Page:The Meaning of Relativity - Albert Einstein (1922).djvu/118

106 The calculation of the planetary motion depends upon equation (90). From the first of equations (108b) and (90) we get, for the indices 1, 2, 3,

or, if we integrate, and express the result in polar co-ordinates,

From (90), for $$\mu = 4$$, we get

From this, after multiplication by $$f^2$$ and integration, we have

In (109b), (111) and (112) we have three equations between the four variables $$s$$, $$r$$, $$l$$ and $$\phi$$, from which the motion of the planet may be calculated in the same way as in classical mechanics. The most important result we get from this is a secular rotation of the elliptic orbit of the planet in the same sense as the revolution of the planet, amounting in radians per revolution to