Ancient Astronomy
This
page includes references to ancient astronomy other than Ptolemy. For Ptolemy
see my discussion of the Copernican Revolution, which appears as another web
page. Students should follow up Ptolemy via the Copernican Revolution leads.
Also, my article entitled “What the Copernican Revolution is All
About” included in the book The Nature of Science goes over some of the same
ground.
Here I have included references to the other topics that
were included in my presentation of astronomy leading up to Ptolemy. There is
not much here that is not in the printed lecture notes except the references to
particular web sites that illustrate and clarify the points that were made in
class.
Eratosthenes of Cyrene
(about 275 – 194 BCE)
After Euclid set out the corpus of mathematics in his Elements
around the year 300 BCE, astronomers were quick to use the mathematical
theorems in Euclid to calculate many things about the heavens, and ultimately,
to work out a complicated system that accounted for the apparent motions of the heavenly bodies, especially the planets.
There were several important mathematicians and astronomers in the period
following Euclid, most of them
working at Alexandria at the great
museum there. Of these, I will mention two prior to Ptolemy.
The first is Eratosthenes of Cyrene, nicknamed “Beta”
because his goal was to be the second-best at every subject to which he turned
his attention. Those subjects included poetry, history, mathematics, astronomy,
and geography. He is remembered most today for his ingenious use of simple
Euclidean geometry to come up with a quite respectable estimate for the size of
the earth.
Hipparchus (around 150 BCE)
About a century after Eratosthenes, Hipparchus,
another astronomer working in Alexandria, developed a number of very useful
tools for studying the heavens. Hipparchus used
Euclidean geometry in a way similar to Eratosthenes to try to determine the
size of the sun and the moon. However, while his method may have been sound,
his results were wildly inaccurate because he had to measure some very small
angles with the naked eye and poor instruments. (For an illustration of his method,
see http://astrosun.tn.cornell.edu/courses/astro201/hipparchus.htm)
Slight inaccuracies in these measurements led to large inaccuracies in his calculations.
However, we was able to calculate accurately a very
slight pattern in the apparent motions of the heavens that causes the vernal
equinox to occur about 20 minutes earlier every year (the year being measured
by the cycle of the sun against the heavens). That phenomenon is known as
precession of the equinoxes. Hipparchus was able to
calculate (correctly) that it took about 26,000 years for the heavens to come
back to the same alignment.
More importantly, Hipparchus developed a
mathematical tool for measuring the relative distances of objects from each
other compared to the observed angle between them, for example, the relative
distance between two stars (relative to the distance that we are from them) as
indicated by the angle between them. This relationship he recorded in a complex
table that measured the comparative lengths of a radius of a circle to a chord
of the circle and related this to the angle subtended by the chord. This
relationship which he discovered and recorded is in fact the same as the
principle of trigonometry. For a brief illustration see http://aleph0.clarku.edu/~djoyce/java/trig/chords.html
Hipparchus is also the probable originator of the
idea of planets moving on an epicycle and deferent system. A web site with a
brief explanation is http://drumright.ossm.edu/astronomy/geocentric2.html
The next major development in ancient astronomy was a full 300 years later,
around 150 CE (A.D.) with the work of Claudius Ptolemy that built directly upon
Hipparchus’ ideas and observations. For Ptolemy, see
the separate web page on the Copernican Revolution.