Asatellite orbits a planet of unknown mass in a circle of radius
2.0×107
m. the magnitude of the gravitational force on the satellite from the planet is f = 80 n.
(a) what is the kinetic energy of the satellite in this orbit?
(b) what would f be if the orbit radius were increased to
3.0×107
m?

Explanation:

It is given that,

Radius of unknown planet,

The magnitude of the gravitational force on the satellite from the planet is F = 80 N, it means,

The gravitational force acting on the satellite is balanced by the centripetal force as :

(a) Let E is the is the kinetic energy of the satellite in this orbit.

Multiply both sides of above equation by 1/2.

So, '        

(b) Let F' is the force if the orbit radius were increased to,

The relation between the force and distance is,

F' = 35.55 N

or

F' = 36 N

Hence, this is the required solution.                                                                                  

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