Gravitation

Newton's law of gravitation states that every particle of matter in the universe attracts every other particle with a force $F=\frac{G{m}_1{m}_2}{r^2}$, acting along the line joining them, where $G$ is the universal gravitational constant, $6.67\times 10^{-11}\mathrm{N}{\mathrm{m}}^2\mathrm{k}{\mathrm{g}}^{-2}$, first measured in the laboratory by Cavendish. Unlike $g$, $G$ is a true constant — the same everywhere

The gravitational potential energy of two point masses $m_1$ and $m_2$ separated by a distance $r$ is $U(r)=-\frac{G{m}_1{m}_2}{r}$, with $U=0$ chosen at $r=\infty$. This is the work done against the attractive gravitational force in bringing the masses together from infinite separation to distance $r$ — since the force itself grows as the masses approach, the work has to be found by summin

Kepler's laws, derived empirically from planetary observations and later shown by Newton to follow from the inverse-square law of gravitation, describe orbital motion:

• The law of orbits: every planet moves in an elliptical orbit with the Sun at one focus.
• The law of areas: the line joining the planet to the Sun sweeps out equal areas in equal times. This follows directly from cons