Kepler ellipses

Further, the co-ordinates of the electrical centre of gravity for a charge revolving in a Kepler ellipse are the time averages of the actual co-ordinates and rj, thus... 

The field of force of the core of an atom is, at a sufficiently great distance, a Coulomb- field of force. In the case of the neutral atom it corresponds to the effective nuclear charge Z=l, in the case of the 1-, 2-. . . fold ionised atom Z=2, 3. . . respectively. The orbits of the radiating electron at a large distance are therefore similar to those in the case of hydrogen. They differ from the Kepler ellipses only by the fact that the perihelion executes a slow rotation in the plane of the orbit. The semi-axes and parameter of the ellipses are, by (9), (10), and (11) of 22,... 

In the normal state, hydrogen (1 H) has an electron in an orbit with the principal quantum number 1. As long as the orbit is regarded as an exact Kepler ellipse the subsidiary quantum number is undetermined. We shall see, however, on taking into account the relativity theory in 33, that the total angular momentum is also to be fixed by a quantum condition, without thereby appreciably altering the energy. The normal orbit of the electron is thus a lj-orbit. 

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