Question

Formula for distance to the horizon for a satellite in orbit.

d = sqrt(2rh+h^2)

d = distance to the horizon
h = height above sea level for the observer.
r = radius of the earth

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Solve for h.

ie. so I can plug in d and r and get a solution for h.

Answer 1

d^2 = h^2 + 2 r h

h^2 + 2 r h - d^2 = 0

quadratic

h = [ -2r +/- 2 sqrt(r^2+d^2) ]/2

Answer 2

which is
-r +/- sqrt(r^2+d^2)

Answer 3

LOL - only use positive root if above ground.