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Figure 1: Two coplanar ellipses, having one common focus, are assumed to rotate about this focus, always remaining within their plane. Let a planet be located at one of the points of the ellipses' intersection, P, and assume that the rotation of the ellipses is such that the planet is always at the instantaneous point of their intersection. At some instant of time, the rotation of one ellipse will be faster than that of the other. On these grounds one may state that the planet is rapidly moving along the slower rotating ellipse. On the other hand, though, it is also true that the planet is slowly moving along the faster rotating ellipse. Both viewpoints are equally valid, because one can divide, in an infinite number of ways, the actual motion of the planet into a motion along some ellipse and a simultaneous evolution of this ellipse. The Lagrange constraint (7) singles out, of all the sequences of evolving ellipses, that unique ellipse sequence which is always tangential to the physical velocity of the planet.

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