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The true anomaly of point P is the angle f. The center of the ellipse is point C, and the focus is point F.
In celestial mechanics, 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 (the point around which the object orbits).
The true anomaly is usually denoted by the Greek letters? or ?, or the Latin letterf, and is usually restricted to the range 0-360° (0-2?c).
As shown in the image, the true anomaly f is one of three angular parameters (anomalies) that defines a position along an orbit, the other two being the eccentric anomaly and the mean anomaly.
An equivalent form avoids the singularity as e -> 1, however it does not produce the correct value for :
or, with the same problem as e -> 1 ,
In both of the above, the function arg(x, y) is the polar argument of the vector (xy), available in many programming languages as the library function named atan2(y,x) (note the reversed order of x and y).