## A Simple Explanation of the Law of Universal Gravitation

Isaac Newton discovered three laws of motion and the law of gravity to explain motions observed on Earth and in space. Gravity acts between everything in the Universe.

### Law of Universal Gravitation

Prior to Newton and Galileo, most people thought that the forces causing motions on Earth and the forces causing the stars and planets to move were different forces. Isaac Newton realized that the same forces and the same laws of physics apply everywhere in the universe. So, his law of gravity is called the law of universal gravitation.

### Force of Gravity

There is a gravitational force acting between any two objects in the universe. There is a gravitational force between you and Earth. There is also a gravitational force between you and the Sun, between you and all the other planets, and between you and the people sitting next to you. Why do we fall down towards Earth rather than towards the Sun, another planet, or the people next to us?

The force of gravity between us and Earth is larger than the force from any of these other objects.

The force of gravity between two objects depends on the masses of the two objects and the distance between the centers of the two objects.

### Gravitational Force and Mass

The more the masses of the objects, the larger the gravitational force between them. Finding the gravitational force between two objects requires multiplying the masses of the two objects. If your mass were to be twice as much, the gravitational force between you and Earth, which is your weight, would double. If Earth were to become twice as massive, without changing its size, your weight would also double. Increasing either mass, increases the gravitational force between two objects; decreasing their mass decreases the gravitational force.

We don’t fall towards the people next to us because they are much less massive than Earth. But the Sun is more massive than Earth. Why don’t we fall to the Sun?

It is much farther away. As the distance between two objects gets larger, the gravitational force between them gets smaller.

### Gravitational Force and Distance

When you are standing on Earth with your toes buried in the dirt, it may seem like the distance between you and Earth is zero. But, the distance is measured between the centers of the two objects not the edges. So the distance between you and Earth is the distance from the center of the Earth to your belly button.

As the distance between two objects gets larger, the gravitational force between them gets smaller. It never gets to zero; it just gets too small to matter. If you were suddenly suspended in space twice as far from the center of the Earth as you are now. the gravitational force would be one fourth as much as it is on Earth’s surface. If you weigh 100 pounds, you would suddenly weigh 25 pounds. No matter how far you got from Earth, there would still be some, very small, gravitational force between you and Earth

Astronauts in space are weightless because they are falling around the Earth, not because there is no gravity in space. There is gravity everywhere.

Notice that if the distance between two objects doubles the gravitational force is one fourth as much. That is because finding the gravitational force requires dividing by the square of the distance between the objects, not the distance. Two squared is four, so twice the distance means one fourth the force. Gravity is an inverse square force.

Along with his three laws of motion, Newton’s law of gravity explains all the motions we see in the universe.

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