Question

two satellite a and b have masses m and 2m respectively.a is in a circular orbit of radius r and b is in the circular orbit of 2r around the earth. what is tha ratio of their kinetic energy?

Answer 1

Kinetic Energy of the satellite = 1/2 mv²

Now, Velocity of the satellite can be calcualted as,

mv²/r = GMm/r²

v² = GM/r

when r will be close to the earth, then it can be equal to R.

∴ v² = GM/R

∴ v² = gR

∴ v = √gR

Now, Kinetic Energy = 1/2 × m × gR

= mgR/2

For first satellite,

K.E. = mgR/2

For second satellite,

K.E. = 2mgR/2 = mgR

∴ There ratio = 1/2

Hope it helps.