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I have found plenty of math for determining duration of satellite eclipse, but I am having trouble finding an equation that produces a simple boolean answer to the question "Is this Earth satellite in eclipse?", given either position and velocity vectors or a TLE + epoch.

Does there exist an equation for determining if any given Earth satellite is in eclipse, given its position/velocity at epoch?

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    $\begingroup$ The source code for Vallado's book has the computation. Of course the equations are in the book, perhaps someone will post them. celestrak.org/software/vallado-sw.php $\endgroup$
    – Greg Miller
    Commented Nov 17, 2023 at 22:58

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As Greg suggested in the comments, there was indeed an equation in Vallado's book:

Part 1 of Algorithm 34, from Fundamentals of Astrodynamics and Applications (Vallado 2013) Part 2 of Algorithm 34, from Fundamentals of Astrodynamics and Applications (Vallado 2013)

See my answer to my own question for information on the Python implementation of it, as well as the assumptions made about the input.

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