Two satellites are moving around the earth in circular orbits at height R and 3R respectively, R being the radius of the earth, the ratio of their kinetic energies is

Q. Two satellites

A

and

B

of the same mass are orbiting the earth at altitudes

R

and

3 R

respectively,where

R

is the radius of the earth. Taking their orbits to be circular obtain the ratios of their kinetic and potential energies.

Join BYJU'S Learning Program

Two satellites, A and B, have masses m and 2m respectively. A is in circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA/TB is:

The correct option is C 1Orbital velocity V=√GMerTA=12mAV2ATB=12mBV2B⟹TATB=m×GmR2m×Gm2R⟹TATB=1

Two satellites, $A$ and $B$ , have masses $m$ and $2 m$ respectively. $A$ is in circular orbit of radius $R$ , and $B$ is in a circular orbit of radius $2 R$ around the earth. The ratio of their kinetic energies, $T_{A} / T_{B}$ is:

The correct option is C $1$
Orbital velocity $V = \sqrt{\frac{G M e}{r}}$
$T_{A} = \frac{1}{2} m_{A} V_{A}^{2}$
$T_{B} = \frac{1}{2} m_{B} V_{B}^{2}$
$⟹ \frac{T_{A}}{T_{B}} = \frac{m \times \frac{G m}{R}}{2 m \times \frac{G m}{2 R}}$
$⟹ \frac{T_{A}}{T_{B}} = 1$