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)]