The Observations of Cassini

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 established 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 5 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.