Suppose the acceleration due to gravity at the earth's surface is g m/s ^2 and at the surface of moon it is g' m/s ^2 . An M kg passenger goes from the earth to the moon in a spaceship moving with a constant velocity (Neglect all other objects in the sky). Which curve best represents the weight (net gravitational force) as a function of time?

Step-by-step solution

Let the mass of the Earth be M_e , the mass of the Moon be M_m , and the distance between their centers be d . When the spaceship is at a distance r from the center of the Earth, the net gravitational force on the passenger of mass M is given by: F_ net = G M_e M r^2 - G M_m M (d-r)^2 Since the spaceship moves with a constant velocity, the distance r increases linearly with time t . At the surface of the Earth ( t = 0 ), the gravitational pull of the Moon is negligible, so the net force is approximately the weight