Question

the additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M,to transfer it from a circular orbit of radius R1 to another radius R2 (R2>R1)​

Answer 1

Given:

A satellite of mass m revolving around a planet of mass M has been transferred from one circular orbit of radius R1 to another radius R2.

To find:

Additional kinetic required.

Calculation:

We will apply Conservation of Mechanical Energy, because the amount of additional kinetic energy given will be equal to the change in the potential energy of the satellite.

$\sf{ \therefore \: \Delta KE = \Delta PE}$

$\sf{ = > \: \Delta KE = \dfrac{GMm}{R1} - \dfrac{GMm}{R2} }$

$\sf{ = > \: \Delta KE =GMm \bigg \{ \dfrac{1}{R1} - \dfrac{1}{R2} \bigg \} }$

$\sf{ = > \: \Delta KE =GMm \bigg \{ \dfrac{R2 - R1}{(R1)(R2)} \bigg \} }$

So, final answer is:

$\boxed{ \red{ \rm{ \: \Delta KE =GMm \bigg \{ \dfrac{R2 - R1}{(R1)(R2)} \bigg \} }}}$