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Question

The orbital speed of a satellite revolving around planet in a circular orbit is v0. if its speed is increased by 10%, then

A
It will escape from its orbit
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B
It will start rotating in an elliptical orbit
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C
It will continue to move in the same orbit
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D
It will move in a circular orbit of radius 20% more than radius of initial orbit
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Solution

The correct option is A It will escape from its orbit

Centripetal force = gravitational force

mv02r=GmMr2

From the above relations, we can conclude that:

The centripetal force balancing the gravitational force on the satellite is directly proportional to the velocity and inversely proportional to the radius of the orbit.

Thus;

i. If the velocity increases, the centripetal force will also increase and to counter that, the radius of the orbit should decrease.


ii. If we keep the radius unaltered in the equation, the centripetal force will increase more than the gravitational force and the satellite will escape.


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