A satellite has a mass of 6190 kg and is in a circular orbit 4.67x10^5 m above t

Question

A satellite has a mass of 6190 kg and is in a circular orbit 4.67x10^5 m above the surface of the planet. The period of the orbit is 1.9 hours. The radius of the planet is 4.26x10^6 m. What would be the true weight of the satellite if it were at rest on the planet’s surface? A satellite has a mass of 6190 kg and is in a circular orbit 4.67x10^5 m above the surface of the planet. The period of the orbit is 1.9 hours. The radius of the planet is 4.26x10^6 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

Explanation / Answer

w = 2pi / T

w = 2 pi / (1.9 x 3600 s) = 9.186 x 10^-4 rad/s

r = (4.67 x 10^5) + (4.26 x 10^6) = 4.727 x 10^6 m

for circular path,

Fg = m w^2 r

G M m / r^2 = m w^2 r

G M = w^2 r^3 = 8.9127 x 10^13  

Weight on surface,

W = G M m / R^2

W = (8.9127 x 10^13) (6190) / (4.26 x10^6)^2

W = 30400 N .....Ans

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