Minimum Altitude of a 4 sat network

[the_pazter]

What the Title says, what is the minimum altitude for a four sat network to see each other and work

[Kerbart]

248.6km. Make it 250. You probably want a bit more above that in case you do not have a perfect 90° spread.

[Hupf]

I forget if links work through Atmosphere (I believe they do), but what you would calculate is this:

Kerbin's equatorial radius r = 600.000km

So the satellites should orbit at Ap = Pe = (R - r), and from the picture above we see that at minimum R = sqrt(2) * r (because it is forming an isoscheles orthogonal triangle with sides r, r and R, so r^2 + r^2 = R^2).

So we get Pe = (sqrt(2) - 1)*600.000 = 249km.

With Atmosphere blocking transmission, it would be 278km.