Universal Law of Gravitation

Newton's law of universal gravitation

Sir Isaac Newton proposed the universal law of gravitation in 1687 and used it to explain the observed motion of the planets and moons. This article introduces Newton's law of universal gravitation.

According to Newton's law of universal gravitation, every particle in the universe attracts every other particle with a force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

The universal gravitation equation thus takes the form

Universal Gravitational Equation

Newton's conclusion about the magnitude of the gravitational force is symbolically summarized  as follows

 where F is the gravitational force between the bodies, m1 and m2 are the masses of the bodies, r is the distance between the centers of the two bodies, G is the universal gravitational constant.

The ratio constant (G) in the above equation is called the universal gravitational constant. Henry Cavendish determined the exact value of G experimentally. The value of G is found to be G = 6.673 x 10-11 N m2/kg2.

The Universal Law of Gravitation can explain almost everything, from how an apple falls from a tree to why the Moon orbits the Earth. Watch the video and understand the beauty of the Universal Law of Gravitation.

Universal Law of Gravitation

Gravitational constant

It is very difficult to accurately measure the value of the gravitational constant. Henry Cavendish developed a clever device to measure the gravitational constant.

Gravitational constant:

As shown in the figure, masses m and m' are attached to each end of the beam. The beam is attached to a strong support with a rope. The thread is tied in the middle of the beam so that it reaches balance. Now two large masses M' and M are placed next to them. The gravitational force between the two pairs of masses causes the wire to twist so that the amount of twist is balanced by the gravitational force. Gravitational force can be measured with proper calibration. Since we know the value of the masses and the distances between them, the only unknown quantity in the law of universal gravitation is G. Thus, the value of G is calculated from the measured quantities.

An example of a universal gravity solution

Calculate the force of attraction between the Earth and a 70 kg person standing at sea level 6.38 x 106 m from the center of the Earth. Solution:


m1 is the mass of the Earth, which is  5.98 x 102 kg

m2 is the mass of a person who is  70 kg

d = 6.38 x 106 m

G-value = 6.673 x 10-11 N m2/kg2

Substituting the values ​​in the gravitational force formula, we get

Weight and the Gravitational Force:

In Newton's law of gravity, we noticed that mass is the deciding factor. We think of mass and weight as the same, but they are actually different. Weight is the gravitational force acting on an object of a certain mass. The weight of an object is obtained by multiplying the mass of the object m by the acceleration g due to the earth's gravity. The gravitational acceleration measured at the Earth's surface is found to be approximately 980 cm/s/s. A measure of how much material is in an object is called mass, while weight is a measure of the gravitational force acting on the material in a gravitational field. Therefore, mass and weight are proportional to the acceleration of the other like a proportionality constant of gravity. Therefore, it is observed that the mass of a particular object is constant, but the weight depends on the location of the object. To better understand, let's consider the following example, suppose we transported a body with mass m to the surface of Neptune, the gravitational acceleration would change because the radius and mass of Neptune are different from those of Earth. So our object has a mass m on the surface of both Earth and Neptune, but it weighs much more on the surface of Neptune because the gravitational acceleration there is 11.15 m/s2.

Universality of Gravity:

Gravitational interaction exists not only between the Earth and other objects, but also exists between all objects with intensity directly proportional to the product of their masses. The law of universal gravitation helps scientists studies the orbits of the planets. Small disturbances in the elliptical motion of the planet are easily explained by the fact that all objects interact with each other under the influence of gravity.

·         Why doesn't the moon hit the earth?

Velocity and gravitational forces keep the Moon in a constant orbit around the Earth. The moon seems to float in the sky, unaffected by gravity. However, the reason why the Moon remains in orbit is precisely because of gravity. In this video, you can clearly understand why the moon does not fall to the earth.

·         Is gravity the same everywhere on Earth? 

·         Gravity is not the same everywhere on earth. In areas with greater underground mass, gravity is slightly stronger than in areas with less mass. NASA uses two spacecraft to measure changes in Earth's gravity. These spacecraft are part of the Gravity Recovery and Climate Experiment (GRACE) mission.

Gravitational variations on Earth

Blue areas have weaker gravity, while red areas have slightly stronger gravity.

The area in blue has weaker gravity while the area in red has slightly stronger gravity.