# Gravitational constant

The Gravitational Constant is an universal constant who value is $6.67408\cdot 10^{-11} m^3 kg^{-1} s^{-2}$. It is commonly denoted as $G$. There is some uncertainty associated with the value of the constant, due to limitations in measurement.

## Derivation

### Historic Attempts

Sir Isaac Newton had attempted to calculate the density of Earth and "also suggested the value of this constant be determined by measuring deflection of pendulum near a large mountain", thus estimating $G = (6.7 \pm 0.6) \cdot 10^{-11} m^3 kg^{-1} s^{-2}$.

The Schiehallion experiment, completed in 1776, was the first successful measurement of the mean density of the Earth, and thus indirectly of the gravitational constant.

The first notable result, differing only by 0.6% of the modern value, was the Cavendish Experiment, which was performed by Henry Cavendish, using Torsion balance. It directly measured the (faint) attraction between two metal spheres. [Source: Wikipedia]

### Modern Value

There have been many experiments conducted regarding this constant. Novel methods have been developed for the same. Current accepted value according to the National Institute of Standards and Technology is $G = 6.67430(15) \cdot 10^{-11} m^3 kg^{-1} s^{-2}$ with uncertainty of 22 parts per million.

## Usage

The Gravitational Constant is used to calculate the magnitude of gravititional force between two objects. The gravititional force is given by $$F = \frac{Gm_1m _2}{r^2}$$ where, $m_1$ and $m_2$ are the masses of the two bodies and $r$ is the distance between them and G represents the Gravititational Constant. (For more details, consult the article on Gravity)