# The Formulas

Useful formulas for calculating simple astronomical data seen in the table on the previous page.

Here are some of the constants used in the formulas:
• pi = ~ 3.14159265358
• G = ~ 6.672 * 10 e -11 (Gravitational constant)
• AU = ~ 149,597,871 km (AU= Astronomical Unit, the average distance between Earth & Sun)

Simple Geometry
Circle, circumference 2 * [pi] * r
Circle, area [pi] * r2
Sphere, volume (4/3) * [pi] * r3
Sphere, area 4 * [pi] * r2
Newton's law of gravity
Useful for calculating the gravitational force (F) on the surface of a planet. (F) is in m/s2 F = G * (m / r2)
m = objects mass in kilograms [kg]
r = objects radius in meters [m]
Calculating escape velocity
Calculate escape velocity vesc. vesc is in m/s vesc = (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 = R3/2
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 / m3. D=m/V
m = objects mass in metric tons [t], (1t=1000kg)
V = objects volume in meters3 [m3]

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