Help! A satellite circles a spherical planet of unknown mass in a circular orbit

Question

Help!

A satellite circles a spherical planet of unknown mass in a circular orbit of radius 1.8 x 107m. The magnitude of the gravitational force exerted on the satellite by the planet is 110N. What would be the magnitude of the gravitational force exerted on the satellite by the planet if the radius of the orbit were increased to 3.2 x 107m ? Express your answer using two significant figures. If the satellite circles the planet once every 2.7h in the larger orbit, what is the mass of the planet? Express your answer using two significant figures.

Explanation / Answer

F = GMm/r^2 = 110

A) r1^2/r^2 = 110/F1

F1 = 110*(1.8*10^7)^2/(3.2*10^7)^2 = 34.8 N

B) R^3 = GMT^2/4pi^2

M = 4*3.142^2*R^3/(GT^2) = 4*3.142^2*(3.2*10^7)^3/(6.67*10^-11*(2.7*3600)^2) = 2.05*10^26 kg

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