Customer Reviews

Selections from Kepler's Astronomia Nova (Science Classics Module for Humanities Studies)

5 star:		(4)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

This is an excellent introduction to Kepler for people not confident in their ability to breeze through the more complex mathematical arguments of his "celestial physics." Kepler's own introduction is enough to enthrall any reader of history/philosophy of science. Anyone who has some geometry and ancient astronomy under their belts will see that he's a stunning mathematician. Even for this edition of selections, I advise having some familiarity with Euclid and Ptolemy. General familiarity (from Wikipedia, even) of Copernicus and Brahe would be very helpful to understand what he's arguing against. I suppose it would be possible to pick this up and read it without any of this other stuff, but I personally would've been lost without the undergirding of first year-and-a-half of the mathematics program at St. John's College.

After reading this I quickly put Kepler at the top of my "Must Read More" list. The editors and translator are very helpful and accommodating.

I recommend this to any mathematics/physics-lover looking for an introduction to Kepler's world.

I love using this as one of my required texts for the History and Philosophy of Science course I teach. It's great at introducing Kepler's work to first time readers and it also has primary sections from his work. What's best is that you can guide your students through these prime selections without having to lose them in mathematics. And if you are so inclined, and it's worth the try, there are some problems you can tackle and you only need a limited amount of geometry.

I also recommend it if you're just into the history of science.

"My aim in the present work is chiefly to reform astronomical theory ... so that what we compute from the tables may correspond to the celestial phenomena. ... Meanwhile, although I place this goal first and pursue it cheerfully, I also ... inquire into celestial physics and the natural causes of the motions. ... Indeed, all things are so interconnected, involved, and intertwined with one another that after trying many different approaches to the reform of astronomical calculations ... none other could succeed than the one founded upon the motions physical causes themselves, which I establish in this work." (Introduction, pp. 4-5).

A decisive step towards this new physical theory is Kepler's proof in chapter 24 that the earth requires an equant, i.e. that the point with respect to which it moves uniformly is not the center of the orbital circle but rather a point close to it. The old theory, without the equant, had worked well for Ptolemy (sun instead of the earth, of course) and Copernicus, since it predicts the angular position very accurately. But Kepler shows that it fails to predict the distance between the earth and the sun. This distance at different times can be determined by observing the sun and Mars at times 687 days apart; this is the period of Mars, so we get a simple trigonometric calculation with both Mars and the sun as fixed points.

Thus the earth now has an equant just as the outer planets did for Ptolemy and Copernicus. "Further, there is nothing to prevent our believing the same of Venus and Mercury. Indeed, I now have a proof that this is the origin of the belief that the centers of these planets' eccentrics move around on a small annual circle. Therefore all planets have this [eccentric circle with an equant]." (Chapter 32, p. 52).

So the equant is no longer just some trick but in fact a universal principle, so we feel that it must have a deeper explanation. The key observation is that the equant (with bisected eccentricity) makes the planet's speed inversely proportional to its distance from the sun (chapter 32). This suggests that "the power that moves the planets resides in the body of the sun" (chapter 33).

Kepler thinks we should pretty much have seen this coming, considering the "worthiness of eminence of the sun" and the fact that "the source of the world's life ... is the same as the source of the light which forms the adornment of the entire machine, and which is also the source of the heat by which everything grows" (pp. 57-58). Indeed, the motive power's "very close kinship with light" is confirmed by its linear deterioration with distance, since it spreads over the circumference of a circle so to speak (p. 59). Of course one might argue that since light, and perhaps also the motive power, spreads in three dimensions, i.e. over the surface of a sphere, it should obey an inverse square law, but Kepler has already made up his mind on the linear law---"And this is true, both of the steelyard or lever, and of the motion of the planets: that the weakening of power is in the ratio of the distances" (p. 56)---so we stick to two dimensions and conclude that "in all respects and in all its attributes, the motive power from the sun coincides with light ... although this light of the sun cannot be the moving power itself" (p. 59).

The motive power instead appears to be of a magnetic nature. "The magnet, however, does not attract with all its parts, but has ... fibers ... extended throughout its length, so that if a little piece of iron is placed in a middle position between the heads of the magnet ... the magnet does not attract it but only directs it parallel to its own fibers. Thus it is credible that there is in the sun no force whatever attracting the planets ... but only a directing force, and consequently that it has circular fibers all set up in the same direction" (chapter 34, p. 69).

But what about the equants? This makes them look artificial and silly. Kepler has the answer: equants are nothing but a pale manifestation of a deeper principle, the law of equal areas (chapter 40). Ok, so equants are out. Now what about the orbits? Actually, circular orbits will have to be abandoned altogether, as Kepler proves in the case of Mars in chapter 44, essentially by switching the roles of Mars and the earth in the argument of chapter 24 above. Donahue notes:

"Interestingly, Kepler's working notes show that when he first made this comparison, he was sure there must be some error and made a note that he must give some thought to how to adjust the planetary positions to make the orbit circular. Several weeks later, when he was comparing the area law with an equant-based theory, he realised that his physical theory demanded an oval orbit. Only then did he trust the observational evidence!" (p. 85).

Ok, so now orbits are ellipses ("ovals"). But what physical principles could possibly explain that? How does the planet know in which direction to turn and at what speed to go if the orbit is so elaborate? "So then, Kepler, would you give each of the planets a pair of eyes? By no means, nor is this necessary, no more than that they need feet or wings in order to move." (sic, chapter 39, p. 75). The magnet analogy suggests a solution. The sun's motive power creates a circular stream, but the planets don't quite follow this stream because they themselves are "magnetic"---this is how the earth can make the moon move---and this interferes with the stream as if the planet held a slowly turning oar in the stream: sometimes it agrees with the stream, sometimes it counteracts it. Kepler does not intend to build a quantitative theory on these grounds, but only to illustrate that the phenomena can be explained by basic physical principles: "I will be satisfied if this magnetic example demonstrates the general possibility of the proposed mechanism." (chapter 57, p. 94).

Bought this book for my husband who teaches astronomy and physics. He says it has given him great insight into the roots of what he now teaches.

Given how well he understood gravity, it is amazing that Kepler is not given more credit than Newton. This has been pointed out several times over the ages, but in English historical texts, we seem to prefer the Englishman over the German. His great mistake was not recognizing that a basic centripetal force (the "animal force" that kept him puzzled) was the only thing needed to counteract the gravity that he was already aware of to explain the observations. He knew gravity increased with mass and that it decreased with distance, and that if you took two stones and placed them in space far from the gravitational effects of earth, they would be attracted to each other. He even knew exactly where in space they would collide which requires knowing that the force for both gravity and inertia is proportional to mass. It does not require knowledge of the correctness of F=ma over F=mv nor of 1/r^2 over 1/r. How did he know gravity decreased with distance if he did not suspect it of being the primary cause of planetary attraction? Here are quotes from the Introduction to this book:

"Every corporeal substance, so far forth as it is corporeal, has a natural fitness for resting in every place where it may be situated by itself beyond the sphere of influence of a body cognate with it. Gravity is a mutual affection between cognate bodies towards union or conjunction (similar in kind to the magnetic virtue), so that the earth attracts a stone much rather than the stone seeks the earth. ...If two stones were placed in any part of the world near each other, and beyond the sphere of influence of a third cognate body, these stones, like two magnetic needles, would come together in the intermediate point, each approaching the other by a space proportional to the comparative mass of the other. If the moon and earth were not retained in their orbits by their animal force or some other equivalent, the earth would mount to the moon by a fifty-fourth part of their distance, and the moon fall towards the earth through the other fifty-three parts, and they would there meet, assuming, however, that the substance of both is of the same density. If the earth should cease to attract its waters to itself all the waters of the sea would he raised and would flow to the body of the moon. The sphere of the attractive virtue which is in the moon extends as far as the earth, and entices up the waters; but as the moon flies rapidly across the zenith, and the waters cannot follow so quickly, a flow of the ocean is occasioned in the torrid zone towards the westward. If the attractive virtue of the moon extends as far as the earth, it follows with greater reason that the attractive virtue of the earth extends as far as the moon and much farther; and, in short, nothing which consists of earthly substance anyhow constituted although thrown up to any height, can ever escape the powerful operation of this attractive virtue."

Englishman Stephen Hawking states in "Brief History of Time" that Kepler thought planetary attraction was magnetism and that Newton was the first to think masses attract, but the above shows neither statement is true. Others mistakenly say he did not think it applied to small objects on Earth, or, conversely, that it did not apply at great distances. Again, the above quotes show the complaints are not true.

As the author of these selections points out, the introduction was the most widely circulated text of Kepler, the only portion translated to English before 1800. He also states that we should not give Kepler too much credit because, he claims, Kepler did not explicitly say gravity applied to anything other than the Earth and Moon. Kepler believed the Earth was just one of the planets which implies he also believed the planets to have gravity. He did not assign anything magical to Earth as seen by his "dream" text that explores the possibility of completely different intelligent living creatures on the moon. Kepler thought magnetism must be in the Sun because it was in the Earth, so why assume he would not extend the idea of gravity? Kepler did say "Cognate", if the translation is correct, which means material of a like kind. This could mean Earth/Moon material is not attracted to Sun material, but this is still jumping to a conclusion about Kepler's beliefs. He also said the force of Earth's gravity extends forever, decreasing with distance, and that it can apply to stones that have been separated from a "3rd cognate body", which implies stones from any planet, rather than restricting himself to Earth. Compare this with the claim of the author: "there is not the least notion that gravity extends to any other bodies than the Earth and the moon". He seems way too insistent and dismissive and of Kepler's knowledge. Do German authors have a similar dismissive attitude?