Page:Mécanique céleste Vol 1.djvu/26

xx Method of finding the perturbations in a series arranged according to the powers and products of the excentricities and of the inclinations of the orbits, [933— 948], .; §47

Development of the function of the mutual distances of the bodies of the system, on which their perturbations depend, in a series. Use of the calculus of finite differences in this development. Reflections upon this series [949 — 963] § 48

Formulas for computing its different terms, [964 — 1008] § 49

General expressions of the perturbations of the motion in longitude and in latitude, and of the radius vector, continuing the approximation to quantities of the order of the excentricities and inclinations, [1009—1034] § 50, 51

Recapitulation of these different results, remarks on farther approximations, [1035 — 1036"]. § 52

CHAPTER VII. ON THE SECULAR INEaUALITIES OF THE MOTIONS OF THE HEAVENLV BODIES. 569 These inequalities arise from the terms which, in the expressions of the perturbations, contain the time without the periodical signs. Differential equations of the elements of the elliptical motion, which make these terms disappear, [1037 — 1051] § 53

In taking notice only of the first power of the disturbing force, the mean motions of the planets will be uniform, and the transverse axes of their orbits constant, [1051' — 1070^^^]. ... § 54

Development of the differential equations relative to the excentricities and to the position of the perihelia, in any system of orbits in which the excentricities and mutual inclinations are small, [1071—1095] §55

Integration of these equations. Determination of the arbitrary constant quantities of the integral, by means of observations, [1096 — 1111] § 56

The system of the orbits of the planets and satellites, is stable, as it respects the excentricities; that is, these excentricities remain always very small, and the system merely oscillates about its mean state of ellipticity, from which it varies but little, [1111'" — 1118] §57

Differential expressions of the secular variations of the excentricity and of the position of the perihelion, [1118^— 1126^] §58

Integration of the differential equations relative to the nodes and inclinations of the orbits. In the motions of a system of orbits, which are very little inclined to each other, the mutual inclinations remain always very small, [1127 — 1139] § 59

Differential expressions of the secular variations of the nodes and of the inclinations of the orbits; first, with respect to a fixed plane; second, with respect to the moveable orbit of one of the bodies of the system, [1140—1146] § 60

General relations between the elliptical elements of a system of orbits, whatever be their excentricities and their mutual inclinations, [1147 — 1161] § 61

Investigation of the invariable plane, or that upon which the sum of the masses of the bodies of the system, multiplied respectively by the projections of the areas described by their radii vectores, in a given time, is a maximum. Determination of the motion of two orbits, inclined to each other by any angle, [1162 — 1167] § 62