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Saturn from Cassini Astronomy 161:
An Introduction to Solar System Astronomy
Prof. Richard Pogge

Notes to Unit 2
Discovering Earth & Sky

These notes give references to sources for information provided in the individual lecture notes, sometimes giving more detail, or more advanced information for those interested. Material in these footnotes is supplementary to the lectures, and is formally outside the scope of the course (in other words, details here will not appear in homework assignments or exams).

Notes for Individual Lectures

Lecture 4: Measuring the Earth

[4.1] Aristotle's arguments for the spherical shape of the Earth are given in On the Heavens, Book 2, Part 14 (350 BCE). A modern translation by J.L. Stokes may be found online at MIT on the Internet Classics Archive.

Aristotle argued that the Earth must necessarily be spherical because the weight of all its parts setting towards the center would naturally form a spherical shape. Today we would recognize the tendency to settle towards the center to be a consequence of gravity (Aristotle does not, of course, use that word).

He noted the curved outline of the shadow of the Earth on the Moon, and the different heights of stars between orthern and southern regions, as mentioned in the lecture, but he also put forth a rather odd argument that one finds elephants in Africa ("Pillars of Hercules" is the Strait of Gibraltar) and India, arguing for "continuity of parts", meaning they are close together on the surface of a sphere (they are far apart across the mediterranian, but closer going west from Africa). The idea being the world conceived by Aristotle is small, but not so small that small changes in place result in dramatic changes in the heights of constellations.

[4.2] The definition of a stadion in modern units has been very contentious. A very compelling case has been made by Donald Engels (1985, American Journal of Philology, 106, 298, full article on jstor.org) for 1 stadion = 184.98 meters (based on 8 Roman miles to 1 stadion). Two numbers reappear in the literature: 148 meters/stadion, which was a mis-calculation by d'Anville in 1759, and 157.4 meters/stadion given by A. Letronne in 1851 (published posthumously). I used to quote the 157m/stadion number in my notes, which gives a circumference of the Earth much closer to that of the modern value. Engels' arguments, however, are very persuasive that Eratosthenes would have used the Attic Stadion based on the Stadium of Athens, which gives the conversion of ~185m/stadion that I quote in these notes.

[4.3] The only description of Erathosthenes' method that survives from antiquity is from On the Orbits of the Heavenly Bodies written by Cleomedes in the 1st or 4th century AD (also known by the first word of its Greek title as the Meteora). We know little or nothing else about Cleomedes, not even his date or place of birth. It is clear that the numbers 5000 stadia and 1/50th of a circle have rounded off for convenience, contributing to the inaccuracy of the final result.

However, while the derived circumference is off by ~15%, the actual difference in latitude between Alexandria (31°13' N) and Syene/Aswan (24°05' N) is 7°08', or about 0.0198 of the arc of a circle, within 1% of the value 0.02 (1/50th) quoted by Cleomedes for Eratosthenes. This is well within any measurement errors expected for the time.

Return to Unit 2 Lecture Notes
Updated: 2007 September 17
Copyright Richard W. Pogge, All Rights Reserved.