At what height above Earth would a 400.0-kg weather satellite have to orbit in o

Question

At what height above Earth would a 400.0-kg weather satellite have to orbit in order to experience a gravitational force half as strong as that on the surface of Earth At what height above Earth would a 400.0-kg weather satellite have to orbit in order to experience a gravitational force half as strong as that on the surface of Earth At what height above Earth would a 400.0-kg weather satellite have to orbit in order to experience a gravitational force half as strong as that on the surface of Earth

Explanation / Answer

Gravitational force on the surface on earth, F1 = GMm/R2
G is the universal gravitational constant, G = 6.67408 x 10-11 m3 kg-1 s-2
M is the mass of earth, M = 5.972 x 1024 kg
m is the mass of satellite, m = 400 kg.
R is the radius of earth, R = 6371 km

Gravitational force at a height h from the surface of earth is
F2 = GMm/(R+h)2
F2 = 1/2 F1
GMm/(R+h)2 = 0.5 GMm/R2
[(R+h)/R]2 = 1/0.5 = 2
Taking square root on both sides
R+h/R = 1.414
R + h = 1.414 R
h = 0.414 R
= 0.414 x 6371 km
= 2638.96 km

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