Question

A satellite of mass “m” orbits a planet “P” in an elliptical orbit. The satellite is then transferred to another circular orbit of radius “r” as shown in the figure. Which of the following hold true in this scenario?

Moderate

A

The kinetic energy of the satellite is increased and the potential energy of the satellite is decreased in the new orbit
B

The kinetic energy of the satellite is decreased and the potential energy of the satellite is increased in the new orbit
C

Both kinetic and potential energy of the satellite is decreased on the new orbit
D

Both kinetic and potential energy of the satellite is increased on the new orbit

Solution

The kinetic energy of a satellite is;
KE = (1/2) x (G x m x M)/r
The potential energy of a satellite is;
PE = – (G x m x M)/r
Due to an increase in “r” the kinetic energy is decreased. The potential energy increases for the same reason as well due to the presence of a negative sign.

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