In celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on the orbits of artificial satellites. Lunar theory, the eccentric anomaly is an angular In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other ( parameter In mathematics, statistics, and the mathematical sciences, a parameter is a quantity that serves to relate functions and variables using a common variable (often t) when such a relationship would be difficult to explicate with an equation. In different contexts the term may have special uses that defines the position of a body that is moving along an elliptic In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is perpendicular to the axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same Kepler orbit In celestial mechanics, a Kepler orbit describes the motion of an orbiting body as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. It considers only the gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag,.
For the point p=(x,y) on an ellipse with the equation
the eccentric anomaly is the angle E such that
The eccentric anomaly is one of three angular parameters ("anomalies") that define a position along an orbit; the other two being the true anomaly In celestial mechanics, the true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse and the mean anomaly In celestial mechanics, the mean anomaly is a parameter that defines the position of a body that is moving in a Kepler orbit. It is defined as the time since the last periapsis times 2π / T, where T is the duration of a full orbit.
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