Kepler's System of AstronomySeptember 9, 2015
While, in Italy, the unfortunate Galileo was adding so many probabilities to the system of Copernicus, there was another philosopher employing himself in Germany, to ascertain, correct, and improve it=
Kepler, in Germany, had great genius but none of the taste or order and method of Galileo. Like other Germans, he had the most laborious industry together with an excessive passion for discovering proportions and resemblances between the different parts of nature.
He had been instructed, by Micheal Maestlin in the system of Copernicus. He wondered=
- why there were six planets
- why they were at such irregular distances from the Sun
- whether there was any uniform proportion between their distances, and the timespan of their revolution
He tried to find it in the proportions of numbers and plain figures, then afterwards, in those of the regular solids. Finally, in those of the musical divisions of the Octave.
Whatever the science Kepler was studying, he seems constantly to have pleased himself with finding some analogy and thus, arithmetic and music, plain and between it and the system of the universe.
Solid geometry, came all of them by turns to illustrate the doctrine of the Sphere, in the explaining of which he was, by his profession, principally employed.
He had presented one of his books to Tycho Brahe who disapproved of his system but was pleased with=
- his genius, and
- his diligence in making the most laborious calculations
Brahe invited the obscure and indigent Kepler to come and live with him , soon as he arrived, his observations upon Mars, in the arranging and methodizing of which his disciples were at that time employed.
Kepler, upon comparing them with one another, found that=
- Mars’ orbit was an ellipse with the Sun as one of its foci.
- Mars’ motion was not equable
- It was swiftest when nearest the Sun and slowest when farthest from it
- Its velocity gradually encreased, or diminished, according as it approached or receded from it.
He found that these two facts were true for all the other Planets.
The calculations of Kepler destroyed the circular orbits of the planets.
An ellipse is, of all curves lines after a circle, the simplest and most easily conceived.
Kepler took from the motion of the Planets the easiest of all proportions, that of equality, he did not leave them absolutely without one, but ascertained the rule by which their velocities continually varied; for a genius so fond of analogies, when he had taken away one, would be sure to substitute another in its room. Notwithstanding all this, notwithstanding that his system was better supported by observations than any system had ever been before, yet, such was the attachment to the equal motions and circular orbits of the Planets, that it seems, for some time, to have been in general but little attended to by the learned, to have been altogether neglected by philosophers, and not much regarded even by astronomers.
Gassendi began to become famous during the latter days of Kepler. But he
did not understand the importance of Kepler’s alterations to that of Tycho Brahe.
Kepler’s rule for the planetary movement was intricate and difficult to comprehend.
He said that if a straight line were drawn from the center of each Planet to the Sun, and carried along by the periodical motion of the Planet, it would describe equal areas in equal times, even if the Planet did not pass over equal spaces.
The same rule took place nearly with regard to the Moon.
The imagination, when acquainted with this law of motion, can follow it more easily. When not acquainted with this law, the mind would wander in uncertainty with regard to the proportion which regulates its varieties.
The discovery of this analogy therefore made Kepler’s system more agreeable to the natural taste of mankind. But it was still too difficult to be comprehended.
Besides this, he introduced another new analogy into the system. It first discovered that there was one uniform relation observed between=
- the distances of the Planets from the Sun, and
- the times employed in their periodical motions.
He found that their periodical times were greater than in proportion to their distances, and less than in proportion to the squares of those distances.
but, that they were nearly as the mean proportionals between their distances and the squares of their distances.
In other words, that the squares of their periodical times were nearly as the cubes of their an analogy, which, though, like all others, it no doubt rendered the system distances;
somewhat more distinct and comprehensible, was, however, as well as the former, of too intricate a nature to facilitate very much the effort of the imagination in conceiving it.
The truth of both these analogies, intricate as they were, was at last fully established by the observations of Cassini.
Kepler first discovered=
- that the moons of Jupiter and Saturn revolved round Jupiter and Saturn according to the same laws which Kepler had observed in the revolutions of planets around the Sun
- that the revolution of the Moon around the earth had described equal areas in equal times
- the squares of their periodic times were as the cubes of their distances
These two last abstruse analogies were initially but little regarded. But when they were found to take place in the revolutions of the four moons of Jupiter, and in the five moons of the Five of Saturn, they confirmed Kepler’s doctrine and added a new probability to the Copernican hypothesis.
The observations of Cassini seem to establish it as a law of the system=
- that, when one body revolved around another, it described equal areas in equal times.
- that, when several revolved around the same body, the squares of their periodic times were as the cubes of their distances.
If the Earth and the Five Planets revolved around the Sun, then these laws should take place universally.
But if, according to Ptolemy’s system, the Sun, Moon, and Five Planets revolved around the Earth, the periodical motions of the Sun and Moon would observe the first of these laws, would each of them describe equal areas in equal times.
but they would not observe the second, the squares of their periodic times would not be as the cubes of their distances= and the revolutions of the Five Planets would observe neither the one law nor the other.
Or if, according to the system of Tycho Brahe, the Five Planets were supposed to revolve round the Sun, while the Sun and Moon revolved round the Earth, the revolutions of the Five Planets round the Sun, would observe both these laws;
but those of the Sun and Moon round the Earth would observe only the first of them.
Only Copernicus’ system preserved the analogy of nature and so must be the true one.
This argument is regarded by Voltaire, Cardinal of Polignac, as an irrefragable demonstration. McLaurin and Newton were more capable of judging this and they mentioned it as the principal evidence for the truth of the Copernican hypothesis.
Cassini supposed the Planets to revolve in an oblong curve. But it was in a curve somewhat different from that of Kepler.
In the ellipse, the sum of the two lines, which are drawn from any one point in the circumference to the two foci, is always equal to that of those which are drawn from any other point in the circumference to the same foci.
In the curve of Cassini, it is not the sum of the lines, but the rectangles which are contained under the lines, that are always equal. As this, however, was a proportion more difficult to be comprehended than the other, the curve of Cassini has never had the vogue.
The only problem with the system of Copernicus was the mind’s difficulty in conceiving that huge planets like the Earth were revolving round the Sun so fast.
Copernicus said that this motion was as natural to the Planets, as it is to a stone to fall to the ground.
The imagination had been used to conceive such heavy objects as resting than moving. This habitual idea of their natural inertness was incompatible with their natural motion.
Kepler connected this natural inertness with their astonishing velocities. He talked of some vital and immaterial virtue, which was shed by the Sun into the surrounding spaces.
This virtue was whirled around with the sun’s revolution around his own axis. This took hold of the Planets and forced them, in spite of their ponderousness and strong propensity to rest, to whirl around the center of the system.
The imagination had no hold of this immaterial virtue, and could form no determinate idea of what it consisted in.
The imagination felt a gap between the constant motion and the supposed inertness of the Planets. It thought that there might be some general idea of intermediate objects to link together these discordant qualities.
Kepler could not explain this invisible chain that he called an immaterial virtue.