From celestial geometry Comte moves to celestial mechanics, which he, naturally, interprets as the application of mechanics – part of mathematics in his classification – to celestial objects. It is important for Comte that there is no essential difference between earthly and celestial mechanics: there is only the arbitrary fact that we can directly observe the trajectories of earthly objects – e.g. thrown projectiles – but the trajectories of celestial objects we must at first determine through geometrical means. Thus, after Kepler had found the laws of planetary movement, the next step was to merely use mechanics to explain them.
Of course, the application presupposed that mechanics had to be developed into a ripe enough state, which is the reason why Kepler himself couldn’t do it, but had to rely on metaphysical notions like attraction, Comte explains. The notion of attraction, he insists, suggests that there is some agent actively pulling things toward the Sun. The Newtonian word gravity, on the other hand, should describe an intrinsic property of all matter in the Solar System, whether in the Sun or anywhere else – even the earthly objects, like the projectiles, have their own gravity.
Comte thinks that Newtonian notion of gravity is essentially based on the observed phenomena, and he goes into great lengths showing how Newton derived this idea from e.g. Kepler’s laws of motions. Importantly, Comte restricts the use of this notion to what he calls the world – our own Solar System – since we do not, and he thinks, probably will not have enough evidence to determine whether the Newtonian theory applies generally in the wider universe.
Having established Newtonian theory of gravitation, Comte notes that the rest of celestial mechanics is just application of this theory to various celestial phenomena. He divides this application into two disciplines, celestial statistics and celestial mechanics. Celestial mechanics regards some celestial object as not moving and tries to determine, for instance, the mass or shape of it. Comte considers an important part of celestial statistics the explanation of tides, which he also thinks as providing a transition from astronomy to earthly physics.
Celestial mechanics, Comte continues, considers the planets as moving and is especially involved in explaining perturbations in the trajectories or rotations of planets, satellites and moons (he notes also that in principle we could also apply celestial mechanics to the Sun, since it moves slightly around the mass centre of the Solar System, but since we do not know the exact position of this centre, this would be an impossible task). Comte divides the perturbations into two classes: sudden changes that involve collisions or explosions and continuous effects of the gravitation of other objects.
An important conclusion Comte makes is that the gravitational effect of other stars and solar systems to our Solar System are so insignificant and always nullified by the effect of other solar systems that this “world” of ours is effectively independent of other potential solar systems. This effectively makes any what he calls sidereal astronomy an impossible discipline, except as regards observations of movements of binary stars or even clusters of several stars. Thus, Comte says, although usually the disciplines with more general subject matter determine the disciplines with more particular disciplines, in case of astronomy this rule breaks down, since we observe no effect the universe as a whole has on our own Solar System.
As a part of rejecting the sidereal astronomy, Comte denies the possibility of ever explaining where the stars have come from. On the contrary, he thinks that we can make reasonable, even if not completely proven conjectures about the generation of planets, satellites and comets within our own Solar System. Comte effectively assumes the Laplacian cosmogony, where the mass of our Sun originally extended to our whole Solar System, and in cooling down, broke down into masses that eventually developed into the system as it now exists, planets moving around the Sun and the satellites around their planets. Comte assumes that eventually the inobservably small, but necessarily existent resistance of the medium in which the planets float must slow the movement of the planets, which will mean their reabsorbment into the Sun. Thus, he concludes, the cosmogony again proves the independence of the Solar System, which has probably been varying between phases of a unified Sun and a diversified system innumerably many times before and will continue to do so no one knows how long.
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