Gravitation

Newton's Law of Gravitation

Any particle in the universe attracts any other particle with a gravitational force whose magnitude is

$$F=G\frac{m_1{m}_2}{r^2}$$

where $m_1$ and $m_2$ are the masses of the two particles, $r$ is the distance between them, and $G=6.67\times {10}^{-11}N\cdot m^2/k{g}^2$ is the gravitational constant.

Acceleration due to gravity at any distance from earth is then given as:

$$a_g=\frac{G{M}_E}{r^2}$$

where $M_E$ is the mass of earth, about $5.98\times {10}^{24}kg.$

A uniform shell of matter exerts no net gravitational force on a particle located inside it.