Newton's Law of Gravity

A more general equation for calculating the force of gravity between two objects is Newton's law of gravity:

Where F is the force of gravity, G is the gravitational constant = 6.67 X 10^-11 , M₁ and M₂ are the masses of the two objects, and R is the distance measured between the center of masses of the two objects.  The force will be attractive and directed toward the centers of the respective objects.

Sample Problem #1

On earth, Jack weighs 450 N, and Jill weighs 400 N. They are in space, far enough away from any celestial objects that we can consider them to be the only forces acting on one another. The distance between them is 10 meters. What is the force of gravity between these two people?

Sample Solution #1

In this problem we are given Jack and Jill's weight, but we need their masses in order to use the gravitational attraction between them. We will use:

We can now plug all our information into Newton's Law of Gravity:

Sample Problem #2

Planet X has a mass of 2·10²⁰ kg, and Planet Z has a mass of 5·10²⁵ kg. The force of gravity between the two planets is 41687.5 N. What is the distance between the two planets?

Sample Solution #2

In this case, R (the distance between them) is unknown, but we have all the information we need to solve for R using Newton's Gravity Law:

It's important to note that in the last step, when we took the square root of both sides, we actually obtained two answers: both positive and negative 4·10¹⁵ m. However, since we are talking about a distance, rather than a displacement, it makes sense to ignore the negative root in this instance.

Note on practice problems: Use Newton's Law of Gravity to solve these problems. In some cases, you may need to research information such as masses of celestial bodies and distances between celestial bodies.

1.

Calculate the weight in newtons of your physics instructor if he has a mass of 75kg and is standing on the surface of the earth. (Earth radius = 6.37x10⁶ m, and the earth's mass is 5.97x10²⁴ kg)

2.

Calculate his weight if he were standing on the surface of the moon. (Moon radius = 1.74x10⁶ m, moon mass = 7.35x10²² kg.)

3.

Find his mass if he were on the surface of the moon.

4.

Find the acceleration of gravity on the surface of the moon.

5.

Calculate the force of gravity between the earth and the moon.

6.

What is the weight of an object which is 6370 km above the surface of the earth if its weight on the surface of the earth is 1000 N?

7.

A newly discovered planet has twice the density of the earth, but the acceleration due to gravity on its surface is exactly the same as on the surface of the earth. What is its radius?

8.

Find the point between the moon and the earth at which their gravitational forces on an object will balance.

9.

A newly discovered planet has the same average density as the earth but only half the earth's diameter. How much does a kilogram weigh at the surface of the planet?