anomaly

Anomaly. The geometry of true anomaly, u, and eccentric anomaly, E. An angle used in describing the motion of a body in an elliptical orbit. The true anomaly, v, is the angle between the line joining the body B to the focus of the ellipse, F, and the line joining F to periapsis the point on the orbit closest to F (see illustration). The mean anomaly, M, is the angle between the line PF and the line joining F to a hypothetical body that has the same orbital period as the real one under consideration but travels at a uniform angular speed. The eccentric anomaly, E, is a useful parameter for expressing the variable length of the radius vector, r. The linking equation is r = a (1 - e cos E) where a is the semimajor axis and e the eccentricity of the elliptical orbit. The relationship between M and E, M= E - e sinE, is known as Kepler's equation.