How to Calculate Orbits

These equations describe the period of a satellite in orbit about the moon.

Orbital period: T = 2 * Pi * a * sqrt( a / mu )

Radius of orbit: a = ( T * sqrt(Mu) / ( 2 * Pi ) )^(2/3)

Where:

T = orbital period, the time it takes for the satellite to make one trip around

Pi = 3.14159
In an Excel spreadsheet, use Pi()

a = semimajor axis of the orbital ellipse (radius for a circular orbit)

Mu = G * mass of the primary

G is the universal gravitational constant

R_moon = 5.70 x 10⁶ feet
mean radius of the moon

Mu_moon = 1.727 x 10¹⁴ ft³/sec²
G * mass of the moon

To convert Mu to km³/sec², multiply by 2.831 x 10^-11. Don't forget to include the mean radius of the moon when calculating a.

Some other useful equations and constants.

V_c = sqrt( Mu/r )
Circular orbital velocity

V_esc = sqrt( 2 * Mu / r )
Escape velocity

V = sqrt( Mu * ( 2/r - 1/a ) )
Velocity for an elliptical orbit when you're distance r from the planet

Mu_Earth = 1.408 x 10¹⁶ ft³/sec²

Mu_Sun = 4.680 x 10²¹ ft³/sec²

Mu_Mars = 1.515 x 10¹⁵ ft³/sec²

MP/PV = i / ( 1 - 1 + i )^^-n
Mortgage payment on your rocket ship

a_geo = 1.38598 x 10⁸ feet
Earth geosynchronous orbit, as a check case

Satellite orbits are often expressed in nautical miles (which are based on the circumference of Earth at the equator).

1 nautical mile = 6076.10333 feet