Tycho and Kepler (42 page)

Tengnagel returned to Prague in October 1602 and found that there had been almost no payment from the royal treasury for the instruments, observational logs, and manuscripts. He also could not discern that Kepler had made any progress on completing the manuscripts. Through machinations
at court, Tengnagel contrived to have the task of composing the Rudolfine Tables transferred to himself, at double Kepler’s salary, though Kepler continued to be imperial mathematician. To Kepler’s way of thinking, he had made plenty of progress, and it was inconceivable that he should relinquish the Mars data when he was so close to answers. He handed over most of the material, but not the
Mars observations. Those he secretly kept, thinking it improbable that Tengnagel would actually consult the observations himself and notice that something was missing.

In the course of this unpleasantness between Kepler and Tengnagel, the emperor in the autumn of 1602 inquired of Kepler what he planned to publish in the near future to justify his employment as imperial mathematician. Kepler
made some rapid decisions. Taking stock of his unfinished works, he promised two books: First, within eight weeks, by Christmas, he would complete
Astronomiae Pars Optica
(The Optical Part of Astronomy). That, he thought, was nearly finished already, the fruit of the summer he had spent in Graz prior to his family’s expulsion. Second, he informed the emperor, by the next Easter (1603) he would
complete “Commentaries on the Theory of Mars.” He had been working on Mars, albeit with many interruptions, since he had first joined Tycho at Benatky.

Kepler was being overly optimistic about completing
Astronomiae Pars Optica
by Christmas. He was still the same man who at age twenty-six had written that his eagerness led him “to think of a lot
⁹
of things as easy, which proved difficult and
time-consuming in the carrying out” and who “in writing [would] continually start thinking about new things.” He had already begun to consider many elements of optics that were relevant to astronomy besides those he had been investigating in Graz—for instance, the extent to which light is refracted
as
it enters the atmosphere, the question that had plagued Tycho. Kepler put his mind to this problem
without complete success, for he used erroneous data. Also, he decided there should be exhaustive treatment in the book of eclipses and the sizes and distances of the Sun and Moon. He anticipated no great problem there, for he was currently producing a treatise on the subject. Soon he decided, however, to keep that material separate and not include it. But he needed to delve into the function
of the human eye.

In this area, Kepler met great success. The question of how the eye works was not new, and there were theories that attempted to explain it, but Kepler’s previous optical analyses gave him the background to discover, after rigorous calculation, that the old theories were wrong. Applying his idea of light rays, he was the first to realize that the image of the outside world
is not captured in the fluid of the eyeball. It is, rather, projected by a lens in the eye onto the surface of the retina. Working like a “pencil of light,” as he called it, the light rays “draw” the image on the retina. Kepler discovered that the image is upside down and backward on the retina. He was not able to explain how the mind compensates for this, but he did arrive at a precise understanding
of the way in which differently shaped eyeglasses could correct nearsightedness and farsightedness. This was a particularly relevant question for him, because he wore spectacles himself.

In the introduction to the book, Kepler spoke of another discovery he had made: the inverse square law of light. If a burning candle is set on a table, the lighted area surrounding it on the table is a circle,
with the candle in the center of the circle. Kepler, thinking in three dimensions rather than two, reasoned that light, starting from one point in space (the candle flame), spreads out not just in a circle but in
all
directions, in the form of a sphere. Wherever you are, within reach of the light, you can think of yourself as being at the edge of a sphere centered on the light source. Someone
a little farther away can also imagine himself or herself being at the edge of a sphere centered on the light source. At that second location, the sphere is
bigger
, and the light looks dimmer. How much dimmer? was the question. Kepler reasoned that the light’s brightness was related to the size (the area) of the sphere. If two observers were both looking at the light, and observer B was twice
as far away as observer A, then observer B’s sphere was four times as large as observer A’s sphere. B saw the light only a fourth as bright as A did. If B was three times as far away as A, B’s sphere was nine times as large as A’s sphere, and B saw the light only a ninth as bright as A did. As Kepler’s inverse square law of light states, the intensity of light is inversely proportional to the square
of the distance. The square of two (two times as far away from the light source) is four. The square of three (three times as far from the light source) is nine, and so forth.

In January 1604, a little more than a year after the Christmas for which he had promised it, Kepler presented the completed manuscript of
Astronomiae Pars Optica
¹⁰
to the emperor, and the book went into publication.
The ideas and discoveries about light and optics that Kepler wrote about in this book and later applied to the telescope in another work,
Dioptrice
, became the foundation for seventeenth-century optical theory.

After their clash in the autumn of 1602, Kepler and Tengnagel were often at loggerheads, but they managed to make some joint progress on the completion and publication of Tycho’s posthumous
works. There had been an extremely uncomfortable moment in the spring of 1603 when Tengnagel, turning his attention to the Rudolfine Tables, had discovered that the Mars observations were missing. Kepler reluctantly surrendered them. He was at that time writing
Astronomiae Pars Optica
, and the removal of the possibility of working on Mars may have caused him to go as deeply as he did into that
other subject.

Tengnagel’s most impressive talents lay in politics and diplomacy, which Tycho had recognized and put to use when courting favor with the royalty of Europe. Hence more and more of Tengnagel’s time was taken up with Hapsburg politics and the deteriorating political situation in Bohemia and Germany. In the summer of 1604 he
conceded
that he could not possibly complete the Rudolfine
Tables by himself. In return for a promise to complete them in a manner satisfactory to Tengnagel and to seek his approval before publishing anything based on the manuscripts, Tengnagel allowed Kepler to use some of Tycho’s observational journals.

The precious Mars observations were once more in Kepler’s hands. However, promises to Tengnagel notwithstanding, he did not set to work on the Rudolfine
Tables. He was again engrossed in his study of Mars’s orbit. His book about that, promised for Easter 1603, was well behind schedule. It would, in fact, not be ready to go to print until late in 1605, and it would have a new and highly appropriate title,
Astronomia Nova
—New Astronomy.

In the autumn of 1604 the Keplers, with Barbara six months pregnant, moved house again, this time to Wenzel
College in the Old Town, nearer the palace but still across the river. One of Kepler’s dearest friends, Martin Bachazek, rector of the University of Prague, lived there. Kepler relished the opportunity to converse with him daily.

That same autumn, not long after the move and while Kepler was wrestling with one of the most difficult problems in his book about Mars, a celestial event occurred
that left him no choice but to abandon his writing desk and his columns of calculations. The event began inauspiciously when a court official in a state of great agitation roused the family at dawn on October 11. When Kepler could make sense of the man, he learned that on the previous evening he had seen a brilliant new star through a gap in the clouds. Kepler was skeptical. Six days of overcast
skies followed. He had almost forgotten the incident when on the evening of October 17 the sky cleared. He saw the star himself and realized that the messenger’s excitement had been justified. As bright as Jupiter, sparkling like a diamond in all the colors of the rainbow, this nova appeared in the sky near Saturn and Jupiter, which were near conjunction. Mars was also close by. Tycho had had his
“star,” and now Kepler had his.

As Kepler’s fateful drawing for his class in Graz had demonstrated, Jupiter and Saturn come into conjunction every twenty years. The regular pattern in which the conjunctions occur means that ten conjunctions happen within each of four areas of the zodiac. Astrologers associate the areas with the four elements identified by Aristotle: fire, water, earth, air (
see figure 12.1
). It takes eight hundred years for the conjunctions to pass through all four areas, known as “trigons.” The conjunction of Jupiter and Saturn at the time of the appearance of “Kepler’s star” marked the beginning of the two-hundred-year period in which the conjunctions would occur in the trigon associated with the element fire, the “fiery trigon.” Any conjunction was considered to
have important effects on human events, mostly bad; a conjunction in the fiery trigon presaged even greater calamity.

In view of the astrological implications of such a conjunction
and
a new star at the same time, Rudolph would not rest until he and all the other nervous citizens of the empire could be informed by the imperial mathematician what they should make of this wonder. Bachazek built
a small wooden tower so that Kepler and he could see the star better, and Kepler almost immediately produced a delightful short report to reassure the emperor and the populace of Prague. Among other possibilities, Kepler predicted (with tongue in cheek) good sales for booksellers, because every theologian, philosopher, physician, mathematician, and scholar would want to publish his own ideas on
the matter.

To help fulfill that prediction, two years later Kepler himself dedicated a book about the nova to the emperor, based on research and continual observation as it faded.
De Stella Nova’s
subtitle was
A Book Full
¹¹
of Astronomical, Physical, Metaphysical, Meteorological and Astrological Discussions, Glorious and Unusual
. There was a widely held opinion that the planets had ignited
the nova. Kepler insisted it was much farther away than the planets, at the distance of the fixed stars, and he made a good case (based on erroneous data) that the fixed stars were not suns. He also rejected the suggestion that a
group
of atoms had come together by pure chance to form a new star. That, he wrote, was like thinking that “if a pewter dish,
¹²
leaves of lettuce, grains of salt, drops
of water, vinegar, oil and slices of egg had been flying around in the air for all eternity, it might at last happen by chance that a salad would result.” He even had mentioned the matter to his wife as she set a salad on the table before him. As he wrote: “‘Yes,’ responded my dear, ‘but not so nice as this one of mine.’”

Kepler ruminated a bit about the astrological implications of the star,
but he ended by telling his readers that the best advice he could give them was to examine their sins and repent. Star or no star, that could certainly do them no harm.

Modern research shows that Kepler’s Star, like Tycho’s in 1572, was a Type 1 supernova. There have been three in our galaxy in the last thousand years. (The other was in 1006.) Kepler’s was the last supernova that would be
visible to the naked eye until 1987, when one occurred in the Large Magellanic Cloud, a satellite galaxy of the Milky Way. Tycho and Kepler had no idea how extraordinarily fortunate they were each to see one. The serendipitous salad was perhaps not so much less likely after all.

The Kepler family kept growing. In early December 1604, Barbara gave birth to a son, Friedrich, who was to be a
great favorite of Kepler’s. The domestic disruption surrounding his birth caused Kepler to exclaim in a letter, “For what a business,
¹³
what an activity, does it not make to invite fifteen or sixteen women to visit my wife, who lies in childbed, to receive them hospitably, to see them out!” Perhaps he should have reconsidered his lament that Barbara had neither heart nor means to make herself
further known in society. Sadly, as Barbara’s house became livelier with children, she herself withdrew further into melancholy.

For Kepler the astronomer, 1604 was both a frustrating and an exhilarating year as he struggled daily to solve the riddle of Mars’s orbit. He came to think of it as a war with Mars, by ancient tradition the
most
warlike of the planets. By the time Friedrich was born,
Kepler still wasn’t sure whether he was nearing success, whether victory might still be several years off, or whether the orbit of Mars was perhaps not mathematically describable at all.
Astronomia Nova
was not a report on the results of completed research. Kepler had written fifty-eight chapters of the book in almost final form before he discovered that Mars’s orbit is elliptical.

Tycho’s
records contained plenty of data on Mars, for the “problem of Mars” had caused him over a long period of time to make that planet the focus of many observations. That “problem” was the catalyst that led Kepler to his first two laws of planetary motion.

Already in antiquity, observations of Mars had made it clear that the speed of the planet does not remain uniform throughout its orbit. Astronomers
in the intervening centuries had used ingenious devices to describe such irregularities in a mathematical/geometrical way. One such device was an “eccentric” orbit—an orbit not precisely centered on the center of the system (not precisely on Earth for Ptolemy; not precisely on the Sun for Copernicus). A straight line drawn through the center of the system (Earth or Sun) and the center of
the eccentric orbit was called the apsidal line. Extended farther, the apsidal line passed through the point where the planet was farthest from the center of the system (at aphelion) and the point where it was closest (at perihelion) (
see figure 19.1
).