An astronaut lands on a new planet. The new planet's mass is half that of the

Earth and the new planet's radius is half that of the Earth. If he weighs 500 N on

Earth, what will the force of gravity be on him on the new planet?

Ah hah! Very nice problem.

- - Since the mass is 1/2 of the Earth's mass, the gravitational forces between him

and the new planet would be 1/2 of what they are on Earth.

- - Since the distance between him and the center of the new planet is 1/2 of the

distance between him and the Earth's center, the gravitational forces between him

and the new planet would be (2) ² = 4 times what they are on Earth.

- - These conditions combine to make his weight (1/2) x (4) = 2 times his earth weight.

- - He weighs 1,000 N (about 224.8 pounds) on the new planet.

(Maybe that's why they selected an astronaut for this mission who only weighs

about 112.5 pounds on Earth.)