Question

A satellite has a mass of 5966 kg and is in a circular orbit
4.12 × 10^{5} m above the surface of a planet. The period
of the orbit is 1.9 hours. The radius of the planet is 4.58 ×
10^{6} m. What would be the true weight of the satellite if
it were at rest on the planet’s surface?

Answer #1

Orbital speed , v = 2pi*[4.58e6+4.12e5]/(1.9*60*60)

= 4586 m/s

v = sqrt(GM/r)

4586^2 = 6.67e-11*M/(4.58e6+4.12e5)

4586^2*(4.58e6+4.12e5)/[6.67e-11] = M

M= 1.574e24 kg

weight on planet surface, F = GMm/r^2

= 6.67e-11*1.574e24*5966/(4.58e6)^2

= 29860 N answer

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