Simple Geometry 

Circle, circumference 
2 * [pi] * r 
Circle, area 
[pi] * r^{2} 
Sphere, volume 
(4/3) * [pi] * r^{3} 
Sphere, area 
4 * [pi] * r^{2} 
Newton's law of gravity 

Useful for calculating the gravitational force (F) on the surface of a planet. (F) is in m/s^{2} 
F = G * (m / r^{2})
m = objects mass in kilograms [kg]
r = objects radius in meters [m]

Calculating escape velocity 

Calculate escape velocity v_{esc}. v_{esc} is in m/s 
v_{esc} = (2 * G * (m / r))^{1/2}
m = objects mass in kilograms [kg]
r = objects radius in meters [m]

Calculating orbital period 

Calculate orbital period for a planet around a star. It's so simple, it's scary! :) 
P = R^{3/2}
P = Orbital period in years (Earth years)
R = Distance between host star and planet in astronomical units (AU)

Hubble's law 

Used to calculate the expansion of the Universe. The speed (v) at which a galaxy seems to move away from us is proportional to the distance (r) to that galaxy. 
v = H * r
v = velocity (speed)
H = Hubble's constant (about 71km/s/Mpc) (Mpc=Mega parsec)
r = Distance

Density 

Density is of course mass/volume. Density (D) is usually in metric tons / m^{3}. 
D=m/V
m = objects mass in metric tons [t], (1t=1000kg)
V = objects volume in meters^{3} [m^{3}]
