Editing Orbital elements (section)

=== Motion over time describing elements ===
One parameter is required to describe the speed of motion of the orbiting object around the central body. However, this can be omitted if only a description of the shape of the orbit is required. Various quantities that do not directly describe a speed can be used to satisfy this condition, and it is possible to convert from one to any other (formula below).

* [[Mean motion]] (''{{Mvar|n}}'') — quantity that describes the average [[angular speed]] of the orbiting body, measured as an angle per unit time. For non-circular orbits, the actual angular speed is not constant, so the mean motion will not describe a physical angle. Instead this corresponds to a change in the [[mean anomaly]], which indeed increases linearly with time.
* [[Orbital period]] (''{{Mvar|P}}'') — the time it takes for the orbiting body to complete one full revolution around the central body. This quantity is undefined for parabolic and hyperbolic trajectories, as they are non-periodic.
* [[Standard gravitational parameter]] (''{{Mvar|μ}}'') — quantity equal to the mass of the central body times the [[gravitational constant]] ''{{Mvar|G}}''. This quantity is often used instead of mass, as it can be easier to measure with precision than either mass or ''{{Mvar|G}}'', and will need to be calculated in any case in order to find the acceleration due to gravity. This is also often not included as part of orbital element lists, as it can assumed to be known based on the central body.
* [[Mass]] of the central body (''{{Mvar|M}}'') — the mass of only the central body can be used, as in most cases the mass of the orbiting body is insignificant and does not meaningfully influence the trajectory. However, when this is not the case (e.g. [[binary stars]]), the mass of the [[Two-body problem|2-body system]] can be used instead.

==== 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>