Gravitation : Law Of Gravitation

What is Gravitation?

Gravitation or gravity is everywhere, it is the force that keeps us stuck to the ground, drives the planets around the sun and the same force that pulls you down a slide. Gravitation is the force of attraction between any two bodies in this universe, yes everything attracts everything else in the universe with some amount of force, but this force is too weak to be observed in most of the cases. Sir Isaac Newton proposed the universal law of gravitation in the year 1680. So what is the law of gravity? The law of gravity states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravitational Force Formula

Gravitational force is explained using Newton’s law of universal gravitation. Gravitational force decides how much we weigh and how far a ball travels when thrown before it lands on the ground. The Newton’s law of gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Calculation of force of gravitation:

Gravitation

Consider two bodies A and B with mass m1 and m2 respectively, then according to newton’s law of gravitation body A and B will attract each other with a same force (F1 = F2 = F) which is proportional to the product of their masses and inversely proportional to the square of the distance between them hence

\(F m_1 m_2\)

\(F~\frac{1}{r^2}\)

To get an equation we will now introduce a proportionality constant in this expression,

\(F\) = \(G \frac{m_1 m_2}{r^2}\)

This constant which is denoted by ‘\(G\)’ is known as the gravitational constant which is approximately \(6.674~\times~10^{−11} \frac{N⋅m^2}{kg^2}\), do not confuse this with ‘\(g\)’ which stands for acceleration due to gravity. So now we know why gravity is so weak between distant bodies and strong on the surface of the earth, it is because the force of gravity reduces exponentially with increase in the distance between the bodies.

On earth the force of gravity acting on a body would be that body’s weight, this explains to us why astronauts experience less weight on the surface of moon and can easily jump and stay airborne for several seconds, as the mass of moon is approximately 80 times less than that of earth and the radius of moon is 1/4 of that of earth’s, therefore, using the law of gravitation the force of gravity on the surface of moon is roughly 1/6 of that on earth.

Applications:

Gravity has various applications, most of our deep space missions and other interplanetary missions like the mars orbiter mission – Mangalyaan made use of what is called interplanetary slingshot which basically means using gravity of other celestial bodies like planets and moons to propel a spacecraft, this is the most efficient mode of transport, gravity is used to power hydroelectric power plants where the flowing of water downstream due to gravity rotates a turbine to generate electricity.

You can go through the above video to gain more knowledge regarding the history of gravitation.

Stay tuned with Byju’s to learn more about gravity, the acceleration due to gravity and much more.

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Practise This Question

The following figure shows the elliptical path of a planet about the sun. The two shaded parts have equal areas. If t1, t2 be the time taken by the planet to go from A to B and from C to D respectively–