A satellite is moved from one circular orbit around the earth to another of lesser radius. Which of the following statement is true?

Moderate

A

The kinetic energy of satellite increases and the gravitational potential energy of satellite-earth system increases.
B

The kinetic energy of satellite increases and the gravitational potential energy of satellite-earth system decreases.
C

The kinetic energy of satellite decreases and the gravitational potential energy of satellite-earth system decreases.
D

The kinetic energy of satellite decreases and the gravitational potential energy of satellite-earth system increases.

Solution

In the circular motion around the Earth, the centripetal force on the satellite is a gravitational force. Therefore, $v^{2} = GM / R$ , where M is the mass of the Earth, R is the radius of the orbit of satellite and G is the universal gravitational constant. Therefore, the kinetic energy increases with the decrease in the radius of the orbit. The gravitational potential energy is negative and decreases with the decrease in radius.

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