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I'm trying to plot ground tracks with the help of TLE data. However, there are some equations that contain "times", and I can't understand which time I should use and format. Like for example, TLE Epoch: 23270.52090061 How to use it? Should I only take .52090061 in consideration and convert it into seconds?

The equations are

$$1. \ \ M - M_0 = n\cdot(t - t_0) $$ and

$$2. \ \ Prime \ \ meridian \ \ Greenwich: \theta = \omega_E \cdot (t - t_0)$$

I wrote a code using TLE Data to transform ECI into ECEF. I calculated the vector $r_X$ and now I made a transformation Matrix like:

'''

def R_3 (prime_meridian): r_3 = np.array([[np.cos(prime_meridian), np.sin(prime_meridian), 0], [-np.sin(prime_meridian), np.cos(prime_meridian), 0], [ 0, 0 , 1]]) return r_3 prime_meridian = w_sid*( t - t_0) R_m = R_3(prime_meridian)

'''

after that, I would like to make the rotation.

$$ r_x' = [R_3(\theta)]\cdot r_X $$

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The TLE epoch is the $t_0$ value you use with the rest of the elements in that TLE. To calculate observables at any other time, you use the TLE, and the amount of time between the epoch and the one you want to know about, as inputs to the SGP4 processor. Do not try to do this by hand, since the numbers in a TLE are mean elements, not osculating ones, so they do not mean what you think they ought to mean.

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    $\begingroup$ +1 for "Do not try to do this by hand". As someone who has attempted it, down that path lies madness. $\endgroup$ Commented Sep 29, 2023 at 19:06

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