Editing Orbit (section)

==Specification==
{{Main|Ephemeris}}
{{See also|Keplerian elements}}
Six parameters are required to specify a [[Keplerian orbit]] about a body. For example, the three numbers that specify the body's initial position, and the three values that specify its velocity will define a unique orbit that can be calculated forwards (or backwards) in time. However, traditionally the parameters used are slightly different.

The traditionally used set of orbital elements is called the set of [[Orbital elements|Keplerian elements]], after Johannes Kepler and his laws. The Keplerian elements are six:
* [[Inclination]] (''i'')
* [[Longitude of the ascending node]] (Ω)
* [[Argument of periapsis]] (ω)
* [[orbital eccentricity|Eccentricity]] (''e'')
* [[Semimajor axis]] (''a'')
* [[Mean anomaly]] at [[Epoch (astronomy)|epoch]] (''M''<sub>0</sub>).

In principle, once the orbital elements are known for a body, its position can be calculated forward and backward indefinitely in time. However, in practice, orbits are affected or [[Perturbation (astronomy)|perturbed]], by other forces than simple gravity from an assumed point source (see the next section), and thus the orbital elements change over time.

Note that, unless the eccentricity is zero, ''a'' is not the average orbital radius. The time-averaged orbital distance is given by:<ref>{{cite book | title=Comets II | first1=M. | last1=Festou | first2=H. Uwe | last2=Keller | first3=Harold A. | last3=Weaver | year=2004 | page=157 | issue=2 | isbn=9780816524501 | publisher=University of Arizona Press | url=https://books.google.com/books?id=ehA8EAAAQBAJ&pg=PA157 }}</ref>

:<math>\bar{r} = a \left(1 + \frac{e^2}{2} \right)</math>

===Orbital planes===
{{Main|Orbital plane}}
The analysis so far has been two dimensional; it turns out that an [[perturbation theory|unperturbed]] orbit is two-dimensional in a plane fixed in space, and thus the extension to three dimensions requires simply rotating the two-dimensional plane into the required angle relative to the poles of the planetary body involved.

The rotation to do this in three dimensions requires three numbers to uniquely determine; traditionally these are expressed as three angles.

===Orbital period===
{{Main|Orbital period}}
The orbital period is simply how long an orbiting body takes to complete one orbit.