In the study of orbital dynamics the mean anomaly of an orbiting body is the angle the body would have traveled about the center of the orbit's auxiliary circle. In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called Unlike other measures of anomaly, the mean anomaly grows linearly with time. The mean anomaly is conceptually an orbital clock that reads from 0 to 360 degrees or from 0 to 2π radians, passing "midnight" (zero) and restarting at perigee when each new orbit begins.

Because of the linear growth with time, the mean anomaly makes calculating the time of flight between two points on the orbit very easy. The mean anomalies for the two points are calculated and their difference is found. Knowing this, the ratio of this difference relative to the entire encompassing one orbit is simply equal to ratio of the time of flight to the period of one whole orbit (i. The orbital period is the time taken for a given object to make one complete Orbit about another object e. $\frac{M_2 - M_1}{2\pi} = \frac{t}{T}$).

When measured in radians the mean anomaly has a value of 0 at the initial crossing of the orbit's point of periapsis, and a multiple of at any later crossing of the point periapsis. The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from In the diagram below, the mean anomaly of point p on the orbit around s is given by angle M (the angle $\angle zcy$).

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. In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae In Geometry, the semi-minor axis (also semiminor axis) is a Line segment associated with most Conic sections (that is with ellipses and In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a Or, in other words, the circular sector area z-c-y is equal to the area x-s-z.

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. Orbital mechanics or astrodynamics is the application of Celestial mechanics to the practical problems concerning the motion of Rockets and other Spacecraft Mean motion, n\\! is a measure of how fast a Satellite progresses around its Orbit.

Alternatively:

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

where:

• $E\,\!$ is orbit's eccentric anomaly,
• $e\,\!$ is orbit's eccentricity. The eccentric anomaly is the angle between the direction of Periapsis and the current position of an object on its Orbit, projected onto the ellipse's circumscribing In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape