Editing Eccentric anomaly (section)

==Graphical representation==
[[File:EccentricAnomaly.svg|thumb|324x324px|The eccentric anomaly of point ''P'' is the angle ''E''. The center of the ellipse is point O, and the focus is point ''F''.]]
Consider the ellipse with equation given by:
:<math>\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, </math>

where ''a'' is the ''semi-major'' axis and ''b'' is the ''semi-minor'' axis.

For a point on the ellipse, ''P''&nbsp;=&nbsp;''P''(''x'',&nbsp;''y''), representing the position of an orbiting body in an elliptical orbit, the eccentric anomaly is the angle ''E'' in the figure. The eccentric anomaly ''E'' is one of the angles of a right triangle with one vertex at the center of the ellipse, its adjacent side lying on the ''major'' axis, having hypotenuse ''a'' (equal to the ''semi-major'' axis of the ellipse), and opposite side (perpendicular to the ''major'' axis and touching the point ''P′'' on the auxiliary circle of radius ''a'') that passes through the point ''P''. The eccentric anomaly is measured in the same direction as the true anomaly, shown in the figure as <math>\theta</math>. The eccentric anomaly ''E'' in terms of these coordinates is given by:<ref name=Wentworth>
{{cite book |title=Elements of analytic geometry |author=George Albert Wentworth |authorlink=George A. Wentworth |page=[https://archive.org/details/elementsanalyti02wentgoog/page/n159 141] |url=https://archive.org/details/elementsanalyti02wentgoog |chapter=The ellipse §126 |edition=2nd |publisher=Ginn & Co. |year=1914}}</ref>
:<math>\cos E = \frac{x}{a} ,</math>

and
:<math>\sin E = \frac{y}{b}</math>

The second equation is established using the relationship
:<math>\left(\frac{y}{b}\right)^2 = 1 - \cos^2 E = \sin^2 E</math>,

which implies that {{nowrap|1=sin ''E'' = ±{{sfrac|''y''|''b''}}}}. The equation {{nowrap|1=sin ''E'' = −{{sfrac|''y''|''b''}}}} is immediately able to be ruled out since it traverses the ellipse in the wrong direction. It can also be noted that the second equation can be viewed as coming from a similar triangle with its opposite side having the same length ''y'' as the distance from ''P'' to the ''major'' axis, and its hypotenuse ''b'' equal to the ''semi-minor'' axis of the ellipse.