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Question:

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only the gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet?

11

13

17

9

Solution:

Fg=mv²/r
GMm/r²=mv²/r
V=√(GM/r)=√((6.67×10⁻¹¹)(8×10²²)/(2.02×10⁶))
V=1.625×10³
T=2πr/V
n×T=24×60×60
n[2π(2.02×10⁶)/(1.625×10³)]=24×3600
n=(24×3600×1.625×10³)/(2π(2.02×10⁶))
n=11