Mean anomaly

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In the study of orbital dynamics the mean anomaly is a measure of time, specific to the orbiting body p, which is a multiple of 2π radians at and only at periapsis. It is the fraction of the orbital period that has elapsed since the last passage at periapsis z, expressed as an angle. In the diagram below, it is M (the angle zcy).

The point y is defined such that the circular sector area z-c-y is equal to the elliptic sector area z-s-p, scaled up by the ratio of the major to minor axes of the ellipse. Or, in other words, the circular sector area z-c-y is equal to the area x-s-z.

In astrodynamics mean anomaly $M\,\!$ can be calculated as follows:

$M - M_0=n(t-t_0)\,\!$

where:

$M_0\,\!$ is the mean anomaly at time $t_0\,\!$ ,
$t_0\,\!$ is the start time,
$t\,\!$ is the time of interest, and
$n\,\!$ is the mean motion.

Alternatively:

$M=E - e \cdot \sin E\,\!$

where:

$E\,\!$ is orbit's eccentric anomaly,
$e\,\!$ is orbit's eccentricity.

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Orbital elements	Inclination ( $i\,\!$ ) • Longitude of the ascending node ( $\Omega\,\!$ ) • Eccentricity ( $e\,\!$ ) • Argument of periapsis ( $\omega\,\!$ ) • Semi-major axis ( $a\,\!$ ) • Mean anomaly at epoch ( $M_o\,\!$ )
Other orbital parameters	True anomaly ( $v\,$ ) • Semi-minor axis ( $b\,$ ) • Linear eccentricity ( $\epsilon\,$ ) • Eccentric anomaly ( $E\,$ ) • Mean longitude ( $L\,$ ) • True longitude ( $l\,$ ) • Orbital period ( $T\,$ )
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