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1. ## Deep Space Relay Networks

This tutorial, Setting Up A Commnet System, suggests placing 6 satellites into a 4Gm Kerbolar orbit, 12 into 25Gm and, optionally, 24 into a 50Gm orbit. To do this in a finite amount of time requires launching them all individually at specific time intervals. I've calculated the following: To launch 6 Comm Sats to a 4Gm orbit, launch each with 13.48 day separation. To launch 12 Comm Sats to a 25Gm orbit, launch each with a 59.30 day separation. To launch 24 Comm Sats to a 50Gm orbit (optional), launch each with a 20.69 day separation. The 3 formulae used in this computation are: v = sqrt(G * M / R) p = 2 * PI * R / v / (6 * 3600) dt = 1 / (N * (1 / p1 - 1 / p2)) where: v is orbital speed G is grav:6.67408e-11 M is mass of Kerbol: 1.7565459E28 R is orbital altitude p is orbital period (days) PI is pi dt is launch separation (days) N is number of satellites to occupy an orbital altitude p1 is orbital period of Kerbin (days) p2 is orbital period of the target orbit (days) Note: dt for inner orbits will be negative which merely indicates the satellites will arrive in counter-revolutionary order 1/p is angular speed expressed as radians/day and subtracting the speed of the target frame of reference form the launch frame of reference is the insight that makes this achieve a full orbit with even spacing (your mileage may vary depending on how timely your launches are) I plan once arriving at apoapsis to not worry too much about the orbital parameters or spacing but to have the exact same orbital period for all sats in the orbit. This will keep them locked in their relative positions over a very long duration. If you're more picky about getting exact spacing, this tutorial, https://wiki.kerbalspaceprogram.com/wiki/Tutorial:Ideal_Orbits_for_Communication_Satellites, particularly the treatment of the Law of Cosines, is quite fascinating. It's most relevant to low altitude orbits, e.g. spacing N space stations around a body. [All of the above may have been covered elsewhere but I haven't seen it/didn't find it and I've just had to create all this from scratch; so I hope it's useful to someone else. Please let me know if you find any errors, as I have not executed this yet.]
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