Gravitation

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 $G = 6.67 \times 10^{-11} N \cdot m^2/kg^2$ is the gravitational constant.

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

\[a_g = \frac{GM_E}{r^2}\]

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.