Tetrahedral constellation

[MAFman]

How do I make a geosynchronous constellation where the orbits are elliptical and the apoapses form the vertices of a tetrahedron?

 

EDIT: The tetrahedron should just rotate in place, with none of the vertices moving relative to each other.

Edited August 6, 2021 by MAFman
Added a detail

[OHara]

You would launch each satellite 1.5 hours, ¼ of a Kerbin day, after the previous launch, and turn north after launch enough that each orbit has about 35° inclination.

Strictly speaking, you would launch when Kerbin has made a ¼ rotation relative to the stars, which is several seconds shorter than ¼ day.  If you want a regular tetrahedron, the eventual inclination would be 35.26° = arcsine (1/√3)

Then with satellites in those inclined circular orbits, you can visualise the tetrahedron and boost the apoapsis of each satellite to the desired corner.  To make the orbit take on Kerbin day, watch the orbit period on the maneuver tab as you boost the apoapsis.  Strictly speaking again, Kerbin rotates relative to the stars once every 5h 59m 9s.

It might be more enjoyable to put four markers into the desired orbits with the cheat menu => Set Orbit.  Then you can pilot rockets with your real satellites and have targets to aim for.

There was a related thread a while back (link) that might be interesting.

[OHara]

3 hours ago, MAFman said:

EDIT: The tetrahedron should just rotate in place, with none of the vertices moving relative to each other.

The apoapses, the highest points on each elliptical orbit, don't move at all in stock KSP, so the tetrahedron formed by those apoapses doesn't move at all.

If you are thinking of having the satellites be in a rotating tetrahedron with vertices not moving relative to each other, the thread a while back (link) was about why that is not possible.

Edited August 6, 2021 by OHara