The masses and radii of the earth and the moon are M 1 , R 1 and M 2 , R 2 respectively. Their centres are at a distance d apart. What should be the minimum speed with which a body of mass m should be projected from a point midway between their centres, so as to escape to infinity?

Step-by-step solution

The P.E. of the body at C is given by U = G M 1 m d 2 - G M 2 m d 2 = - 2 G m d M 1 + M 2 Initially it is at rest, hence its K.E. = 0 ∴ Total energy of the body = - 2 G m d M 1 + M 2 and Binding energy = 2 G m d M 1 + M 2 Let v e be the escape velocity that should be given to the body and its K.E. = Binding energy ∴ 1 2 m v e 2 = 2 G m d M 1 + M 2 ∴ v e = 2 G M 1 + M 2 d