Newton’s Law of Universal Gravitation

The gravitational attraction between any two objects is directly proportional to both object’s masses and inversely proportional to the distance between them.

The equation below is a numerical representation of Newton’s law. Since the gravitational force is directly proportional to the masses of both interacting objects, the force between them increases as mass increases. Using this equation, we can calculate gravitational attraction between any two objects of masses m1 and m2 with a distance r between them.

G is the universal gravitational constant, 6.6741 x 10^-11 m³*kg^-1*s^-2. It is the same for any two particles at any point in space.

Watch the following video to learn about the Law of Gravitation and how Newton’s equation can be applied to find the strength of gravitational fields.

If an object was inside a sphere such as the earth, gravitational force decreases closer to the center. Exactly at the center, the earth’s gravitational force on the object is zero. Courtesy of Google Images.

The gravitational effect outside two spherically symmetric objects is the same as if all the mass of the object was concentrated at the center of the sphere. This is important for many moons, stars, and planets, which are spherically symmetric.

Application

Jupiter is spherical because of the gravitational attraction of all its parts, and it has a large mass of 1.90 x 10²⁷ kg.

However, Jupiter’s moon Amalthea has a relatively smaller mass of 7.17 x 10¹⁸ kg with weaker gravitation. This is why Amalthea has an irregular shape.