At a distance H above the surface of a planet, the true weight of a remote probe is six percent less than its true weight on the surface. The radius of the planet is R. Find the ratio H/R.

Answer 1

just plug and chug. The weight is GMm/r^2 and GMm is constant, so

(1/(R+H)^2) / 0.94 (1/R^2)

It's a bit messy to solve that for H, but since H=kR for some k, we just want to solve for k. H/R = k.

(1/((1+k)R)^2) / 0.94 (1/R^2)
R^2/(R(1+k))^2) = 0.94
1/(1+k)^2 = 0.94
(1+k)^2 = 1/0.94
1+k = 1/√0.94
k = 1/√0.94 - 1 = 0.0314