Editing Orbital elements (section)

=== Classical Keplerian elements {{anchor|Keplerian}} ===
While in theory, any set of elements that meets the requirements above can be used to describe an orbit, in practice, certain sets are much more common than others.

The most common elements used to describe the size and shape of the orbit are the semi-major axis ({{Mvar|a}}), and the eccentricity ({{Mvar|e}}). Sometimes the semi-parameter ({{Mvar|p}}) is used instead of {{Mvar|a}}, as the semi-major axis is infinite for parabolic trajectories, and thus cannot be used.<ref name=":02" /><ref name=":0">{{Cite web |last=Weber |first=Bryan |title=Orbital Mechanics |url=https://orbital-mechanics.space/intro.html |access-date=21 February 2025 |website=Orbital Mechanics |at="Orbital Nomenclature", and "Classical Orbital Elements"}}</ref>

It is common to specify the period ({{Mvar|P}}) or mean motion ({{Mvar|n}}) instead of the semi-major axis in Keplerian element sets, as each can be computed from the other provided the [[standard gravitational parameter]] (<math>\mu</math>) is known for the central body though the relations above.

For the epoch, the epoch time ({{Mvar|t}}) along with the [[mean anomaly]] ({{math|''M''<sub>0</sub>}}), [[mean longitude]] ({{math|''L''<sub>0</sub>}}), [[true anomaly]] (<math>\nu_0</math>) or (rarely) the [[eccentric anomaly]] ({{math|''E''<sub>0</sub>}}) are often used. The time of periapsis passage ({{math|''T''<sub>0</sub>}}) is also sometimes used for this purpose.<ref name=":0" />

It is also quite common to see either the mean anomaly or the mean longitude expressed directly, without either {{math|''M''<sub>0</sub>}} or {{math|''L''<sub>0</sub>}} as intermediary steps, as a [[Linear function (calculus)|linear function]] of time. This method of expression will consolidate the mean motion as the slope of this linear equation. An example of this is provided below:{{Indent|5}}<math>M(t)=M_{0}+n(t-t_{0})</math>