# Newton’s Law of Universal Gravitation

## Newton’s Law of Universal Gravitation

Newton’s Law of Universal Gravitation is derived by Isaac Newton who made a comparison of the acceleration of the moon to the acceleration of objects on Earth. He believed that gravitation forces are accountable for each and therefore drawn an imperative assumption regarding the need of gravity upon distance. This assessment led to the conclusion that the force of gravity between the Earth and all other substances is contrariwise proportional to the distance separating the Earth’s midpoint from the object’s center. Though this distance is not just one variable affecting the magnitude of a gravitational force. Consider the following Newton’s equation:

Fnet = m • a

According to Newton, the apple’s acceleration (gravity) is dependent on the mass of the apple. Subsequently, the force acting cause the apple’s downward acceleration as well as cause the earth’s upward acceleration in accordance to Newton’s third law. For that reason, the force must also depend on the mass of the earth. The theory shows that the gravitational force acting between the earth and other objects is directly relative to the mass of the earth, directly proportionate to the mass of the object and inversely proportional to the square of the distance separating the centers of the earth and the object.

The following equation represents the Newton’s Law of Universal Gravitation:

F = Gm1m2/r2

F= Gravitational force of attraction

m1 and m2= Interacting masses (kg)

r= distance separating the masses

Moreover, G is the universal gravitational constant and one should not confuse it with little g. It gives the strength of the gravitational interaction in a way that if it was doubled, so would all the gravitational forces. This law is applicable between point masses since their mass is concentrated at the center. The force is always attractive and you will often see a minus sign in the equation such as:

F = -Gm1m2/r2

The minus sign indicates that the force is purely attractive and the simplest equation to calculate the magnitude of the force. The direction is given by the fact that the force is attractive. According to the law, each object with a mass in the universe attracts the other. Though the actual size of the force becomes very little for objects that are far away. For instance, Sun is one million times more massive than the Earth as its extremely far away. The pull on us from the Sun is dwarfed by the pull on us from the Earth which is about 1650 times greater. With the increasing separation between two objects, the separation 2 also increases while the gravitation force decrease by the same factor since separation 2 is present in the denominator of the equation. The example illustrates the reverse square law as the force of attraction varies in reverse proportion to the square of the separation.

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