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.