Investigation of inequalities in the motion of the moon produced by the action of the planets

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1907 Excerpt: ...determining the action of the Sun itself. It would therefore be necessary, in strictness, to include the effect of any corrections that may be necessary to the elements of the Sun's motion employed by Delaunay. But as the eccentricity of the Earth's orbit enters as a symbolic quantity into the theories of both Delaunay and Brown, it will not be necessary to apply any correction on this account. The same remark applies to the position of the Earth's perihelion. But as the solar elements are assumed to be constant in the first integration it is necessary to take into account the effects of their secular variations, as well as of the periodic inequalities. Moreover, in developing the action of the Sun upon the Moon for the first integration, it is assumed that the mean distance of the Earth's orbit is strictly connected with its mean motion by the fundamental relation cfn2 = m' + p It is therefore necessary to include in Sp' the constant correction arising from the action of the planets. We may conveniently classify the various terms of 8v' and 8p' which are to be used in the expressions (60) as follows: 1. The terms arising from the secular variation of the eccentricity of the Earth's orbit. 2. Constant and periodic terms independent of the mean longitude of the disturbing planet. 3. Periodic terms containing that mean longitude. § 44. Secular terms arising from the variation of the eccentricity of the Earth's orbit. The action of the Sun upon the Moon being a function of the eccentricity of the Earth's orbit it follows that the indirect action will vary with that element. The variation may be taken account of by assigning to Sv' and 8p' the increments of the 87 f Earth's polar coordinates due to the variation of the eccentricity. It is not necessary to ...