Selections from the History of Astronomy

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Another post from the History Book Club, this time based on three books:

• To Explain the World: The Discovery of Modern Science, by Steven Weinberg.
• The Sun in the Church: Cathedrals as Solar Observatories, by J.L. Heilbron.
• The Composition of Kepler’s Astronomia Nova, by James Voelkel.

Steven Weinberg, the physics Nobelist, liked to write popular science books. In 2015 he published To Explain the World: The Discovery of Modern Science; this made fur fly among historians. The title of Steven Shapin’s review was “Why Scientists Shouldn’t Write History”. Turf-defending? Partly. But mostly a disagreement about the proper approach to history. Weinberg himself lays out the bone of contention early in the book:

…[T]he task of a historian depends on what he or she is trying to accomplish. If the historian’s aim is only to re-create the past, to understand “how it actually was”, then it may not be helpful to judge a past scientist’s success by modern standards. But this sort of judgment is indispensable if what one wants is to understand how science progressed from its past to its present.

Weinberg takes an unapologetically ‘presentist’ or ‘Whiggish’ approach, judging the past by the standards of the present. This was par for the course up to about 1930, but is largely anathema today. His book offers a time capsule of the strengths and weaknesses of presentism. His lovingly detailed treatment of astronomy, from the predecessors of Ptolemy through Newton, delves into technical aspects with clarity, assurance, and aplomb. But his discussion of Aristotle gives almost no insight into how he set the framework for medieval European thought. Aristotle figures purely as an obstacle on the road to Newton.

On the evergreen flare-ups between science and religion, Weinberg writes:

It was essential for the discovery of science that religious ideas be divorced from the study of nature. Once one invokes the supernatural, anything can be explained….

Weinberg here echoes a view often called the Draper-White thesis after two late 19th-century writers. I imbibed this sentiment early in my own education, and appreciate Weinberg’s pithy phrasing. Problem is, the history of science for the period in question decisively refutes it.

Here’s the opening paragraph of The Sun in the Church: Cathedrals as Solar Observatories, by the noted science historian J.L. Heilbron:

The Roman Catholic Church gave more financial and social support to the study of astronomy for over six centuries, from the recovery of ancient learning during the late Middle Ages into the Enlightenment, than any other, and, probably, all other, institutions. Those who infer the Church’s attitude from its persecution of Galileo may be reassured to know that the basis of its generosity to astronomy was not a love of science but a problem in administration. The problem was establishing and promulgating the date of Easter.

Determining the date of Easter soaked up so much mathematical energy during the middle ages that it was called simply computus: the computation. Heilbron succinctly diagnoses the difficulty:

The old theologians decreed that Easter should be celebrated on the Sunday after the first full moon after the vernal equinox … Since neither the lunar nor the solar year contains an even number of days, and, moreover, the year does not contain an even number of full moons, and, again, Sundays do not occur regularly on the same calendar dates, the computation of the Easter canon was neither easy nor accurate.

And we’re off to the races. Heilbron recounts the entangling of the Easter date with the Hebrew lunar calendar:

Unfortunately, only the rabbis could say when [the month of] Nisan began. Early Christian communities had to apply to the leaders of a rival church to learn when to celebrate their principal feast. The ignominy of this procedure, and the difficulty of a timely dissemination of the result as the church spread, forced the bishops into arithmetic.

Pages and centuries later, we come to the section title “A Scandal in the Church”:

… the problem was urgent. The calculated Easter differed from the true date by eight days in 1345 and a month in 1356. … Easter was celebrated five weeks late in 1424 and one week off in 1433 and 1437.

Along the way we learn the gensis of AD dating: in the year 242 of the era of Diocletian, the monk Dionysius Exiguus was revolted at the idea of keying a table of Easter dates to the reign of a persecutor of the Church. So he took the year Diocletian 242 and christened it 526 anno Domini.

The year 1571 AD finds us in Florence, where one Egnatio Danti has convinced Cosimo dei Medici, Grand Duke of Tuscany, to gain immortal fame through the avenue of calendar reform. The project requires precise measurements of the tropical year and other astronomical constants. With Cosimo’s patronage, Danti installs an armillary sphere and a quadrant on the façade of Santa Maria Novella. They are still there.

Thus commences the era of cathedrals as solar observatories. The introduction remarks, “This book originated in the pleasant viewing of meridian lines installed in four Italian and one French cathedral.” Reading it I was tempted to hop on the next flight to Italy.

A meridian line—meridiana—is a line running precisely north-south, carefully leveled, in a huge darkened space, placed where a narrow beam of sunlight can cross it once per day. The canonical instance: the Grand Meridiana of San Petronio in Bologna, constructed in 1665 under the direction of Giovanni Domenico Cassini. Seventeen years older than Isaac Newton, Cassini became the premier astronomer of his generation. The San Petronio meridiana remained a precision astronomical instrument for many decades, undergoing extensive and expensive renovations in 1695. The pope, not to be upstaged by Bologna, had his own meridiana built in Michelangelo’s church, the Santa Maria degli Angeli, in 1702. Before then however the Sun King had lured Cassini to France to found the new Paris Observatory.

Weinberg’s history devotes most of its attention to the big revolutions in science: Copernicus, Kepler, Newton. But as Thomas Kuhn pointed out (ironically in his book The Structure of Scientific Revolutions), 90% of science consists of more mundane activities: refining parameters, resolving discrepancies, applying established theories to new situations. Without this foundation of what Kuhn called “normal science”, the exciting revolutions could never happen.

The transition from Ptolemy to Kepler resulted in roughly a 50-fold increase in accuracy. The next hundred years produced another 50-fold increase, more or less—this time thanks to such down-to-earth factors as better parameters, and corrections for atmospheric refraction. The meridiane (and Cassini) played a major role.

A technicality of Kepler’s astromy furnishes a good example, returns us to the science/religion interface, and serves to introduce the last book: James Voelkel’s The Composition of Kepler’s Astronomia Nova. In the Astronomia Nova Kepler unveiled to the world his first two laws, well-known to generations of high-school students. But a larger fraction of this work deals with another issue: do the same rules govern the earth’s orbit as the other planetary orbits?

This question has a counterpart in Ptolemaic astronomy: is the sun’s orbit special? Ptolemy said Yes!, and everyone after him, including Copernicus—but not Kepler—agreed. (Copernicus switched the roles of the sun and earth, but otherwise it’s the same thing.) Since the earth is our observing platform, this error propagated throughout the whole of astronomy.

Specifically, in Ptolemy’s system the sun moves at a uniform speed in an eccentric circular orbit. ‘Eccentric’ means simply that the earth is not at the center of the orbit. Thus purely as an optical effect, the sun appears to move faster to us when it’s closer to the earth. But the actual speed, according to Ptolemy, is always the same.

In contrast, and using Mars as an example: its motion is  described using two circles (the deferent and the epicyle) and a special point called the equant. If you pull the Copernicus trick and change your frame of reference so the sun is motionless, then the epicycle disappears. The deferent is reborn as the orbit of Mars around the sun. Now the key point: Mars’s motion along this reborn deferent is non-uniform: its speed varies, and only appears uniform when viewed from the equant.

Long before Kepler laid eyes on Tycho’s treasure trove of observations, he said No! to this. The earth must be the same as every other planet. If Mars has a variable speed, so must the earth. Kepler came to this conclusion by a combination of theological and physical reasoning. The theology came perilously close to Sun worship. Kepler, deeply devout, drew a parallel between the Trinity and Copernican astronomy, with the sun as the Father, the fixed stars as the Son, and the space in between as the Holy Ghost. Hence the sun must drive the planets around in their orbits. The resulting physics had an Aristotelian cast.

Kepler’s elliptical orbits met with less resistance than his claim about the varying speed of the earth. The issue was finally decisively resolved in 1655 by Cassini and collaborators, using the meridiana of San Petronio.

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