Question

The additional K.E. to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R1 to another radius R2 (R2 > R1) is

(A) GMm[(1 / R12) – (1 / R22)]

(B) GMm[(1 / R1) – (1 / R2)]

(C) 2 GMm[(1 / R1) – (1 / R2)]

(D) (1/2) GMm[(1 / R1) – (1 / R2)]

Answer 1

Correct option: (D) (1/2) GMm[(1 / R1) – (1 / R2)]

Explanation:

KE in orbit of radius R1

E1 = – [(GMm) / (2R1)]

KE in orbit of radius R2

E2 = – [(GMm) / (2R2)]

hence addition KE to transfer it from orbit of radius R1 to R2 = E

Therefore

E + E1 = E2

E = E2 – E1

= – [(GMm) / (2R2)] + [(GMm) / (2R1)]

E = [(GMm) / 2][(1 / R1) – (1 / R2)]