CollegeBoard SAT Physics Study Guide PT1 Q29

CollegeBoard's Book

29) Question 29 asks us to find the weight of an astronaut on a planet that has twice the mass of Earth and the same diameter. It is important to know that the force of gravity acting on an object, is the same as its weight. There are two equations we will need for this problem.

Where F is the force, m is mass of astronaut, g is the acceleration of gravity on Earth, G is the universal constant of gravity, M is the mass of the planet the astronaut is on, and r is the distance from the center of the planet to the astronaut

The first equation can only be used on Earth, but the second equation can be used anywhere. So when the astronaut is on Earth, we can set up this equation.

Since the diameter of the Earth and the that of the other planet are the same, the radii will be the same, so we don't need to change the radius. Now since the mass of the planet the astronaut is standing on is twice the mass of Earth we can replace M with 2M. But remember, since it is an equation, if we multiply one side by 2 we must do the same on the other side.

Now we can substitute back our original equations for force of gravity.

Where F(g) is force of gravity

In this form, it is noticeable that the weight(force of gravity) has doubled.

Answer: B