This plane remains invariable so long as no third body acts; when it does act the position of the plane changes very slowly, continually rotating round the radius vector of the planet as an instantaneous axis of rotation.

From the law of angular motion of the latter its radius vector will run ahead of PQ near A, PQ will overtake and pass it at apocentre, and the two will again coincide at pericentre when the revolution is completed.

This is the simplest case of generation of a plane figure by a moving ordinate; the corresponding figure for generation by rotation of a radius vector is a circle.

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The third law enables us to compute the time taken by the radius vector to sweep over the entire area of the orbit, which is identical with the time of revolution.

As the planet revolves around the centre, each radius vector describes a surface of which the area swept over in a unit of time measures the areal velocity of the planet.

P is the position of the planet at any time, and we call r the radius vector FP. The angle AFP between the pericentre and the position P of the planet is the anomaly called v.

The problem of finding a radius vector satisfying this condition is one which can be solved only by successive approximations, or tentatively.

Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

The anomaly is then the angle BFP which the radius vector makes with the major axis.