In this laboratory you will be introduced to the practice of astronomy in the period between Claudius Ptolemy, whose Almagest established the principles of astronomical theorizing in around 150 CE, and Nicolaus Copernicus, who rejected those principles almost a millenium and a half later. You will see what an astronomer did - not at all what a modern one does - and why. You will also become acquainted with some of the more important instruments and observational techniques that would have been used. And you will be placed in the position of an astronomer yourself, using the computer to construct and assess astronomical theories in the manner of a Renaissance mathematician.
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Astronomy is the oldest as well as the most prestigious of the mathematical sciences. Observing the heavens for the purposes of predicting eclipses and other phenomena occurred in the time of the Babylonians, if not earlier. Well before the beginning of the Christian era, astronomy was a demanding technical enterprise. It required long training and intense dedication of its practitioners. In this module, the computer will stand in for that training, and provide you with the theoretical toolkit possessed by a practitioner of Ptolemaic astronomy.
For much of its history, planetary astronomy, at least, has been dominated by a relatively simple set of conceptual tools. Any late-medieval or Renaissance astronomer was familiar with these tools. This module recreates the practice of astronomical theorizing pursued by such an astronomer.
What does an astronomer do, and why does he or she do it? In this period, an astronomer's duty was to predict planetary positions and eclipses. To achieve those ends, he might have to construct both observational instruments and theoretical constructs. By contrast, there were some surprising things that an astronomer did not do. He did not concern himself with the nature of the heavens and heavenly bodies themselves - at anything beyond a fairly elementary level, at least. He was regarded as unqualified to speculate extensively on the causes of celestial motions, nor, indeed, to probe far beyond the numerical figures themselves that he derived from observed planetary positions. And he was not very concerned, even within this calculational work, about the actual paths followed by the planets through the heavens. These were matters on which the mathematical techniques of astronomy could yield no certain or authoritative knowledge. They were more appropriate to the philosopher than the mathematician, since they related to real, physical entities, not abstracted, numerical ones. An astronomer was correspondingly something of a subordinate figure. His was a service industry, dedicated to providing dates and times for others of higher status (physicians, churchmen, philosophers) to put to use.
Ptolemaic astronomers thus avoided controversial speculation on the nature and mechanisms of the heavens. But their basic assumptions were nonetheless supposed to be compatible with natural philosophy -- and in particular the natural philosophy of Aristotle.
As seen here in a hand-colored image from a seventeenth-century atlas, Aristotelian natural philosophy portrayed a cosmos with the Earth stationary at its center. The four elements of earth, water, air, and fire all had their own proper spheres concentric to the earth, followed by the sphere of the Moon. This marked the boundary between the "sublunary" world, in which things came into being, changed, and died, and the "superlunary" realm, in which things were eternal. Beyond lay the planets, or "wandering stars," which moved around the earth in perfect spheres. The sphere of the fixed stars contained all of these, with nothing beyond it except God. Christians changed the gloss slightly to assert that the cosmos as a whole was not eternal - it had been created by God, they insisted, and would eventually suffer annihilation at his hand - but they kept the natural-philosophical principles largely intact. On this basis, Christianized Aristotelianism provided coherent and largely convincing knowledge of natural processes for some 450 years, from the reintroduction of Greek philosophy in around 1200 to its eclipse in the "Scientific Revolution" around 1600-1650.
But astronomers were not philosophers. They accepted the basic structure of the Aristotelian cosmos, but did not see their task as one of explaining its nature. Their role was to predict significant celestial events (like eclipses and conjunctions ), provide astrological forecasts, and identify propitious days on which to administer medicines. For such purposes Aristotelian cosmology proved not so much inadequate as inappropriate. Astronomers instead developed their own, rich, mathematical tradition. But the result was a multiplicity of different theories, all unique, but all properly called "Ptolemaic" because they embodied the theoretical devices of the Almagest.
What was it like to pursue this kind of enterprise - an enterprise very different from the modern science of astronomy, and yet of which that modern science is the descendant? In this module you are given the chance to find out. You yourself become a Ptolemaic astronomer. The computer provides you with the theoretical armoury an astronomer possessed as a result of his training at university or through dedicated reading. You are faced with an observed path of a planet. Your task is effectively that faced by any astronomer of the Middle Ages or Renaissance seeking to placate his prince or advance in his university. Can you achieve success?
The ground-rules for medieval and Renaissance astronomy were set by Claudius Ptolemy, who lived and worked in
in around 150 CE. In his Almagest, Ptolemy developed sophisticated mathematical techniques to address the problem of planetary motions, and provided theoretical mechanisms capable of accounting very successfully for the perceived paths of all the planets. This work would survive the end of the Alexandria Roman Empirein Greek and Arabic versions; in the twelfth century they would be translated into Latin and made available again to Christendom. The recommendations in the Almagest then dominated the practice of astronomers for the next half a millenium. So the enterprise simulated here is one that formed the core of astronomy during a large part of its entire history.
Ptolemaic astronomers began with the observed positions of the heavenly bodies. The first part of their enterprise was to use instruments to obtain these observations. They did so at relatively few points in a planet's path through the sky, however. It was not until around 1600 that regular, systematic observations began to be taken as a matter of course.
The astronomer's main duty was then to reproduce the observed motions of the planets in order to predict their positions at specific future dates. There were two axiomatic rules. The first was that the Earth must lie at the center of the cosmos; this was self-evidently true to most people, and an uncontroversial part of Aristotelianism for those acquainted with the subject. The second was that the planets' positions must be explained in terms of regular circular motions. This was an ancient conviction, and was scarcely ever questioned until Kepler abruptly abandoned it altogether in the early seventeenth century. The belief was that celestial motions, being to all appearances eternal, must be as close to perfection as anything observed in nature; as such, they must be composed of the most perfect components, which were universally agreed to be regular circles. Aristotelian cosmology, with its insistence on a central, immobile earth, endorsed these axioms. For a Christian Aristotelian, the realm below the Moon was the domain of change; that above the Moon saw eternal perfection until the day that God chose to end the world.
However, accounting for actual planetary motions in this elegant way proved rather difficult. To a very crude approximation, a planet's observed path could indeed be thought of as uniform. But when it came to predicting its future positions, any such representation proved hopelessly inaccurate. It had long been recognised that there were points in some planets' paths at which they seemed temporarily to double back on themselves, retracing their steps before doing another about-turn and continuing on their way. This is the kind of path that might be taken by Mars, for example, seen against the fixed stars as the planet proceeds from left to right across the sky.
These instances of "retrograde" motion, as it was called, were seemingly impossible to reconcile with the notion of regular circular paths. Aristotelians did develop systems of nested spheres that could account for the general form of these phenomena, but none of these systems, however unwieldy, could be used to provide accurate forecasts. This problem of planetary motion therefore became the major difficulty in astronomy.
Ptolemaic astronomers adopted three ingenious theoretical mechanisms to solve theproblem of the planets.
First, they allowed themselves to combine uniform circular motions. A planetmight move uniformly on the circumference of one circle, but that circle in turn might beallowed to move on the circumference of another. The first circle was then called an epicycle,and the second a deferent. The combination is shown here.
Or perhaps another epicycle moved on the circumference of the first. Before long,astronomers found that by combining enough circles in these ways they could model almostany series of observed positions to a high degree of accuracy.
Secondly, astronomers allowed that the Earth might be positioned away from the centerof a planet's deferent. In this case, the circle was said to be eccentric. Suchorbs provided an alternative to epicycles.
And thirdly, astronomers allowed in certain circumstances for an eccentric circle to havewhat they called an equant. An equant was a point in space, separate from boththe earth and the orb's geometric center, from which its motion appeared to be uniform.(In our terms, angular velocity remained constant about this point.) This was still, in adistinctly strained sense, uniform circular motion - but it was not uniform about thecircle's center, nor about the Earth.
By various combinations of these three mechanisms, astronomers produced predictions of the heavenly appearances that allowed them to fulfill their task of predicting future heavenly appearances. In this you can recreate their enterprise. You can either read more detailed instructions, or move straight to the simulation.
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