Game:

Kerbal Space Program (2015)

Category:

Tutorial

Duration: 19:43

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In this tutorial we cover how to evenly space out satellites for a communications relay network. This is needed for when you want to send unmanned vessels to a planet or moon. We also derive the math behind the method to show how and why this works.

Derivation of sum of internal angles of a polygon by Khan Academy:
https://www.youtube.com/watch?v=qG3HnRccrQU


Here are the relevant equations for this method to evenly space out satellites:

Minimum satellite orbit (circular) for the communications relay network
d ≥ -r [ 1-csc( π/2 (1-2/n)) ]

Drop ship's new apoapsis when deploying satellites:
a = 2/n^(2/3) * (n+1)^(2/3) * (d+r) - (d + 2r)

where
n = number of satellites to be deployed
r = radius of planet or moon where the satellites are to be deployed


*Other useful stuff*:
Below is a google spreadsheet that calculates *d* and *a* for all known planets and moons. Also contains the radius of all known moons and planets.
https://docs.google.com/spreadsheets/d/1iX3v3IY3M8xD8DPYJPzzyojvUuxxGx6BWICcjgfb6LY/edit#gid=0

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