Page:Mécanique céleste Vol 3.djvu/26

xviii Inequalities depending on the third dimension, which become sensible in the theory of Mercury, disturbed by the earth [3869, &c.] §10

The inequalities depending on the second dimension, which affect the motion in latitude of the disturbed planet, introducing similar ones in the motion of the disturbing planet. These are the only inequalities in latitude, which are sensible in the planetary system, among those which depend on the product of the excentricities and inclinations [3886, &c.] §11

CHAPTER II. INEQUALITIES DEPENDING ON THE SQUARE OF THE DISTURBING FORCE 87

Development of the analytical expressions, given in § 65, 69, of the second book. They result from the influence, which the inequalities with a long period have on the terms depending on the square of the disturbing masses [3890, &c.]. The variations of the exoentricities and perihelia may introduce similar inequalities in the mean motions; but, it is proved, that the terms, which arise from these inequalities, mutually destroy each other [3906']. Hence it follows, that the mean motions and the great axes suffer no alteration by the effect of these terms [3906"] § 12

Variations of the excentricities, of the perihelia, of the nodes, and of the inclinations, arising from the second power of the disturbing masses [3908—3936] § 13, 14

These variations do not alter the relations, found in the second book, between the elements of the orbits [3964, &c.] § 15

Examination of the terms of the order of the square of the disturbing masses, which have a sensible influence on the great inequalities of Jupiter and Saturn [3970, &c.] § 16

Corrections which must be introduced in the mean motions of these two planets, in consequence of their great inequalities [4006', &c.] § 17

The coefficients of the inequalities of the planets vary, on account of the secular variations of the elements of the orbits. Method of noticing this subject [4017, &c.] § 18

CHAPTER III. PERTURBATIONS DEPENDING ON THE ELLIPTICITY OF THE SUN 161

This ellipticity gives to the perihelion of the planet a direct motion; and to the nodes of the orbit, upon the plane of the solar equator, a retrograde motion, equal to the preceding [4037', 4045']. These motions decrease rapidly as the distance from the sun increases; they are sensible only in Mercury [4046]. The sun's ellipticity, having no influence on the excentricity of the orbit, nor on the inclination, cannot alter the stability of the solar system [4046] § 18'

CHAPTER IV. PERTURBATIONS OF THE MOTIONS OF THE PLANETS, ARISING FROM THE ACTION OF THEIR SATELLITES 168

These perturbations are found by the theorems of § 10, of the second book. Their magnitudes depend on the masses of the satellites, in comparison with that of the planet, and on their elongations, as seen from the sun. They are sensible only in the theory of the earth disturbed by the moon [4054] § 19

CHAPTER V. CONSIDERATIONS ON THE ELLIPTICAL PART OF THE RADIUS VECTOR, AND ON THE MEAN MOTION OF A PLANET § 20 171