Gravitational Constant and Universal Law Of Gravitation

Universal Law Of Gravitation

According to Newton’s Universal Law of Gravitation, the force exerted between two objects, by each other is given by the following relation.

\(F_g  ∝ \frac{m_1.m_2}{r^{2}}\)

Where,

\(\small g\): gravitational force between two bodies
\(\small m_1\): mass of one object
\(\small m_2\): mass of the second object
\(\small r\): distance between the centers of two objects

Gravitational Constant

The actual force exerted between two bodies can be given by the following equation

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

Where,

\(\small G\) is the universal gravitational constant with a value of;

\(\small G = 6.674 \times 10^{-11} N · (m/kg)^{2}\)

\(\small G\) here is an empirical constant of proportionality.

What is interesting here is that, even though it is Newton’s Universal Law of Gravitation, the value of G wasn’t given by him. This was calculated by Henry Cavendish in 1798 through a series of experiments and observations. It is hypothesized the influence of the earth’s core on the experiments alters its rotational inertia because of which the value of G given is not always constant throughout the globe.

Another theory regarding the universal gravitational constant (fun fact: it is also referred to as Big G) is that, if it is true that the universe is expanding since the Big Bang, then the value of G will keep decreasing!

The universal gravitational constant is used in Newton’s Universal Law of Gravitation, Einstein’s General Theory of Relativity and also Kepler’s Third Law of Planetary Motion, to calculate the time period of a planet to complete one full revolution in its orbit.

To know about the history of gravitation watch this video,


Practise This Question

The atmosphere is held to the earth by