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centre of gravity falling within the mass of the primary body, its varia-
tions from that centre may be neglected as having no appreciable influ-
ence on the motion of translation) and thus, celestial mechanics pre-
sents, in this branch, no other problems than those treated, under an-
other point of view, by celestial geometry.
The simplest problem is here, as before that of the planets, and for
the same reasons, the smallness of their eccentricities, and of the incli-
nations of their orbits. There is also a considerable uniformity of pertur-
bations, since each planet remaining in the same regions of the sky,
continues in the same mechanical relations, though their intensity varies
within certain limits. The least privileged of these bodies in these mat-
ters is unhappily our own planet, on account of the heavy satellite which
escorts it so closely, and to which its chief perturbations are due; though
this does not save it from being sensibly troubled by others, at the period
of opposition, and especially by such a mass as that of Jupiter. No other
planet with satellites, not even Jupiter, is in so unfavourable a case; for
Jupiter s motion could not be very much deranged by the action of his
satellites, however near in position, since the mass of the largest is less
than a ten thousandth part of his, while the mass of our moon is a sixty-
eighth part of that of the earth. Jupiter s circulation is sensibly affected
Positive Philosophy/203
by Saturn alone. The simplest case of all seems to be that of Uranus,
from its being the last planet, and very remote from the next; and its six
satellites do not appear to trouble its motion.
The problem of the satellites is necessarily more complicated than
that of the planets, on account of the instability of the focus of the prin-
cipal motion, as in celestial geometry. Besides their own perturbations,
the satellites have reflected upon then all those to which their planet is
liable. The founders of Celestial Mechanics were long perplexed, for
instance, by the perpetual acceleration of the mean motion of the moon;
it was considered inexplicable, till Laplace discovered its cause in the
slight variation to which the eccentricity of the earth s orbit is subject.
In regard to the direct perturbations of the satellites, there is an essential
distinction between the case of one, and that of several satellites. In the
first, the single case of our moon, the disturbing body is the sun, on
account of its unequal action on the planet and the satellite. If the diffi-
culties arising out of this position are greater than in the case of any
other satellite, it is partly because the case more immediately concerns
us, and because our opportunities of observation disclose more fully the
imperfection of our means. For, in the mathematical point of view, there
must be more complexity in the case of several satellites; all that is true
in regard to one being true in regard to each one, with the addition of the
mutual action of the members of the group. Their perturbations are
reduced by the preponderating size of their planet; but from there being
so many of them. of such nearly equal sizes and direction, and all so
close together, the difficulty of calculating their motions is so great that
the only theory as yet established is that of the satellites of Jupiter. For
the motions of three of them, Laplace found means completely to ac-
count. Those of Saturn and Uranus are known only geometrically, we
having not even an approximate estimate of their masses. It is to be
remembered, however, that we do not need so perfect a knowledge of
them as of the moon; and that a much less exact theory will suffice for
them than for the moon, whose slightest irregularity is very evident to
us.
The comets intervene to increase our difficulties about the satel-
lites. From the extreme prolongation of their orbits, and their inclination
in all directions, comets are in a state of ever variable mechanical rela-
tions, from the number of bodies that they approach in their course;
whilst the planets, and even the satellites, have always the same rela-
tions, the variation being only in the intensity. The perturbation which,
204/Auguste Comte
in every other case, bears a very small proportion to the gravitation,
may, in the case of comets, exceed it: so that it is conceivable that a
comet might be diverted from its orbit, and become a satellite, when it
passes near so considerable a body as Jupiter, Saturn, or even Uranus.
Besides the eccentricities of comets, there are other circumstances, such
as their small weight, and their possible loss of weight by parting with
some of their atmosphere to the bodies they approach, which tend to
perplex the study of their perturbations. These are the incidents which
malice it so difficult to foresee exactly the return of these little bodies.
When we have studied them so long and so laboriously as to have, to the
best of our belief, mastered their case, we find that their periods are
entirely changed through one omitted circumstance. A memorable ex-
ample of this was the comet of 1770, calculated be Lexell. This comet
had then a revolution of less than six years: but it has never appeared
since, having been entirely deranged by passing too near Jupiter. The
imperfection of our knowledge about these small bodies is from the
same cause that renders them of very little consequence to us. From
their vast distances, their action upon any one body of the system is
little more than momentary, and their lightness prevents even the satel-
lites from being affected by their passage. The passage of the comet of
1770 among the satellites of Jupiter proved this, in a striking manner.
Their tables, constructed beforehand, without any idea of such an inci-
dent, perfectly agreed with direct observations; a proof that the intru-
sion of the comet did not sensibly affect their motions. There is, there-
fore, no more occasion for the puerile fears of our day than for the
religious terrors of former times, in regard to the passage of comets.
Their collision with the earth is all but im- possible; and they could not
otherwise be felt at all. Their mere approach, however near, could have
no other effect than to raise somewhat the corresponding tide. If a comet
could pass two or three times nearer to us than the moon (which no
known comet could do) its very small mass could produce no other
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