## 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 10^{6} feet

*mean radius of the moon*

Mu_{moon} = 1.727 x 10^{14} ft^{3}/sec^{2}

*G * mass of the moon*

To convert Mu to km^{3}/sec^{2},
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 10^{16} ft^{3}/sec^{2}

Mu_{Sun} = 4.680 x 10^{21} ft^{3}/sec^{2}

Mu_{Mars} = 1.515 x 10^{15} ft^{3}/sec^{2}

MP/PV = i / ( 1 - 1 + i )^^{-n}

*Mortgage payment on your rocket ship*

a_{geo} = 1.38598 x 10^{8} 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

ASI W9700389r1.0.
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Updated Sat, Oct 4, 1997.