Tycho and Kepler (3 page)

The University of Copenhagen was one of the
premier universities of Europe. King Christian III, at whose coronation Tyge’s great-uncle had carried the scepter, had set the university on a sound financial
footing
, and Frederick II, the present king, had enlarged its endowment, ensuring an income from landed estates, tithes, and church properties. Among other benefits, the university had the curious right to every eighth swine grazing in
the university forests, which perhaps helped to supply the long tables in the professors’ households.

The quality of a student’s education depended heavily on whose household he belonged to, and there is no record of where Tyge lodged.
³
His uncle and aunt may have placed him in the household of Nicolaus Scavenius, a professor of mathematics, for Tyge’s mathematical interests began early, and
Scavenius was a client of the Oxe family. On the other hand, he may have lodged in the establishment of Niels Hemmingsen, a renowned professor of theology who would play an interesting walk-on role later in Tycho’s life. Anders Sørensen Vedel, who would accompany Tyge on educational journeys abroad, lodged there. Tyge studied Greek and possibly some Hebrew and acquired a classical education with
skills in logic, rhetoric, debate, and public speaking, all traditionally considered useful for a young man who intended to follow his forebears into the ranks of the ruling elite.

However, education at Lutheran universities such as Copenhagen went beyond these subjects, largely thanks to Martin Luther’s influential follower and friend Philipp Melanchthon. Melanchthon believed that the church
could succeed in its mission to teach the path to salvation only if it made education a priority and produced a clergy of scholars strongly grounded in the “liberal arts”:
⁴
In order to understand the Scriptures and the writings of the church fathers, one had to have Latin, Greek, and Hebrew. Knowledge of literature and history lent authority to preaching, which benefited even more directly from
mastery of rhetoric and dialectic. Thorough comprehension of both the secular and sacred realms called for arithmetic and geometry. Besides their practical applications, these also helped one understand astronomy, which was considered to be the most heavenly
of
the sciences. Every Lutheran university had at least one professorial chair in these mathematical disciplines. Astronomy established the
calendar of the church and opened one to the inspiration of nature and the mind of the Creator, but it also had its practical use as a basis for astrology. The two subjects were in fact not separate then, and one of the primary motives for practicing astronomy and training astronomers was to improve horoscopes. Though his mentor Martin Luther scoffed at such ideas, Melanchthon, along with many
other educated people, thought the fate of human beings was closely linked to the stars and planets. Most significantly for Tycho Brahe and, twenty-five years later, for Johannes Kepler, the Philippist university curriculum promulgated by Philipp Melanchthon also embodied the humanist ideal that one could not truly comprehend and master any part of all this knowledge unless one comprehended and mastered
the whole of it.

It was in the atmosphere of such broad intellectual ambitions that Tyge’s interest in astronomy took shape. An eclipse of the Moon on August 21, 1560, that he either witnessed or heard about when he was thirteen years old, set fire to his already considerable fascination with the subject.
^fn2

A surviving list of books Tyge purchased provides some information about the astronomy
he studied. The books included Johannes de Sacrobosco’s
On the Spheres
, the preeminent introductory astronomy text of the Middle Ages, which Professor Scavenius used in his lectures; Peter Apian’s
Cosmography
, a more advanced book; Johann Regiomontanus’s
Trigonometry;
and an ephemeris (a table showing the positions of heavenly bodies on a number of dates in a regular sequence) from Stadius. Tyge
inscribed his name and the date of purchase, “Anno 1561,” in the Apian
Cosmography
, using a Latinized form of Tyge—Tycho. Tycho spelled the name sometimes with
ij
,
sometimes
with
ÿ
, never as Taecho, indicating that he intended it to be pronounced Teeko, or (closer to the Danish pronunciation) as though the
y
were a German
ü
.

A
STRONOMERS
IN THE ERA
when Tycho lived thought of their subject as being separated into two parts, described as the
primum
and
secundum mobile
. The
primum
dealt with the way the celestial sphere as a whole “rose” and “set” every night, and the fact that the particular portion of that celestial sphere visible at night changes throughout the year in a regular annual cycle. One needed trigonometry, the most
advanced form of mathematics then known, to understand these phenomena in detail, so classroom discussions usually took place on a more general, qualitative level. The
secundum mobile
, involving planetary positions and motions, did require trigonometry.

Typical study of the
secundum mobile
began with Euclid’s
Geometry
, a work that had endured since around 300
B.C
. (Euclidean geometry is still
taught in basic geometry classes.) From there the course went on to trigonometry and planetary theory. In Tycho’s university years, planetary theory still meant theory according to Ptolemaic astronomy.

When Greek and Alexandrian scholars such as Aristotle, Hipparchus, and Claudius Ptolemaeus (known as Ptolemy) peered at the night sky, they saw virtually the same panorama that is visible with
the naked eye on a clear night now, far enough away from city light. Thirteen centuries after Ptolemy, Copernicus and Tycho Brahe also had no other view than that, for they too lived before the advent of the telescope. Ancient sky-watchers, by scrutinizing the sky with care over long periods of time, had discovered that the motions of the heavenly bodies are not random. Stellar and planetary movement
is intricate, but it was possible to calculate well in advance what paths these objects would take and where they would be at a future time. Close observers knew early on that though change, chance, and whim seem to
be
the rule on Earth, the heavens perform a complex but predictable dance. That dichotomy became a key part of the ancient and medieval worldview.

The best way to describe and
explain what one observed in the skies with the naked eye was to think of Earth as the center, with everything else moving around it. That concept still works admirably for purposes of navigation. In fact, to think that things might operate differently demands a leap of fancy that would seem ludicrous to anyone not steeped since childhood in Sun-centered astronomy.

Early astronomers knew,
however, that there are phenomena that one observes looking at the sky with greater care over a period of time that seem at odds with a system in which Earth is the center and everything else is in motion around it. Rather than decide that these glitches were significant and stubborn enough to require one to discard the Earth-centered view of the universe entirely and look for another, they chose
to attempt to explain the glitches, if they could,
within
an Earth-centered system. Ptolemy’s success in doing so was one of the most impressive intellectual achievements in history.

Ptolemy did not begin with a tabula rasa in the second century
A.D
. by gazing up at the night sky as it appeared to him from near the mouth of the Nile at Alexandria. Instead, he drew together the results of centuries
of previous speculation and observation and pondered all of this afresh, applying his own superb mathematical talents. The result, set down in his
Almagest
and other works, was a cohesive explanation of the cosmos that endured and dominated Islamic and, later, Western thinking for fourteen centuries. Finally, even as it was rejected, it provided the springboard for Copernican astronomy and all
that has followed from that.

Part of the intellectual worldview of the era in which Ptolemy lived was that the actual appearance of things had to be taken into account in trying to figure out what constitutes “reality.” To be plausible,
an
explanation had to “save the appearances,” not contradict them. Though in the early seventeenth century, after Tycho’s death, some Ptolemaic astronomers
refused to look through Galileo’s telescope when it seemed to reveal things that contradicted Ptolemy, Ptolemy himself did not ignore “what can be seen up there” in favor of some mathematical fable. He would have looked through Galileo’s telescope. However, nothing about the appearance of the heavens, as Ptolemy and his predecessors were able to study them, forced them or him to reject the intellectual
tradition that held that all heavenly movement occurred in perfect circles and spheres.

The “spheres” were not the planets themselves, but transparent glass spheres in which the planets traveled. Astronomers spoke of “crystalline” spheres, each having an inner and an outer wall, with space between the two walls for the planet to move. The spheres were nested one within the other, with each
successive sphere just small enough to fit within the one outside it. They were tightly packed with no extra space left between them, but not so tightly as to prevent their moving, one against the other, with the outer surface of one sphere scraping against the inner surface of the next larger.

Sitting at the center of this system of nested crystalline spheres was Earth. The outermost sphere
in the arrangement was the sphere of the stars. The innermost sphere—nearest Earth—was the sphere in which the Moon moved. The others each contained a planet, except for the one that contained the Sun. Each body could move only between the outer and inner walls of its own sphere. Not all scholars agreed about the nature and mechanics of these spheres, but there was general agreement that a planet
couldn’t break through those walls and enter another planet’s sphere. In fact, in this system,
no
heavenly body could break through the walls of a sphere. That would shatter it. This last restriction became significant for Tycho Brahe and Johannes Kepler.

One of the most stubborn problems for ancient astronomers was
how
to explain a phenomenon known as the “retrograde” movement of the planets.
A planet normally moves from west to east against the background of stars. However, during a period known as its “opposition,” when it is on the opposite side of Earth from the Sun, a planet appears for a while to move from east to west. Scholars were faced with the problem of explaining this in a model that required uniform movement and perfect circles and spheres. The solution, devised before
Ptolemy, was ingenious.

Figure 1.1: Early astronomers thought of the planets and the Sun and Moon as each moving in its own “crystalline” sphere (a), with these spheres nested one within the other and Earth at the center (b).

A carousel is a helpful analogy for understanding the idea: On the simplest carousel, the horses are bolted directly to the floor, which is a large, rotating disk. They circle, as the disk
rotates, but they have no other motion. If the amusement park is dark and there is a light attached to the head of one horse, an observer, positioned at the center of the carousel in such way as not to move with the rotating disk, sees the light circle steadily. It will have no “retrograde motion”—never seem to back up.

Suppose instead that the observer does occasionally see the light stop,
back up for a while, and then resume its former motion. This isn’t a random occurrence, as it might be if the light were on the cap of the ticket taker as he moves among the riders, or if a large firefly happened to venture into the carousel. The backing up happens regularly and predictably. The observer decides that the horse with the light on its head must not be bolted directly to the rotating
disk. Instead, each horse is part of a minicarousel perched near the edge of that disk. Hence, in addition to their motion with the disk, the horses are moving around in smaller circles, chasing their tails.