Question

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?

Answer 1

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.