Tycho and Kepler: solid myth versus subtle truth

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

As the year progressed, Tycho must have realized that his new complement of instruments actually made possible an assault on the great cosmological problem--that is, to decide observationally between the Ptolemaic and Copernican systems on the basis of the distance to Mars. In fact, the end of 1582 provided the first opposition of Mars at which Tycho had his large instruments available. An examination of Tycho's surviving observations shows that on December 26-27, 1582, and January 17, 1583, he had clearly attempted to find the diurnal parallax of Mars by morning and evening observations.

Since the mural quadrant could be used only for meridian observations, it was not helpful for the diurnal parallax measurements, which involved observing Mars near the eastern horizon in the evening and near the western horizon in the morning. Similarly the larger quadrants were not especially useful. The 1582-83 campaign chiefly employed the trigonal sextant. This instrument could record the position of Mars with respect to comparison stars, and was the primary tool for his observational program. In mid-January Brahe wrote in his observing log, "Note that I am taking Mars's distance from this star because it is as if [Mars's] course proceeds from it, as comparison of the evening and morning distances will show the parallax." As Kepler later demonstrated definitively in his Astronomia nova, the campaign was unsuccessful, since the observations displayed no convincing parallactic effect.

Nevertheless, at the next opposition of Mars, in January 1585, Tycho instructed his staff to make morning and evening observations. However, his observations pointed to a nonsensical negative parallax, which implied that Mars was more than infinitely far away, so he wrote in his log book "there is some underlying error." No doubt he was not merely puzzled, but deeply troubled by these anomalous results. The failure to find the cause of the error no doubt sensitized Tycho to possible interference from refraction by the earth's atmosphere, a phenomenon he had recognized in connection with his solar observations. In effect, the layered density of the earth's atmosphere acted like a lens, slightly raising the apparent positions of the stars or planets the closer they are to the horizon. If Mars, which in the evening observation was a few degrees closer to the horizon than the comparison star, suffered from greater refraction than the star, this could have explained the negative parallax. Thus, in the following fall a thorough examination of the effects of refraction entered strongly into his research program.

Two years after the puzzling and inconclusive 1585 Martian observations, with the approach of the March 1587 opposition, the scene was entirely different, for Tycho's great equatorial armillary was now available. It was the most impressive instrument at the new Stjerneborg Observatory, which Tycho had built alongside his original Uraniborg castle observatory. This large device enabled him to measure directly a star's or planet's position with respect to the celestial equator. Furthermore, by January 1587, Tycho's view of the significance of the Martian parallax had changed. Though he still had only the ambiguous measurements of 1582-1583 and the useless results of 1585 to look back to, he clearly anticipated positive results in the upcoming opposition. In a letter to Landgrave Wilhelm IV written several weeks before the actual observations would begin, he outlined his efforts. A careful look at the text reveals some nuances in his claims; while mentioning the earlier 1582-83 observations, he was in fact cagey about the measurements, explaining his observations in principle but without definitively claiming success: