Question

The minimum energy required to launch a satellite of mass m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2R from the surface of the earth is ______.

Options

• `(5 GmM)/(6 R)`

• `(2 GmM)/(3 R)`

• `(GmM)/(2 R)`

• `(GmM)/(3 R)`

Answer 1

The minimum energy required to launch a satellite of mass m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2R from the surface of the earth is `bbunderline((5 GmM)/(6 R))`.

Explanation:

Let us apply the energy conservation law, we get.

U + K = U + K

⇒ `-(GMm)/R + K_i = - (GmM)/(3 R) + 1/2 mv^2`

⇒ `- (GMm)/R + K_i = - (GmM)/(3 R) + 1/2 xx m xx (GM)/(3 R)`

⇒ K_i = `-1/6 (GMm)/R + (GMm)/R`

= `5/6 (GMm)/R`