Editing Mean anomaly (section)

==Definition==
Define {{mvar|T}} as the time required for a particular body to complete one orbit. In time {{mvar|T}}, the [[radius vector]] sweeps out 2{{pi}} radians, or 360°. The average rate of sweep, {{mvar|n}}, is then 

<math display="block">n = \frac{\,2\,\pi\,}{T} = \frac{\,360^\circ\,}{T}~,</math> 

which is called the ''[[mean motion|mean angular motion]]'' of the body, with dimensions of radians per unit time or degrees per unit time.

Define {{mvar|&tau;}} as the time at which the body is at the pericenter. From the above definitions, a new quantity, {{mvar|M}}, the ''mean anomaly'' can be defined 

<math display="block">M = n\,(t - \tau) ~,</math> 

which gives an angular distance from the pericenter at arbitrary time {{mvar|t}}<ref>
{{cite book 
 | last = Smart
 | first = W. M.
 | title = Textbook on Spherical Astronomy
 | publisher = Cambridge University Press, Cambridge
 | year = 1977
 | edition = sixth
 | ISBN = 0-521-29180-1
 | page = 113
}}</ref> with dimensions of radians or degrees.

Because the rate of increase, {{mvar|n}}, is a constant average, the mean anomaly increases uniformly (linearly) from 0 to 2{{pi}} radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, {{pi}} radians (180°) at the [[apsis|apocenter]], and 2{{pi}} radians (360°) after one complete revolution.<ref>Meeus (1991), p. 183</ref> If the mean anomaly is known at any given instant, it can be calculated at any later (or prior) instant by simply adding (or subtracting) {{mvar|n⋅δt}} where {{mvar|δt}} represents the small time difference.

Mean anomaly does not measure an angle between any physical objects (except at pericenter or apocenter, or for a circular orbit). It is simply a convenient uniform measure of how far around its orbit a body has progressed since pericenter. The mean anomaly is one of three angular parameters (known historically as "anomalies") that define a position along an orbit, the other two being the [[eccentric anomaly]] and the [[true anomaly]].

===Mean anomaly at epoch===
The ''mean anomaly at epoch'', {{mvar|M}}{{sub|0}}, is defined as the instantaneous mean anomaly at a given [[Epoch (astronomy)|epoch]], {{mvar|t}}{{sub|0}}. This value is sometimes provided with other orbital elements to enable calculations of the object's past and future positions along the orbit. The epoch for which {{mvar|M}}{{sub|0}} is defined is often determined by convention in a given field or discipline. For example, planetary ephemerides often define {{mvar|M}}{{sub|0}} for the epoch [[J2000]], while for earth orbiting objects described by a [[two-line element set]] the epoch is specified as a date in the first line.<ref>{{Cite web |title=Space-Track.org |url=https://www.space-track.org/documentation#/tle |access-date=2024-08-19 |website=www.space-track.org}}</ref>