📂Classical Mechanics

Law of Universal Gravitation: Gravity

Law of Universal Gravity¹

The law of universal gravity, announced by Newton through his Principia in 1687, is a physical law that simply states “every object attracts every other object”. To describe this concept in detail:

Every particle of matter in the universe with mass 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 their centers.

The above statement, when expressed in mathematical terms, is as follows:

$$\mathbf{F}_{ij} = G\frac{m_{i}m_{j}}{r_{ij}^{2}}\frac{\mathbf{r}_{ij}}{|\mathbf{r}_{ij}|}$$

$\mathbf{F}_{ij}$ denotes the force experienced by a particle $i$ with mass $m_{i}$ due to the influence of another particle $j$ with mass $m_{j}$. According to the law of action-reaction, $\mathbf{F}_{ij}=-\mathbf{F}_{ji}$ holds true. The proportionality constant $G$ is known as the gravitational constant, and its value in SI units is as follows:

$$G=(6.67259\pm0.00085)\times 10^{-11}\mathrm{Nm^{2}kg^{-2}}$$

This force $\mathbf{F}$ is called gravity.