Two satellites A and B of the same mass revolve around the earth in circular orbits. They are at heights of R and 3R respectively from the surface of the earth (R=radius of the earth). Find the ratio of their kinetic energies and potential energies.

Explanation

Height of satellite A from the centre of the earth =R+R=2R and height of satellite B from the centre of the earth =R+3R=4R. If the mass of each satellite is m and the mass of the earth is M,
potential energy of satellite A,`U_A=-(GMm)/(2R)`
and potential energy of satellite B, `U_B=-(GMm)/(4R)`
`therefore (U_A)/(U_B) =(GMm//2R)/(GMm//4R)=2/1`
If orbital speeds of the two satellite are `v_1 and v_2`, then kinetic energy of satellite A, `K_A=1/2 mv_1^2`
and kinetic energy of satellite B, `K_B=1/2 mv_2^2`
As `v_1=sqrt((GM)/(2R)) and v_2=sqrt((GM)/(4R))`
`(K_A)/(K_B)=(v_1^2)/(v_2^2)=(GM//2R)/(GM//4R)=2/1.`