If an astronaut landed on a planet that had the same radius as Earth but 4 times its mass,then the astronaut's weight on the planet would be
A) 2 times her weight on Earth.
B) the same as on Earth because weight is independent of location.
C) 4 times her weight on Earth.
D) 16 times her weight on Earth.

Question

Quizplus · Accepted Answer

Weight is directly proportional to mass and the gravitational force acting upon an object. The greater the mass of the planet, the greater the gravitational force and therefore the greater the weight of an object on that planet. The formula for gravitational force is F = G(m1m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers. Since the radius is the same for both Earth and the planet in question, the only variable affecting the gravitational force is the mass. Since the planet has four times the mass of Earth, the gravitational force will also be four times as strong, and therefore the weight of the astronaut will be four times her weight on Earth.

If an Astronaut Landed on a Planet That Had the Same