Question

A satellite has a mass of 5850 kg and is in a circular orbit 4.1 * 105 m above the surface of a planet. The time period of the satellite is 2 hours. The radius of the planet is 4.15 * 106 m. Find:

a) The orbital radius of the satellite.
b)The weight of the satellite in its orbit.
c) The weight of the satellite when it is at rest on the surface of the planet.

EXPERT ANSWER ONLY.

Answer 1

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ΣF = ma 

GMm/R² = m(2π/T)²R 

but the true weight or satellite in orbit is 

w = mg 

w = mGM/R² 

w = m(2π/T)²R 

w = 6000(2π/(2 * 3600))² (4.25 * 10^6 + 4.8 * 10^5) 

w = 21612.61 N