THE ARTEMIS PROJECT PRIVATE ENTERPRISE ON THE MOON Orbital Mechanics Section M 3.12.
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## 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

Rmoon = 5.70 x 106 feet
mean radius of the moon

Mumoon = 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.

Vc = sqrt( Mu/r )
Circular orbital velocity

Vesc = 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

MuEarth = 1.408 x 1016 ft3/sec2

MuSun = 4.680 x 1021 ft3/sec2

MuMars = 1.515 x 1015 ft3/sec2

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

ageo = 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
 Orbital Mechanics
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