thumb|the eccentric anomaly of point p is the angle e. the center of the ellipse is point c, and the focus is point f. in celestial mechanics, eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic kepler orbit. for a point p orbiting in an ellipse, the eccentric anomaly is the angle e in the figure to the right. it is determined by drawing a vertical line from the major axis of the ellipse through the point p and locating its intercept pâ² with the auxiliary circle, a circle of radius a (the semi-major axis of the ellipse) that enscribes the entire ellipse. this intersection pâ² is called the corresponding point to p. the radius of the auxiliary circle passing through the corresponding point makes an angle e with the major axis.  the eccentric anomaly is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the true anomaly and the mean anomaly. ==coordinates== if the center of coordinates is taken as the center of the ellipse, the coordinates of a point p(x, y) on the ellipse satisfy the equation :\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \ , where a and b are the semi-major and semi-minor axes determining the length (2a) and width (2b) of the ellipse. the eccentric anomaly e in terms of these coordinates is given by: : \cos e = \frac{x}{a}\quad \mathrm {and} \quad \sin e = \frac{y}{b} \ . the above equations can be established by drawing the auxiliary circle of radius a enclosing the elliptical path and the minor auxiliary circle of radius b inscribed within the path. the first equation is established by the definition of e. by extending a vertical line through point p to the auxiliary circle, a right triangle is formed with base that is the x-coordinate of p, and hypotenuse a, establishing the first equation. the second equation is established using the minor auxiliary circle. a horizontal line through p intersects this minor auxiliary circle of radius b, establishing another right triangle with altitude y and hypotenuse b. labeling the adjacent angle eâ²: : \sin e' = \frac{y}{b} \ . it is next established that eâ² = e. from the equation for the ellipse and the pythagorean trigonometric identity: : \frac{y}{b} = \sqrt { 1 - \left( \frac {x}{a}\right) ^2 } = \sqrt { 1 - \cos^2 e } = \sin e \ , establishing eâ² = e. ==formulas== ===radius and eccentric anomaly=== the eccentricity e is defined as: :e=\sqrt{1 
Orbits