Barron's 2nd Edition PT1 Q43

Barron's Book

43) This question asks us to determine what happens to the acceleration of gravity as we move 2 Earth radii away from the surface of Earth. Since we are looking at gravity on a planetary level, we will use Newton’s universal gravitation equation. We can start by looking at the acceleration of gravity when an object is at the surface.

Where F[g] is gravitational force, G is the universal constant of gravity, m is mass of the object, M[E] is mass of the Earth, and r is radius

While this isn’t important for this question, it is important to realize that, as proved above, the acceleration of gravity doesn’t depend on the mass of the object.

Where r[E] is the radius of Earth.

What many people forget to factor, is that 2 Earth radii away from the surface of Earth is actually 3 Earth radii from the center of Earth.

Now, let’s look at the effect on the gravitational acceleration when the object is moved to 2 Earth radii away from the surface.

Where g is acceleration of gravity, G is the universal gravitation constant, M[E] is the mass of the Earth, and r[E] is the radius of the Earth

Answer: A