Aspacecraft is launched from earth toward the moon. where will the spacecraft be when the gravitational forces acting on it are equal? a. closer to earth than to the moon because the moon has greater mass than earth. b. closer to the moon than to earth because the moon has greater mass than earth. c. closer to earth than to the moon because earth has greater mass than the moon. d. closer to the moon than to earth because earth has greater mass than the moon.

Option D: Closer to the moon than to Earth because Earth has greater mass than the moon.

We know that the gravitation force is directly proportional to the masses of two bodies and inversely proportional to the distance (r) between them.

G is the gravitational constant.

We know that mass of Earth is greater than the mass of moon .  It means, the point where gravitational force would be equally acting would be closer to the moon.

Let the mass of the earth be , mass of the spacecraft be and mass of moon be , is the distance between earth and spacecraft and is the distance between moon and spacecraft.

Let the force acting on spacecraft due to Earth be:

Let the force acting on spacecraft due to moon be:

For forces to be equal,

This means that the distance of the spacecraft from the Earth would be larger than the distance from the moon where the gravitational force would be equally acting by Earth and Moon.

wvbbvvv