Tycho and Kepler (46 page)

And then, “As if I were roused from a dream and
saw a new light,” a torrent of answers fell into place. An elliptical orbit halfway between his approximating ellipse and a circle had a feature that was deeply satisfying to one who loved geometric harmony. The Sun was one of its foci. Kepler had arrived at his “first law of planetary motion.”

This
, as Kepler put it, was “the sort of thing nature does.” With this ellipse, the orbit made physical
sense, supporting his conviction that a force residing in the Sun moves the planets. What was more, if the area rule was correct, this model agreed “to the nail” with the long-trusted heliocentric longitudes of his Vicarious Hypothesis. This one shape of orbit, and
only
this shape, got the planet to the right place at the right time. The man who had said of himself, “There was nothing
⁹
I could
state that I could not also contradict,” had discovered a piece of incontrovertible truth.

At Easter 1605, the second Easter after the one for which he had promised his book, Kepler decided definitely on the ellipse. He finished the manuscript that year, adding a subtitle to emphasize that his “New Astronomy” was “Based on Causes, or Celestial Physics.” Kepler ended
Astronomia Nova
with the
hope that God, having so richly endowed his creatures with analytical brains and insatiable curiosity, and
his
Creation with surpassing beauty and ingenuity, would allow humans sufficient time on this Earth to resolve questions he, Kepler, had not yet been able to answer.

Figure 20.5: Kepler’s first law of planetary motion: A planet moves in an elliptical orbit, and the Sun is at one focus of the ellipse.

The adventure begun on Hven when Tycho first made the decision to train his fabulous instruments on Mars had taken Kepler to a new astronomy. He had made sense of the positions of Mars spread over many pages of observational logs. In this miraculous cohesion
of observations and mathematical theory, the numbers, in the words of Kepler scholar Max Caspar, “no longer stand together
¹⁰
unrelated but rather each can be calculated from the other.” The limits of accuracy of Tycho’s observations had turned out to be exactly right for the task Kepler undertook: “[They were] narrow enough so that Kepler could not afford to neglect those very important eight
minutes . . . but had they been considerably narrower, he would certainly have been caught in a fine meshed net, because in many of his calculations he would no longer have been permitted to overlook certain inaccuracies, as was necessary for the progress of his research.” Nevertheless, the precision of Tycho’s observations made it possible for Kepler to find the elliptical orbit of Mars even though
it is so near to being a circle that any
drawing
of it on the page (such as the ones in this chapter) that makes it look even slightly elliptical is a gross exaggeration.

Figure 20.6: Comparing the eccentric circle, the true ellipse, and the approximating ellipse. F designates the two foci of the approximating ellipse. E and the Sun are the foci of the true ellipse. The drawing greatly exaggerates the eccentricity of the ellipses. Correctly drawn at this scale, they would be impossible to distinguish from one another or from a circle.

Kepler’s discoveries
that Earth behaves like a planet, and of his first and second laws of planetary motion, were towering landmarks in human intellectual and scientific history. He had indeed plumbed the depths of a complicated universe and found harmony. He had also given Tycho Brahe his earthly immortality.

fn1
Eight minutes of arc is the equivalent of a little less than the thickness of a penny held at arm’s
length and viewed edgewise.

fn2
In order to appreciate fully the manner in which Kepler used Tycho’s observations, it would be necessary to follow him in far greater detail than is possible here.
Appendix 3
describes in a much simplified fashion just this one short phase of the work to give a flavor of the interplay between Tycho’s data and Kepler’s use of it. The process did not “draw Earth’s
orbit” for Kepler though it might seem it could have. It did not lead him to conclude that the orbit is elliptical. That would come later.

fn3
An isosceles triangle is a triangle having two sides of equal length. (
See figure 20.3[a]
, though it does not show an infinite number of triangles.)

21

T
HE
W
HEEL OF
F
ORTUNE
C
REAKS
A
ROUND

1606–1618

THE AGREEMENT STRUCK
earlier between Kepler and Tengnagel required Kepler to submit the manuscript of
Astronomia Nova
to Tengnagel for approval. Tengnagel was not pleased: The book clearly argued for the Copernican rather than the Tychonic system. The difficulty was settled when Kepler agreed to allow Tengnagel to write a preface. Hence
Astronomia Nova
, like Copernicus’s
De Revolutionibus
, begins with an unpromising warning, in this case that readers should “not be swayed
¹
by anything of Kepler’s, especially his liberty in disagreeing with Brahe in physical arguments.” Both Tengnagel and Osiander (in the case of
De Revolutionibus
) emerge looking foolish in prefaces to two of the most significant astronomy books in history.

The publication of Kepler’s book moved at a snail’s pace. The printing didn’t even begin until 1608. It was Rudolph’s right to distribute all copies of a book by his imperial mathematician, but when it appeared in the summer of 1609, Kepler had to give the entire edition back to the printer in Heidelberg to sell to cover unpaid costs.

January 1610 marked ten years since Kepler had first arrived
in Prague in Hoffmann’s carriage. There was abundant reason to celebrate
the
anniversary. Kepler’s reputation as scientific heir to Tycho Brahe, and the books Kepler had written, had elevated him from the status of an impoverished provincial mathematics teacher to that of a celebrated figure in educated circles all over Europe and in Britain. This success redounded to the emperor’s credit as well.
Rudolph lavished praise on Kepler and granted him a bonus of two thousand talers, which would have been splendid had it been paid.

Sadly, Kepler’s decade of superb scholarly achievement, warm friendships, and almost universal respect was marred not only by his problems collecting his salary, but also by the decline of both his wife and his patron. Barbara had made some friends among the more
pious Protestant women of Prague, but after a decade in the city she was still miserably homesick. In spite of her discontent, the Keplers had seldom been out of Prague at all during the years since Tycho’s death, except for a sojourn in Moravia when the plague came back in 1606. In the autumn of 1607 they had moved to new lodgings near the great bridge over the river. Ludwig, their second son,
was born there that December. In 1608 Regina, Barbara’s daughter and Kepler’s stepdaughter, married Philip Ehem, who was descended from a prominent Augsburg family and was currently a representative at the imperial court for Elector Frederick IV of the Palatinate. There were many reasons for happiness and pride, yet Barbara suffered chronic bad health and deepening depression.

As for the emperor,
by the time he granted Kepler’s celebratory bonus, Rudolph had been stripped of almost all his power. Oddly enough, his habitual state of political indecision and inaction had stood him in rather good stead for many years. He had kept up an endless, stalemated war with the Ottoman Turks and held together, often only by failure to act or react, an empire forever threatening to disintegrate.
Rudolph had always been quirky and pathologically shy, but over time his indecision and stubbornness had degenerated to paralysis, and his mental state had continued to deteriorate until he was rumored to be insane. Though he was such a recluse that it was
difficult
to confirm or deny the rumor, he had clearly become a threat to the royal house of Hapsburg and the empire.

The Austrian Hapsburg
family had met in secret in April 1606 and agreed to recognize Rudolph’s younger brother Matthias as the head of the family instead of Rudolph. Two years later, Matthias led an army from Vienna into Bohemia to within a day’s march of Prague. Rudolph abdicated, ceding to Matthias the kingdom of Hungary and the archduchies of Austria and Moravia, keeping only Bohemia (including Prague), Silesia,
and Lusatia for himself, with Matthias named as his successor there.

In the spring of 1610, a few months after Kepler’s anniversary celebration, nature for a time upstaged domestic or political concerns, at least for Kepler and some of his close acquaintances. On March 15 a carriage stopped at Kepler’s door. Its passenger was Kepler’s friend Wackher von Wackenfels, who was an imperial councillor
twenty years Kepler’s senior, a distant relation, and a brilliant man with many scholarly and scientific interests. Von Wackenfels stuck his head out of the carriage window to call Kepler to come down immediately, for there was stupendous news: Galileo Galilei, with his new telescope, had discovered four new planets. Von Wackenfels and Kepler were so overcome they could do little more than
babble with excitement. Kepler’s enthusiasm was tinged with anxiety over whether these discoveries were planets, or moons around one of the other planets. Von Wackenfels was not sure, but Kepler said they surely must be moons, because he had established with his polyhedral theory that there could be only six planets.

A copy of Galileo’s book
²
reporting the discovery—
Sidereus Nuncius
(The Starry
Message)—reached the emperor, who loaned it to Kepler. Kepler’s own copy arrived soon after via the Tuscan ambassador with a request that the imperial mathematician send his opinion back with the same courier before the week was out. To Kepler’s relief, he read that the “planets” were four moons orbiting Jupiter.

Kepler’s response enthusiastically agreed with Galileo that the
discovery
of
Jupiter’s moons supported Copernican astronomy, for it was evident that not everything in the universe was revolving around Earth. The fact that through a telescope the planets looked like disks but the stars remained points—no larger than they appeared to the naked eye—indicated that the stars were indeed as far away as Copernican theory required. As for Kepler’s theories, it no longer seemed such
an oddity that Earth should have its own version of a “planet-moving force” to keep a moon orbiting. Kepler suggested that Jupiter must have intelligent inhabitants; otherwise, why should God have given Jupiter moons that would go unappreciated by any creature except the few Earth dwellers who had telescopes? Kepler was not among those fortunate Earth dwellers.

Kepler’s letter was ready on
April 19, in time for the courier’s return trip. Galileo’s response was not so rapid in coming. It took him four months, but it was effusive: “I thank you
³
because you were the first one, and practically the only one, to have complete faith in my assertions.”

There was widespread curiosity about Kepler’s reaction to Galileo’s discovery. Kepler published the letter he had written to Galileo
as a thirty-five-page book,
Dissertatio cum Nuncio Sidereo
(Conversation with the Starry Messenger). One of the most surprising things about it was that Kepler felt called on to defend the use of the telescope as a reliable scientific instrument. Some astronomers had voiced suspicions that Galileo’s discoveries might be nothing more than artifacts of the instrument, not something really there.
Kepler’s reassurance about the use of telescopes, though he had seen only inferior models in Prague and was relying on his knowledge of optics, was almost as valuable as his defense of the plausibility of Galileo’s discoveries. Kepler had hinted broadly to Galileo that he would like to have one of the telescopes Galileo was sending to important people all over Europe, but Galileo did not send him
one, so, unable to confirm the discoveries himself, “plausibility” was as far as Kepler could go.