Question

A satellite of mass m is revolving in an orbit of radius r around a planet of mass m it lost some energy against the work in air resistanceand shifted to an orbit of radius R/2the lost energy

Answer 1

Answer:

The lost energy is $\frac{GMm}{2R}$

Explanation:

The total energy of the satellite in the orbit of radius R

$E=-\frac{GMm}{2R}$

When the satellite shifts to the orbit of radius R/2, the total energy will be

$E'=-\frac{GMm}{2\times (R/2)}$

$\implies E'=-\frac{GMm}{R}$

The energy lost = Change in total energy

$W=E-E'$

$\implies W=-\frac{GMm}{2R}-(-\frac{GMm}{R})$

$\implies W=-\frac{GMm}{2R}+\frac{GMm}{R}$

$\implies W=\frac{GMm}{2R}$

Hope this helps.