Tycho and Kepler: solid myth versus subtle truth

Social Research, Spring, 2005 by Owen Gingerich, James R. Voelkel

TYCHO HAS THE WORLD'S FINEST OBSERVATIONS," JOHANNES KEPLER wrote to his teacher, Michael Maestlin, "but he only lacks an architect to construct an edifice out of them."

Kepler's remark, echoing down through the centuries, has reinforced a mythic view of these two geniuses of the scientific revolution: Tycho Brahe, the eccentric and arrogant builder of astonishing instruments who didn't know what to do with his observations except to use them for an obviously awkward and desperately backward-looking cosmology, and Kepler, the indefatigable mathematician armed with a cornucopia of Brahe's data who fit a curve through the triangulated points on Mars's orbit and showed it to be an ellipse, thereby solving the outstanding problem of the solar system. Like many hoary myths, this one contains a smidgen of truth. Tycho was far and away the most astute and prolific observer of his century, and Kepler, whose "warfare on Mars" lasted five years, did indeed succeed in improving the accuracy of Mars's predicted positions by nearly two orders of magnitude. But the actual circumstances of this critical episode in the scientific revolution are considerably more subtle than the well-honed legend. In particular, Tycho's instrument building and observational program were brilliantly targeted, and Kepler's use of Tycho's data was far more creative than mere empirical curve-fitting.

TYCHO'S COPERNICAN CAMPAIGN

Tycho Brahe (1546-1601) was born in Denmark three years after the publication of Copernicus's epoch-making De revolutionibus. A young prodigy who entered Leipzig University at age 15, Tycho took an early interest in astronomy, and in 1563 he observed the once-in-20-years conjunction of the two slowest moving naked-eye planets, Jupiter and Saturn. He was shocked to learn not only that the prediction of the event from the antique Alfonsine tables erred by a month, but that even the modern Copernican tables placed the event a few days too early (or so he tells us). This single observation has created its own mythology: that Copernicus, by rearranging the blueprint of the cosmos into a heliocentric system, had wrought an enormous improvement in the calculation of planetary positions. In truth, because Copernicus's system was essentially just a geometrical rearrangement of the ancient Ptolemaic system, relatively little immediate improvement could be expected, and this proved to be the general case. As Tycho himself later learned, and as Kepler would put into print, the Copernican predictions were sometimes less accurate than the Alfonsine ones. The conjunction of 1563 proved to be an unusual exception, where the Copernican prediction was even better than the mature Tycho remembered. (As a teenager he had not, in fact, observed the conjunction at its closest approach, and the error in the Copernican tables was a mere 16 hours, not two or three days as claimed by Tycho.)

Tycho made his initial astronomical reputation by determining that the nova of 1572 and the comet of 1577 lay beyond the moon, in the incorruptible aethereal regions where Aristotle had declared that no birth or decay should take place. To achieve this iconoclastic result, Tycho made clever use of what is called the diurnal or horizontal parallax: the position of the moon against the distant starry background will be different for an observer who sees the moon directly overhead and an observer at the same moment but a quarter of the world away who sees the moon on his horizon. The difference in the baseline, the earth's radius, shifts the moon's apparent position by approximately 1 degree (twice the moon's diameter), an amount easily observed by an astronomer such as Tycho. It was not necessary for Tycho to compare results with a distant colleague. In Copernican terms, he could let the rotation of the earth carry him to another position (hence the term diurnal parallax), and he could compare his own observations made several hours apart.

Young Tycho's success with the nova of 1572 led to a royal grant of the island of Hven as a fiefdom and to royal patronage for building Uraniborg, a "heavenly castle" and an observatory the likes of which the world had never seen. His observations in 1577 of the most brilliant comet of the century, and one of the most spectacular in recorded history, occurred before his observatory was well equipped, but the decisive observations were not particularly difficult even with the limited instrumentation then available: an armillary sphere and a vertical sextant. (Before the comet disappeared a larger and more versatile sextant came on line. All of Tycho's observations were of course made with naked-eye sights, as the telescope was not invented in his lifetime.)

By 1580, however, the complement of precision instruments on Hven was much stronger, and Tycho, with his full familiarity with diurnal parallax, could dream of a far more challenging use of that technique. Four decades earlier Copernicus had no way to establish empirically which cosmological arrangement was valid. Philosophical arguments were on his side despite the apparent ridiculousness of the earth's motion, but essentially the heliocentric system was merely an unconfirmed "theory pleasing to the mind." Tycho, however, saw the prospect of a subtle observational test to distinguish the two systems. In the Ptolemaic system, the orbit of Mars lay forever beyond the sun; on the other hand, in the Copernican system Mars would regularly approach the earth to half that distance.