Page:Practical astronomy (1902, John Wiley & Sons).djvu/20

2 In Mechanics it was shown that the Earth's undisturbed orbit is an ellipse, having one of its foci at the sun's center, and that the earth's angular velocity is $$ $$ $$ $$

In these expressions $$\theta^\prime$$ is the angle made by the earth's radius vector with any assumed right line drawn through the sun's center, $$\theta$$ that included between the radius vector and the line of apsides estimated from perihelion, and $$n$$ is the mean motion of the earth in its orbit.

From (551), (615) and (616), we have $$ $$ and therefore $$

Since $$e$$ varies but little from $$0.01678$$ (see Art. 185, Young ), we may omit all terms containing the third and higher powers of $$e$$ in the development of the second member of the preceding equation.