Page:Eddington A. Space Time and Gravitation. 1920.djvu/222

206 The earth's speed, $$v$$, is approximately 30 km. per sec., or $1⁄10000$ in terms of the velocity of light. The radius of its orbit, $$r$$, is about 1.5. 108 km. Hence, $$m$$, the gravitational mass of the sun is approximately 1.5 km.

The radius of the sun is 697,000 kms., so that the quantity $$2m/r$$ occurring in the formulae is, for the sun's surface, .00000424 or 0″.87.

Note 9 (p. 123).

See Report, §§ 29, 30. The general equations of a geodesic are

From the formula for the line-element we calculate the three-index symbols and it is found that two of the equations of the geodesic take the rather simple form  which can be integrated giving  where $$h$$ and $$c$$ are constants of integration.

Eliminating $$dt$$ and $$ds$$ from (1), (2) and (3), we have or writing

Differentiating with respect to $$\theta$$