Page:Relativity (1931).djvu/171

proximity to the sun—to perihelion) would differ from 360°. The line of the orbit would not then be a closed one, but in the course of time it would fill up an annular part of the orbital plane, viz. between the circle of least and the circle of greatest distance of the planet from the sun.

According also to the general theory of relativity, which differs of course from the theory of Newton, a small variation from the Newton-Kepler motion of a planet in its orbit should take place, and in such a way, that the angle described by the radius sun-planet between one perihelion and the next should exceed that corresponding to one complete revolution by an amount given by

$+{\frac {24\pi ^{3}a^{2}}{T^{2}c^{2}\left(1-e^{2}\right)}}$.

(N.B.—One complete revolution corresponds to the angle $2\pi$ in the absolute angular measure customary in physics, and the above expression gives the amount by which the radius sun-planet exceeds this angle during the interval between one perihelion and the next.) In this expression $a$ represents the major semi-axis of the ellipse, $e$ its eccentricity, $c$ the velocity of light, and $T$ the period of revolution of the planet. Our result may also be stated as follows: According to the general theory of relativity, the major axis of the ellipse rotates round the sun in the same