Newton's Law of Gravitation for AP Physics B & C

Practice problems for these concepts can be found at:

Gravitation and Circular Motion Practice Problems for AP Physics B & C

Gravity is an amazing concept—you and the Earth attract each other just because you both have mass!—but at the level tested on the AP exam, it's also a pretty easy concept. In fact, there are only a couple equations you need to know. The first is for gravitational force:

This equation describes the gravitational force that one object exerts on another object. M₁ is the mass of one of the objects, M₂ is the mass of the other object, r is the distance between the center of mass of each object, and G is called the "Universal Gravitational Constant" and is equal to 6.67 × 10–¹¹ (G does have units—they are N·m²/kg²—but most problems won't require your knowing them).

This is simple plug-and-chug (remember to convert km to m).

Notice that the amount of force that the Earth exerts on the sun is exactly the same as the amount of force the sun exerts on the Earth.

We can combine our knowledge of circular motion and of gravity to solve the following type of problem.

The force of gravity exerted by the sun on the Earth is what keeps the Earth in motion—it is the centripetal force acting on the Earth.

v = 29,000 m/s. (Wow, fast … that converts to about 14 miles every second—much faster than, say, a school bus.)

Along with the equation for gravitational force, you need to know the equation for gravitational potential energy.

We bet you're thinking something like, "Now hold on a minute! You said a while back that an object's gravitational potential energy equals mgh. What's going on?"

Good point. An object's gravitational PE equals mgh when that object is near the surface of the Earth. But it equals no matter where that object is.

Similarly, the force of gravity acting on an object equals mg (the object's weight) only when that object is near the surface of the Earth.

The force of gravity on an object, however, always equals, regardless of location.

Practice problems for these concepts can be found at:

Gravitation and Circular Motion Practice Problems for AP Physics B & C