Equations

velocity = distance/time

Kepler 3: P² = a³ where P = period in years and a = semi-major axis in AU's. This equation can only be used for objects orbiting a 1 $\rm M_{\odot}$ star (i.e. the Sun).

A better form is

$$P^2 = \frac{4 \pi^2 a^3}{ G(M1 + M2)}$$ (1)

P is in seconds, M in kilograms and a in meters here. This can be used for ANY system.

Newton's Universal Law of Gravitation

$$F = G \frac{M1 M2}{r^2}$$ (2)

where F is in Newtons, M1, M2 are in kg and r, the distance separating the objects, is in m.

Newtons Second Law F=ma where a here is acceleration (i.e. acceleration due to a planets gravity = g on Earth) in m s^-2

Small Angle Formula

$$D = \frac{\alpha d}{206265}$$ (3)

where D and d are in meters and $\alpha$ is in arcsec ('')