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Given the orbital parameters of a satellite, how can I predict the ground path of its shadow? (The path from where it will appear to transit the Sun).

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    $\begingroup$ It's going to be a "use specialized software or programming libraries" answer, if you want values with any sort of accuracy. $\endgroup$
    – notovny
    Jul 7, 2023 at 22:15
  • $\begingroup$ That's what I'm looking for. $\endgroup$
    – LostXOR
    Jul 7, 2023 at 23:24
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    $\begingroup$ Horizons can calculate trajectories of satellites from user-supplied TLEs, see ssd.jpl.nasa.gov/horizons/manual.html#tles So if you can code, and you know a little 3D vector geometry, you could write a program for this, with Horizons doing most of the work. I haven't quite done that myself, but the Python code here: space.stackexchange.com/a/61065/38535 finds the ground speed of the ISS. $\endgroup$
    – PM 2Ring
    Jul 8, 2023 at 3:02
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    $\begingroup$ The equations are exactly the same as those for solar eclipses and are covered in a lot of works. All editions of the Explanatory Supplement to the Astronomical Almanac, Chauvenet's Manual of Spherical and Practical Astronomy (vol 1), Meeus' "Transits". And many others. "Besselian Elements" would be a good search term. $\endgroup$ Jul 8, 2023 at 3:17
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    $\begingroup$ I'll add to my previous comment, that all you really need is the equations to compute the central line. I have most of the pieces of the puzzle implemented in javascript at celestialprogramming.com. The only piece missing would be computing the geocentric RA/Dec of the satellite (instead of the moon). $\endgroup$ Jul 8, 2023 at 14:25

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