Problem 7P

IP A spaceship of mass m travels from the Earth to the Moon along a line that passes through the center of the Earth and the center of the Moon. (a) At what distance from the center of the Earth is the force due to the Earth twice the magnitude of the force due to the Moon? (b) How does your answer to part (a) depend on the mass of the spaceship? Explain.

Solution 7P

Part (a)

Step 1 of 4:

A spaceship travels from the Earth to the Moon. Our aim here is to find the distance from the center of the Earth where the gravitational force due to the Earth on the spaceship is two times greater than that of the Moon on the spaceship.

The mean distance between the center of the Earth to the center of the Moon

R = 3.844 x 108 m

The distance from the Earth to the spaceship = r1

The distance from the Moon to the spaceship = r2

The gravitational constant G = 6.67 x 10-11 N m2/kg2

The relationship between masses of the Earth (Me) and the Moon (Mm) Me = 81Mm