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.

[edit] Calculation

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.

[edit] See also

v • d • e Orbits
Orbit types	Box orbit • Circular orbit • Ecliptic orbit • Elliptic orbit • Highly Elliptical Orbit • Graveyard orbit • Hyperbolic trajectory • Inclined orbit • Osculating orbit • Parabolic trajectory • Capture orbit • Escape orbit • Semi-synchronous orbit • Subsynchronous orbit • Synchronous orbit
Earth-centered orbits	Geosynchronous orbit • Geostationary orbit • Sun-synchronous orbit • Low Earth orbit • Medium Earth Orbit • Molniya orbit • Near equatorial orbit • Orbit of the Moon • Polar orbit • Polar sun synchronous orbit • Tundra orbit
Other orbits	Areosynchronous orbit • Areostationary orbit • Lissajous orbit • Lunar orbit • Heliocentric orbit • Heliosynchronous orbit
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 ( $T\,$ )
Orbital maneuvers	Bi-elliptic transfer • Geostationary transfer orbit • Gravitational slingshot • Hohmann transfer orbit • Orbital inclination change • Orbit phasing • Space rendezvous
Other orbital mechanics topics	Apsis • Celestial coordinate system • Delta-v budget • Epoch • Ephemeris • Equatorial coordinate system • Ground track • Interplanetary Transport Network • Kepler's laws of planetary motion • Lagrangian point • List of orbits • n-body problem • Orbit equation • Orbital state vectors • Retrograde and direct motion • Specific orbital energy • Specific relative angular momentum