Note that this coefficient doesn’t depend on mass. Good—if it did, we’d need tires made of different
materials depending on how heavy the car is.
Newton’s Law of Gravitation
We now shift our focus to gravity. 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. m 1 is the mass of
one of the objects, m 2 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·m^2 /kg^2 —but most problems won’t require your knowing them). The negative sign
indicates that the force is attractive. We can leave it off unless we are doing calculus with the equation.
The mass of the Earth, ME , is 5.97 × 10^24 kg. The mass of the sun, MS , is 1.99 × 10^30 kg. The two
objects are about 154,000,000 km away from each other. How much gravitational force does Earth
exert on the sun?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.
What is the speed of the Earth as it revolves in orbit around the sun?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.