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Thus mean anomaly is also [6] = . Mean angular motion can also be expressed, = , where μ is the gravitational parameter, which varies with the masses of the objects, and a is the semi-major axis of the orbit. Mean anomaly can then be expanded, = , and here mean anomaly represents uniform angular motion on a circle of radius a. [7]
Expanding mean motion by expanding μ, = (+), where M is typically the mass of the primary body of the system and m is the mass of a smaller body. This is the complete gravitational definition of mean motion in a two-body system.
Mean anomaly, a measure of time in the study of orbital dynamics Pioneer anomaly , the observed deviation of the trajectories of some uncrewed space probes, and especially Pioneer 10 and Pioneer 11 South Atlantic Anomaly , an area where the Earth's inner Van Allen radiation belt comes closest to the Earth's surface
An orbiting body's mean longitude is calculated L = Ω + ω + M, where Ω is the longitude of the ascending node, ω is the argument of the pericenter and M is the mean anomaly, the body's angular distance from the pericenter as if it moved with constant speed rather than with the variable speed of an elliptical orbit.
Anomaly detection finds application in many domains including cybersecurity, medicine, machine vision, statistics, neuroscience, law enforcement and financial fraud to name only a few. Anomalies were initially searched for clear rejection or omission from the data to aid statistical analysis, for example to compute the mean or standard deviation.
Gravity anomaly, difference between the observed gravity and a value predicted from a model Bouguer anomaly, anomaly in gravimetry; Free-air anomaly, gravity anomaly that has been computed for latitude and corrected for elevation of the station; Iridium anomaly, an unusual abundance of what is normally a very rare element in the Earth's crust
Such functions can be expressed as periodic series of any continuously increasing angular variable, [6] and the variable of most interest is the mean anomaly, M. Because it increases uniformly with time, expressing any other variable as a series in mean anomaly is essentially the same as expressing it in terms of time.
where the epoch is expressed in terms of Terrestrial Time, with an equivalent Julian date. Four of the elements are independent of any particular coordinate system: M is mean anomaly (deg), n: mean daily motion (deg/d), a: size of semi-major axis (AU), e: eccentricity (dimensionless).