Tycho and Kepler (21 page)

Figure 9.1: The Tychonic system of the world, compared with the Ptolemaic and Copernican systems.

Tycho had used parallax measurements to try to find the distances to the nova of 1572 and the comet of 1577. In order to use the equivalent of two eyes (as in the finger-before-the-face demonstration) in observing the parallax shift of Mars against the background stars, one “eye” must be very
far away from the other. About ninety years after Tycho attempted the measurement, Gian Domenico Cassini succeeded in measuring Mars’s parallax by placing one observer in Paris and another in Cayenne in South America. Such an option was not available to Tycho, nor were Cassini’s telescopes. However, Tycho had another method, the one he had used for the nova and the comet: An observer could stay
in place and let the rotation of the celestial sphere (or of the Earth, if he thought like a Copernican) transport him from one viewing position to the other. A shift in the position of a celestial object viewed in this manner is called
diurnal parallax
.

Tycho knew that the parallax of Mars as viewed from Earth would be tiny and that the attempt to measure it would stretch his capability of
precise observation to the maximum. Mars does of course come nearer to Earth than the Sun, but not so near as to make its diurnal parallax ever more than twenty-seven arcseconds. Observing Mars’s parallax shift was, in fact, not possible with Tycho’s instruments, but he did not know that. Tycho, in fact, thought the Sun was much closer than it actually is, and that its parallax was three arcminutes
rather than the nine arc
seconds
we know it to be.

If three arcminutes was the right measurement, and if the Ptolemaic model was correct and Mars was always farther away than the Sun, Mars’s parallax would always be
smaller
than three arcminutes. But if Copernicus (or the still evolving Tychonic system) had it right, Mars would come to within half or even a third the distance to the Sun and,
when it did, have a noticeably
larger
parallax than three arcminutes.
^fn1

The best time to make the measurement was when Mars made its closest approach to Earth, and that was when it was at “opposition”—on the opposite side of Earth from the Sun. Some oppositions bring Mars closer to Earth than do others, and unfortunately, the oppositions when Mars was closest were in summer, when the Danish
nights were too short for making the measurement. Nevertheless, Tycho hoped that Mars would approach near enough to Earth at the winter oppositions. If the Copernican or the Tychonic system was correct, he judged that Mars’s diurnal parallax at the winter oppositions would be about five arcminutes, a shift that would be just barely possible to observe with his best instruments. On this tiny possibility,
he pinned all his hopes.

The great mural quadrant was ready in June 1582, and Tycho began using that magnificent instrument, placed so conveniently across the corridor from his winter dining room, to find the positions of the background reference stars he needed for measuring the parallax. In late December and January, Mars was at opposition. Tycho and his staff made observations of Mars on
the eastern horizon in the evening and near the western horizon in the morning. The observations showed no parallax.

So far it was victory for Ptolemy, defeat for Copernicus and Tycho. However, that was not to be the end of the matter. This campaign would involve Tycho for much of the remainder of his life at Uraniborg and be his chief motivation for building more precise and powerful instruments
and the new observatory to support them. Searching for an answer that they would never find, he and his assistants, quite unaware, were doing the essential background research for Johannes Kepler.

Tycho had to wait two years, after the 1582–83 observations, for the next opposition of Mars, in January 1585. This time his results were nonsensical—a
negative
parallax. Also, Mars’s retrogression—the
“backing up” that occurs during opposition—was smaller than expected. Perplexed, he wondered whether the refraction of light by Earth’s atmosphere might be to blame.

Refraction is the change in the direction of light waves as they pass from one medium to another, in this case from empty space to the atmosphere. The most familiar demonstration is the way a rod appears to bend when partly immersed
in water. Refraction was not well understood in Tycho’s day. In 1585, though he had encountered refraction in studies of the Sun, he did not know whether starlight was refracted or, if it was, whether a planet would suffer the same degree of refraction. But it was reasonable to suspect that refraction might be affecting the accuracy of his Mars observations. In the evening, Mars was a few degrees
closer to the horizon than the star Tycho was using for comparison, and he wondered whether this might cause Mars to suffer greater refraction than the star. Tycho began to devise observations that would help him determine the degree of refraction to be expected for stars. As he continued to ponder the problem, the instruments of Stjerneborg finally came on-line.

When Mars next came into opposition
in March 1587, Uraniborg and Stjerneborg were poised for the assault as never before, with the equatorial armillary and two large azimuth quadrants installed in
Stjerneborg
and numerous assistants awaiting Tycho’s orders. Shortly before that opposition, Tycho wrote a letter to Landgrave Wilhelm of Kassel, voicing his optimism about finding the parallax.

March 10 was a typical night.
^fn2
In
some cases there were simultaneous observations with the sextant and the quadrant, and sometimes with the equatorial armillary. Most of them were noted in Tycho’s handwriting.

6:27
P.M
.—a meridian altitude
²
of Jupiter [its altitude above the horizon as it crossed the meridian], made using the revolving quadrant, followed by a series of lunar positions and then a measurement of Mars’s declination,
all made using the equatorial armillary.

Just before 7
P.M
.—measured distance between Mars and the star Regulus, then between Mars and Cauda Leonis, and then between Mars and Arcturus.

For the next hour—triangulation of distances between these stars, then some measurements of Saturn and Jupiter.

8:30—break

9:45—a few observations of Regulus and Spica “for learning the refraction
of Mars”; and shortly after that a few positions of the Moon.

11:22–12:02 (twenty minutes before and after the meridian passage of Mars)—assistants recorded distances with the equatorial armillary and trigonal sextant.

Shortly after midnight—bedtime. [Perhaps many of them piled up on the beds in the underground room at the center of Stjerneborg.]

4:14–5:16
A.M
.—a new set of Mars observations
with the armillary and sextant, once more for finding its angular distance from Arcturus and Cauda Leonis (which by this time stood above Mars in the sky) and to Spica. [The Mars to Arcturus measurements showed that refraction was altering Mars’s position by an amount that was consistent with Tycho’s refraction table for the Sun.]

Night after night in the starlit darkness on Hven near the
grazing cattle and sheep . . . the trigonal sextant carefully adjusted against the sky . . . the great equatorial armillary swinging around into place . . . the planet blinking against the sites of the revolving quadrant—from the observatories in the castle, from the amphitheater steps of the sunken observatory beyond the walls—the magnificent barrel-chested, red-bearded astronomer and his retinue
of assistants and interested visitors stayed up most of the night and carried out this systematic program of observations . . . all to capture and pin down a planet that had so tantalizingly orbited Earth—or was it the Sun?—since the world began, to fix its positions and understand its motions as no one had ever done before.

Tycho put all this data together and computed what it meant, correcting
the position of Mars to take refraction into account, based on his solar refraction table. He was elated with what he found. He had measured a diurnal parallax for Mars of about five and three-quarters arcminutes, meaning that the planet
did
come closer to Earth than the Sun did. The parallax agreed with Tycho’s computation of what it should be in the Copernican model. For a little while, Tycho
had reason to hope that he would indeed be remembered for one of the greatest achievements in the history of science—overturning Ptolemaic astronomy.

During this same year, 1587, Tycho’s book about the comet of 1577, much of which he’d written shortly after the comet’s appearance, was finally on press, and Tycho felt he had to add a chapter describing the position of the comet relative to
the planets. This was no
small
decision, for in doing so he would have to announce his conclusions about the planetary system.

T
HE DETAILS OF
the full Tychonic system had begun to come together in Tycho’s mind in about 1583. After that, during numerous lengthy discussions in the Winter Room, nights of observations and days of calculation,
he refined his model. In 1584, though not yet completely satisfied with it, he sketched out his precious idea with a piece of chalk on a green tablecloth for a guest, Erik Lange. And just there the crack first appeared in Tycho’s supreme self-confidence. A chain of events began
³
that would eventually turn this proud, well-focused man into someone at times resembling a wounded, cornered animal.
Perhaps the change had started earlier and happened more gradually, but this is where it first appears in the surviving documents about him.

Erik Lange was a good friend and a relative by marriage. He had been present at the dedication of Uraniborg. By 1584 he governed Bygholm Castle in Jutland, which meant that when he visited he came with a considerable retinue. Among them, this time, was
a young man named Nicolaus Reimers Bär, a surveyor. Though he was the son of a pig farmer from the Dithmarsch in Holstein, Bär was a gifted mathematician and a likely candidate to join Tycho’s band of assistants. He composed some flattering verses in an attempt to ingratiate himself with Tycho.

Tycho and his household sensed something underhanded, even sinister, about Bär, and Tycho took a
distinct disliking to him. The problem initially had to do with the fact that while Tycho was entertaining Lange and other noble guests, Bär lurked in the library and leafed through Tycho’s manuscripts, making notes on scraps of paper. He also surreptitiously examined and sketched Tycho’s instruments. One of Tycho’s assistants, Anders Viborg, called attention to this peculiar, secretive behavior.
Viborg baited Bär, leading him into preposterous
arguments
, which ended with Bär in a rage. Tycho silenced one of his outbursts at the dinner table with the jocular dismissal, “Those German fellows are all half-cracked.” But Tycho was far from taking the matter lightly. Before he sketched his system on the tablecloth, he insisted Bär leave the room, and he erased the sketch before Bär returned.

The investigation of Bär moved to a new stage. His quarters were changed so that he shared a room with Viborg. While Bär slept, Viborg managed to empty one of his pockets and found “four whole handfuls
⁴
of tracings and writings.” When Bär discovered that some of his surreptitiously written notes were missing, he began “shrieking, weeping, and screaming so that he could hardly be calmed down.”
Both Tycho and Lange promised that anything that actually belonged to him would be returned, and both men, on the surface, treated the episode as a disagreeable joke. But Tycho worried that Bär might have seen material having to do with Tycho’s new planetary model.

In the spring of 1586, Bär surfaced at the court of Landgrave Wilhelm IV of Hesse, in Kassel, where Tycho himself had visited
with such success eleven years earlier. Tycho was still carrying on a friendly correspondence with the landgrave who had so enthusiastically encouraged him and praised him to King Frederick. Wilhelm now heard from Bär of a new planetary system that Bär claimed to have invented during the past winter. The landgrave was deeply impressed and commissioned a mechanical model of Bär’s system.