Editing Orbital elements (section)

==== Relations between elements ====
This section contains the common relations between the set of orbital elements described above, but more relations can be derived through manipulations of one or more of these equations. The variable names used here are consistent with the ones described above.

Mean motion can be calculated using the standard gravitational parameter and the semi-major axis of the orbit (''{{Mvar|μ}}'' can be substituted for {{Math|GM}}). This equation returns the mean motion in radians, and will need to be converted if ''{{Mvar|n}}'' is desired to be in a different unit.{{Indent|5}}<math>n=\sqrt{\frac{\mu}{a^{3}}}</math> when <math>a>0</math>, <math>n=\sqrt{\frac{\mu}{-a^{3}}}</math> when <math>a<0</math>

Because the semi-major axis is related to the mean motion and standard gravitational parameter, it can be calculated without being specified. This is especially useful if ''{{Mvar|μ}}'' is assumed to be known, as then ''{{Mvar|n}}'' can be used to calculate ''{{Mvar|a}}'', and likewise for specifying ''{{Mvar|a}}''. This can allow one less element to specified.

Orbital period can be found from ''{{Mvar|n}}'' given the fact that the mean motion can be described as a frequency (number of orbits per unit time), which is the inverse of period.{{Indent|5}}<math>P=\frac{2\pi}{n}</math>if ''{{Mvar|n}}'' is in radians, or <math>P=\frac{360^\circ}{n}</math> if ''{{Mvar|n}}'' is in degrees.

The standard gravitational parameter can be found given the mean motion and the semi-major axis through the following relation (assuming that ''{{Mvar|n}}'' is in radians):{{Indent|5}}<math>\mu=n^{2}a^{3}</math>

The mass of the central body can be found given the standard gravitational parameter using a rearrangement of its definition as the product of the mass and the gravitational constant.{{Indent|5}}<math>M=\frac{\mu}{G}</math>