angle. The unit of OMEGA dot is radians/second.

Bstar has only indirectly something to do with OMEGAdot. It is a parameter that is related to air resistance and is only used in the SGP4 model. For the accuracy that we achieve here, BStar for Iridium satellites can be neglected.

Hope it helps you.

Best regards,

Maurizio

Dear Dr. Maurizio Scaramuzza

Thank you for the reply. Please excuse me the delay with response. I found your answer very helpful. I'm going to implement your code into my calculation. I will let you know about the result. Best regards, PSD