<p>As Greg suggested in the comments, there was indeed an equation in Vallado's book:</p>
<p><a href="https://i.sstatic.net/dNdRK.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/dNdRK.png" alt="Part 1 of Algorithm 34, from Fundamentals of Astrodynamics and Applications (Vallado 2013)" /></a>
<a href="https://i.sstatic.net/3lS0q.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3lS0q.png" alt="Part 2 of Algorithm 34, from Fundamentals of Astrodynamics and Applications (Vallado 2013)" /></a></p>
<p>See <a href="https://astronomy.stackexchange.com/a/55531/47994">my answer</a> to <a href="https://astronomy.stackexchange.com/q/55519/47994">my own question</a> for information on the Python implementation of it, as well as the assumptions made about the input.</p>

CC BY-SA 4.0
2023-12-15T18:47:05.913Z
2023-12-15T18:47:05.913Z
Michael Bonnet
<p>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 &quot;Is this Earth satellite in eclipse?&quot;, given either position and velocity vectors or a TLE + epoch.</p>
<p><strong>Does there exist an equation for determining if any given Earth satellite is in eclipse, given its position/velocity at epoch?</strong></p>

CC BY-SA 4.0
2023-11-17T22:58:53.990Z
The source code for Vallado's book has the computation.  Of course the equations are in the book, perhaps someone will post them. http://celestrak.org/software/vallado-sw.php
Greg Miller
<the-sun><orbital-mechanics><mathematics><python><artificial-satellite>
Equation for calculating boolean answer to "is this Earth satellite in eclipse"
Michael Bonnet
# Equation for calculating boolean answer to "is this Earth satellite in eclipse"

(Asked by: username_0 on 2023-11-17)

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?**

**Tags:** the-sun, orbital-mechanics, mathematics, python, artificial-satellite
> **Comments:**
> **username_1**: The source code for Vallado's book has the computation.  Of course the equations are in the book, perhaps someone will post them. http://celestrak.org/software/vallado-sw.php  

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## 1 answers

### Answer by username_0 on 2023-12-15. Score: 3 | Accepted answer

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)](https://i.sstatic.net/dNdRK.png)](https://i.sstatic.net/dNdRK.png)
[![Part 2 of Algorithm 34, from Fundamentals of Astrodynamics and Applications (Vallado 2013)](https://i.sstatic.net/3lS0q.png)](https://i.sstatic.net/3lS0q.png)

See [my answer](https://astronomy.stackexchange.com/a/55531/47994) to [my own question](https://astronomy.stackexchange.com/q/55519/47994) for information on the Python implementation of it, as well as the assumptions made about the input.


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