Suppose a person weighs 100 pounds. If he travels to a planet with 5 times the mass of Earth and 10 times the radius of Earth, what will his new weight be?

1 Answer
Jun 16, 2018

5 lb

Explanation:

The weight of a person is the force that their mass exerts in the local gravitational field.

The force due to gravitation between two objects of masses m1 and m2 is F=Gm1m2r2, where G is the "gravitational constant", approximately equal to 6.67×1011m3kg1s2, m1 and m2 are masses of the object in kg, and r is the distance between the objects in m.

Let the person's mass be m, the mass of Earth be mE, and the radius of Earth be rE. Then the weight of the person on Earth will be FE=GmmEr2E.

On the other planet, the planetary mass is 5mE and the planetary radius is 10rE. So the weight of the person on that planet will be FP=Gm5mE(10rE)2=G20mmEr2E=FE20.

So, perhaps counter-intuitively, the person will weigh only 1/20 as much on the surface of this much larger planet as they do on Earth's surface. If they weigh 100 pounds on Earth, then they will weigh 5 pounds on the second planet.