Gravitation — Formula Sheet

All planets move in elliptical orbits with the Sun situated at one of the foci

The line that joins any planet to the Sun sweeps equal areas in equal intervals of time

The square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet.

\Delta A / \Delta t = \frac{1}{2} (r \times p) / m = L / (2 m)

|\mathbf{F}| = G \frac{m_1 m_2}{r^2}

\mathbf{F} = G \frac{m_1 m_2}{r^2} (-\hat{\mathbf{r}}) = -G \frac{m_1 m_2}{r^2} \hat{\mathbf{r}}

G \frac{Mm}{d^2} L = \tau \theta

g = \frac {G M _ {E}}{R _ {E} ^ {2}}

g (h) \equiv g \left(1 - \frac {2 h}{R _ {E}}\right)

g(d) = g \frac{R_E - d}{R_E} = g(1 - d / R_E)

V = -\frac{G m_1 m_2}{r}

W(r) = -\frac{G M_E m}{r} + W_1

U(r) = \frac{G M}{r}