The gravitational attraction F exerted by an airless moon on a body of mass m at a distance s from the moon’s center is given by the equation F = -mg R²s^-2, where g is the acceleration of gravity at the moon’s surface and R is the moon’s radius. The force F is negative because it acts in the direction of decreasing s.

a. If the body is projected vertically upward from the moon’s surface with an initial velocity ν₀ at time t = 0, use Newton’s second law, F = ma, to show that the body’s velocity at position s is given by the equation

Thus, the velocity remains positive as long as ν₀ ≥ √2gR. The velocity ν₀ = √2gR is the moon’s escape velocity. A body projected upward with this velocity or a greater one will escape from the moon’s gravitational pull.

b. Show that if

Transcribed Image Text:

F = mgR2 82 Mass m Moon's center R S