Index:Mécanique céleste Vol 4.djvu
CONTENTS OF THE FOURTH VOLUME. PARTICULAR THEORIES OF THE MOTIONS OF THE HEAVENLY BODIES. EIGHTH BOOK. THEORY OF THE SATELLITES OF JUPITER, SATURN, AND URANUS. Object of this theory [6019] 1 CHAPTER I. EQUATIONS OF THE MOTIONS OF THE SATELLITES OF JUPITER 1 The reciprocal action of the satellites, the sun's attraction, and the oblateness of the spheroid of Jupiter, arc noticed [6020—6077] § 1, 2 CHAPTER II. ON THE INEQAULITIES OF THE MOTIONS OF JUPITER'S SATELLITES, WHICH ARE INDEPENDENT OF THE EXCENTRICITIES AND INCLINATIONS OF THEIR ORBITS 17 Development of the equations of the motions of these satellites. Analytical expressions of the perturbations of their radii vectores and of their longitudes. The sun*s action produces an inequality analogous to the variation in the lunar theory [6078–6125] § 3 Investigation of the terms of these expressions which can acquire considerable values by the divisors introduced by integration; these divisors being very small, in consequence of the nearly commensurable ratios of the mean motions of the three inner satellites. Necessity of retaining, in these small divisors, the terms depending on the product of the constant part of the disturbing force by the variation of the radius vector, this product having a sensible influence upon their values [6125′–6171] § 4 Effect of terms of this kind on the times of the eclipses of the three inner satellites. All the inequalities produced by such terms depend upon the same angle, having a common period of 437days,650. This result is conformable to observation [6173–6193] §5 CHAPTER III. ON THE INEallALmES OF THE MOTIONS OP THE SATELLITES DEPENDING ON THB BXCBfTRICITIES OF THE ORBITS « 38 Expression of the different equations of the centre of the satellites, and of the motions of their [6194–6244″] § 6 Investigation of the terms which can become sensible by the effect of small divisors, introduced by integration, although they may be multiplied by the excentricitics, which are very small [6245–6270] § 7 The sun's action produces also in the motion of the satellites some sensible inequalities, depending on the excentricities. Expression of these inequalities. That which affects the longitude is composed of two parts analogous to the evection and to the annual equation in the lunar theory [6271–6294] § 8 CHAPTER IV. ON THE INEQUALITIES OF THE SATELLITES IN LATITUDE 62 Analytical expressions of the latitude of a satellite and of the motion of its nodes [6295–6336] § 9 The part of this expression which depends on the displacements of the equator and of the orbit of Jupiter, represents the latitude which each satellite would have, if it should move in an intermediate plane which passes between the equator and orbit of Jupiter, through their common intersection. This effect is analogous to that which the earth produces upon the moon, as we have seen in [5352, &c.], but it is much more sensible. Determination of its value [6337–6431]; § 10 Investigation of the terms which acquire very small divisors by integration in the expression of the latitude, in consequence of the nearly commensurable values of the mean motions of the three inner satellites. Estimates of their values [6432–6486] § 11 CHAPTER V. INEQUALITIES DEPENDING ON THE SQUARES AND PRODUCTS OF THE EXCENTRICITIES AND INCLINATIONS OF THE ORBITS 102 Calculation of these inequalities. It is sufficient to notice those only which have a long period [6487–6524] § 12 The terms which become the most important in the secular equations of the satellites, are those which depend on the secular variations of the equator and of the orbit of Jupiter, and on the motion of the nodes of the fourth satellite. They are analogous to those which produce the moon's secular equation, and the equation of the moon's motion depending on the longitude of its nodes. Calculation of these terms [6525–6555'] § 13 CHAPTER VI. ON THE INEQUALITIES DEPENDING ON T[IE SQUARE OF THE DISTURBING FORCE. 126 The most remarkable of these inequalities has already been discussed under its general form, in Book II. [1214' — 1242y]. It depends on the circumstance, that, at the origin of the motion, the mean longitude of the first satellite, minus three times that of the second, plus twice that of the third, was very nearly equal to the semi-circumference π ; and subsequently, by means of the mutual action of the three bodies upon each other, it became accurately equal to π. Development of the theory of these motions by a different method from that which is used in [1214', &c.]. From this it follows, as in [1242v], that the mean motions of the three inner satellites are subjected to a species of libration, and it is of importance for astronomers to investigate and determine the limits of this libration by observations. Hitherto it has appeared to be insensible. From this it follows that the relation which now exists between the mean motions of the three inner satellites, will continue unchanged to future ages. 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