### May 5, 1997

Quotation needed from Blind Watchers, p49, Kepler about himself. Nearsighted, multiple vision.

What are Kepler's three remembered laws?

• 1. Orbits are ellipses. What is an ellipse? There are two models, how do we know they are the same? This is not at all obvious unless you understand high school algebra well. (Algebra was invented during Kepler's lifetime by french lawyers, but that is another story).

• 2. The area swept out (in relation to sun) is proportional to the elapsed time. Equal areas exist in equal times.

• 3. For all planets, the annual period squared is proportional to the cube of the distance to the sun.

Isaac Newton derived his first principle from these laws after he invented the foundations of calculus. But how did Kepler come up with them?

Arguments for his system from Astronomia Nova, "Chapter 1", Kepler.

The sun's apparent position is that which it is perceived to occupy through its inequality. The mean position is that which it would have occupied it had not had its inequality. P 48

Before looking at the data: why does it matter where the planes intersect?

Now my first step in investigating the physical causes of the motions was to demonstrate that [the planes of] all the eccentrics intersect in no other place than the very centre of the solar body (not some nearby point), contrary to what Copernicus and Brahe thought. Ptolemy will have to investigate not the motion of the centre of the epicycle, about which the epicycle proceeds uniformly, but the motion of some point whose distance from that centre bears the same ratio to the diameter [of the eccentric] as does the distance of the centre of the solar orb from the earth for Ptolemy, which point is also on the same line, or one parallel to it.
Astronomia Nova, "Author's Introduction", page 48.

What is Kepler talking about in the quotation above? What is the role of ellipses in putting the sun back at the center?

Physical:

... If the earth is moved, show that most of this can be done with physical rather than animate faculties, namely, magnetic ones....using a physical conjecture, that the source of five planets' motion is in the sun itself. It is therefore very likely that the source of the earth's motion is in the same place as the source of the other five planets' motion, namely, n the sun as well. It is therefore likely that the earth is moved, since a likely cause of its motion is apparent. p52,

Physical:

It is impossible that, in moving its body, the form of a stone seek out a mathematical point (in this instance, the centre of the world), without respect to the body in which this point is located. Let the physicists prove that natural things have a sympathy for that which is nothing. ..It is likewise impossible for heavy bodies to tend towards the centre of the world simply because they are seeking to avoid its spherical extremities. For compared with their distance from the extremities of the world, the proportional part by which they're removed form the world's centre is imperceptible ....Nor are heavy bodies driven in towards the middle by the rapid whirling of the primary mobile, as objects in whirlpools are. That motion .... Does not carry all the way down...All these absurdities are consequences of our opponents' view, and it therefore appears that the common theory of gravity is in error. P54

Metaphysical p53 Does the sun, which moves the est of the planets, move the earth, or does the earth move the sun, which moves the rest, and which is so many times greater? Unless we are to be forced to admit the absurd conclusion that the sun is moved by the earth, we must allow the sun to be fixed and the earth to moved...What shall I say of the motion's periodic time of 365 days, intermediate in quantity between the periodic time of Mars of 687 days and that of Venus of 225 days? Does not the nature of things cry out with a great voice that the circuit in which these 365 days are used up also occupies a place intermediate between those of Mars and Venus about the sun, and thus itself also encircles the sun, and hence that this circuit is a circuit of the earth about the sun, and not of the sun about the earth? These points are however more appropriate to my Mysterium cosmographicum, and arguments that are not going to be repeated in this work should not be introduced here.

Political:

Indeed, all things are so interconnected, involved, and intertwined with one another that after trying many different approaches to the reform of astronomical calculations, some well trodden by the ancients and others constructed in emulation of them and by their example, one other could succeed than the one founded upon the motions' physical causes themselves, which I establish in this work. p48

Astronomical:

My aim in the present work is chiefly to reform astronomical theory (especially of the motion of Mars) in all three forms of hypotheses so that our computations from the tables correspond to the celestial phenomena. Hitherto, it has not been possible to this with sufficient certainty. p48

Theology:

There are, however, many more people who are moved by piety to withhold assent from Copernicus, fearing that falsehood might be charged against the Holy Spirit speaking in the scriptures if we say that the earth is moved and the sun stands still....But let them consider that since we acquire most of our information, both in quality and quantity, through the sense of sight, it is impossible for us to abstract our speech from this ocular sense. Thus many times each day we speak in accordance with the sense of sight, although we are quite certain that the truth of the matter is otherwise. p59

Advice for idiots:

But whoever is too stupid to understand astronomical science, or too weak to believe Copernicus without affecting his faith, I would advise him that, having dismissed astronomical studies and having damned whatever philosophical opinions he pleases, he mind his own business and betake himself home to scratch in his own dirt patch, abandoning his wandering about the world. He should raise his eyes ( his only means of vision) to this visible heaven and with his whole heart burst forth in giving thanks and praising God the Creator. He can be sure that he worships God no less than the astronomer, to whom God has granted the more penetrating vision of the mind's eye, and an ability and desire to celebrate his God above those things he has discovered. p.65

clergy: As for the opinions of the pious on these matters of nature, I have just one thing to say: while I theology it is authority that carries the most weight, in philosophy it is reason. Therefore, Lactantius is pious, who denied that the earth is round, Augustine is pious, who though admitting the roundness, denied the antipodes, and the Inquisition nowadays is pious, which, though allowing the earth's smallness, denies its motion. To me, however, the truth is more pious still, and (with all due respect for the Doctors of the church) I prove philosophically not only that the earth is round,not only that it is inhabited all the way around a the antipodes, not only that it is contemptibly small, but also to that it is carried along among the stars. p.66

A little about Kepler. From Blind Watchers, p.41, then Kepler's own words on p. 47, 48

Much space is given to showing the equivalence of Copernicus, Ptolemy and Brahe in explaining what is called the second motion, first inequality. What does this mean, and why does Kepler care that these three systems should be equivalent?

... in order to separate the second inequality from the first one, they could proceed no otherwise than by considering the planets on those nights at whose beginning they rise while the sun is setting, which thence were called akonychioi, or night rising. For since the presence and conjunction of the sun makes them go faster than usual, and the opposition of the sun has the opposite effect, before and after these points they are surely much removed from the position they were going to occupy through the action of the first inequality...Ptolemy chose the mean motion of , thinking that the difference (if any) between taking the mean sun and the apparent sun could not be perceived in the observations, but that the form of computation of the proofs would be easier if the sun's mean motion were taken. Copernicus and Thycho followed Ptolemy, carrying over his assumptions. I, as you see in Chapter15 of my Mysterium Cosmographicum, take instead the apparent position, the true body of the sun as my reference point and will vindicate that position with proofs in part 4 and 5 of this work.
Astronomia Nova, "Chapter 1".

What does he mean when he says there shouldn't be a different theory of the sun for each planet?
What are equants and epicycles?

What comments would you make about Kepler's writing style? To whom does Kepler compare himself as a writer?

p.78? A fourth axis in history of science: the personal.

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