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 m_1 and m_2 is F=G(m_1m_2)/r^2, where G is the "gravitational constant", approximately equal to 6.67xx10^(-11)m^3kg^(-1)s^(-2), m_1 and m_2 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 m_E, and the radius of Earth be r_E. Then the weight of the person on Earth will be F_E=G(mm_E)/r_E^2.

On the other planet, the planetary mass is 5m_E and the planetary radius is 10r_E. So the weight of the person on that planet will be F_P=G(m*5m_E)/(10r_E)^2=G/20(mm_E)/r_E^2=F_E/20.

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.