FROM READERS.(Letter to the Editor).

EX CATHEDRA

In his article "The Sun in the Church" [September/October 1999], J.L. Heilbron claims that cathedral-based solar observations made by Giovanni Domenico Cassini "disproved the very geocentric dogma they [early modern astronomers] were supposed to uphold." But that claim is not even supported by Mr. Heilbron's own account. Cassini carefully measured an image of the sun projected on a meridian line embedded in the floor of a cathedral in order to determine the variation in distance between the earth and the sun at the summer and winter solstices. Although Mr. Heilbron tells us that Cassini's resultant calculation of the eccentricity of the earth-sun orbit was in disagreement with Ptolemy's geocentric model by a factor of two, he fails to note that the result was equally in disagreement with Copernicus' helio-centric model, which had precisely the same eccentricity as Ptolemy's model.

Moreover, both models readily could have been modified to account for Cassini's observations by extending the Ptolemaic concept of the equant point. As described in the Almagest, Ptolemy introduced the equant point to account for observed variations in the angular distance of Venus from the sun and in the retrograde arc of Mars. The bisection of the eccentricity by the equant point for those planetary orbits was a consequence of fitting the parameters of his model to observations, not because of any "uncanny intuition" on Ptolemy's part. In the absence of any direct observation of the variation in the earth-sun distance, however, Ptolemy did not see any need to introduce an equant point for his solar orbit; for that same reason, Copernicus simply copied Ptolemy's result. Hence it cannot be argued that Cassini's observations "disproved the geocentric dogma."

Kepler first determined the variation in the distance between the earth and the sun almost half a century before Cassini's observations. With access to Tycho Brahe's excellent planetary and solar observations, Kepler obtained the earth-sun distance through triangulation with the position of Mars. He found an "eccentricity just half that which Tycho Brahe had found through equations of the sun's motion" that were derived by assuming a circular earth-sun orbit. Mr. Heilbron also concludes that Cassini's "observation unambiguously agreed with the predictions of Kepler's model." But Heilbron is referring here to the model in which the earth traces an elliptical orbit with the sun at one focus, not to the model in which the earth traces a circular orbit, as Kepler originally envisioned. To establish conclusively that the earth-sun orbit is approximately elliptic and not circular would have required Cassini to measure the size of the solar image approximately a hundred times more accurately than he did, and to include observations near the equinoxes. For Cassini, such accuracy was clearly impossible: his measurements were already at the limits of sensitivity for his meridian.

The geocentric dogma was not overthrown by "exquisitely sensitive observations made within the very edifice of a church," but by the successful agreement of Kepler's three empirical laws for his heliocentric model with astronomical observations, and by Newton's development of celestial mechanics.

MICHAEL NAUENBERG University of California Santa Cruz, California

J.L. Heilbron replies: Readers of The Sciences will no doubt be as pleased as I am that Michael Nauenberg has troubled to dilate a point slighted in the process of excerpting and condensing portions of my book, The Sun in the Church. As he writes, Cassini's project was to settle whether an eccentric circle with whole or with bisected eccentricity better represented the sun's (or the earth's) orbit. Cassini found for the half-eccentrics (Keplerians) against the complete eccentrics (Ptolemaic astronomers, including, in this case, Copernicus). The finding did not defeat geocentrism but (as the book puts it) added one more piece of evidence in favor of Kepler's version of the Copernican system. Or, as the first royal astronomer, John Flamsteed, put it, referring to Cassini's observations, "The Suns Excentricity is bisected as the Copernicans affirmed."