STS 109. Lecture 5. Greek Astronomy

							HPSC 109. Lecture 5. Greek Astronomy.
 “Eudoxus of Cnidus was the first to engage in such hypotheses... for as Sosigenes says, Plato had set the problem to
those who were engaged in these studies; What circular, uniform and orderly motions must be assume in order to
account for the motions of the heavens ?” - Simplicius.

"Aristarchus of Samos brought out a book of certain hypotheses, in which it follows from what is assumed that the
universe is many times greater than that now so called. He hypothesises that the fixed stars and the sun remain
unmoved: that the earth is borne round the sun on the circumference of a circle... and that the sphere of the fixed
stars, situated about the same centre as the sun, is so great the circle in which he hypothesises that the earth revolves
bears such a proportion to the distance of the fixed stars as the centre of a sphere does to its surface."

The celestial phenomena.
Viewed from the earth, firstly there is the motion of the stars, apparently circular about the pole star.
There is the motion and phases of the moon. There is the motion of the sun, and there are eclipses to be accounted
for. There are the complex motions of the planets. The planets move relative to the stars. All the planets move across
a band of sky 8 degrees wide which is known as the zodiac The planets ill occasionally halt in this movement, and
sometimes perform a loop. This motion is known a retrogression.

Concentric Sphere Astronomy.
Plato.
Plato sets parameters for astronomy that are to last for 2000 years; he asks astronomers to theorise the motions of the
heavenly bodies solely in terms of uniform circular motion or compounds of such motions. In his Timaeus he produces
the first, albeit somewhat crude attempt on these lines.
Eudoxus.
In a brilliant mathematical synthesis, Eudoxus produces a system of concentric circular motions which give a
reasonable description of the major celestial phenomena.
Aristotle.
Firstly Callippus builds on the work of Eudoxus by adding more circles to get more accurate results; Aristotle does the
same with Callippus‟ work, and also gives a physical model. According to him, there are a series of concentric
crystalline spheres which carry the heavenly bodies on their orbits, the interaction of these spheres producing the
complex motions of the planets.

A Glossary of some ancient astronomy terms.
Apogee and perigee.                                             was considered a good argument for geocentrism. Due
The perigee is the nearest point a body comes to the            to the size of the universe, parallax is actually a very
centre of its (non-circular !) orbit, the apogee the            small effect, and was not measured until 1838.
furthest point.                                                 Concentric sphere.
Inferior and Superior                                           System proposed by Aristotle whereby a series of
An inferior planet has an orbit around the sun but              crystalline spheres, concentric on the earth, produce
inside that of the earth, while a superior planet has an        the motions of the heavens; some of these spheres
orbit outside that of the earth; thus Mercury and Mars          interact to produce the more complex planetary
are the inferior planets.                                       motions.
Ecliptic.                                                       Ptolemaic astronomy.
The Line traced by the sun‟s annual motion as viewed            A system synthesised by Ptolemy which superseded
from the earth.                                                 the concentric sphere model by use of epicycles,
Zodiac.                                                         eccentrics, and equants.
The band of sky within 8 degrees of either side of the          Epicycle.
ecliptic. The motions of the planets all stay within this       A small circle, the centre of which moves in a larger
band. The zodiac can be divided into 12 house for               circle centred on the earth.
astrological purposes.                                          Eccentric.
Retrogression.                                                  An epicyclic model, but with the centre of the larger
Or regressive motion; when a planet reverses its path           circle moved away from that of the earth, usually along
through the zodiac, before carrying on.                         the line of the apogee and perigee to help account for
Geocentrism.                                                    these phenomena.
A cosmology with the earth at the centre of the                 Equant.
universe.                                                       Again, an epicyclic model, and with the centre of the
Heliocentrism.                                                  larger circle moved away form that of the earth as with
A cosmology with the sun at the centre of the universe.         the eccentric. In both of these models, the line made
Heliostatism.                                                   by the centre of the smaller circle and its centre of
A cosmology with a sun that does not move, though it            rotation (the earth, or the eccentric point) has a
may not necessarily be at the centre of the universe.           constant velocity. With the equant, it is the line
Parallax.                                                       between the centre of the smaller circle and another
A change in the apparent position of the stars due to           point that has constant velocity.
the motion of the earth. Inability to measure parallax
Greek Astronomy.
Beginnings. At the outset, there is a gap between the observational astronomy tradition and the cosmological
tradition. There are those who observe the heavens. There are those who produce cosmological models. No-one
produces cosmological models that are anywhere near explaining, in a precise manner, the phenomena that have
been recorded though. Explanations of what eclipses are, but no complete predictive model. Perhaps first attempt is
the Pythagoreans, though this is still rather vague and speculative. In the centre of the cosmos is a fire (not the sun !),
but this is shielded form the earth by a counter-earth, and the other bodies revolve around the fire outside the earth.
Pythagoreans have the rather strange idea of a „harmony‟ of the heavens.

Plato.
First serious attempt to unite the astronomical and cosmological traditions comes with Plato. Presumption of regular,
circular motions for all of the heavenly bodies - they do not wander. Two sphere model - the sphere of the fixed stars,
and the sphere of the planets. Need for some schizophrenia when dealing with ancient astronomy - the (real)
heliocentric explanations and the ancient geocentric ones. Ancients believe that the earth is central and stable. All the
motions of the heavens must then be real, and not apparent motions. E.g. apparently the stars circle the earth, but we
know in reality that this is only apparent and seems so to us due to the earth‟s daily revolution.
The ancients believe the earth to be stable so the stars really do have a daily circular motion. With Plato‟s model sun
moon and planets all move around in one plane but with different speeds.

Eudoxus.
Plato‟s model, though an advance, is still qualitative and does not account for either retrograde motion or the deviation
of planets from the line of the sun. The band within which the planets are seen to move is called the zodiac. Eudoxus
takes Plato‟s model and makes it rather more complex. Each of the planets has four spheres to move it (instead of
two). This allows for Eudoxus to cope with the main deficiencies of Plato‟s model. In one of the most brilliant pieces of
ancient science, Eudoxus does all the mathematics required to make this system work as a real model of the cosmos.
Quite amazing to do all this from scratch. System is improved slightly by Callipus who adds some more spheres in
order to improve the accuracy of the system.

Aristotle.
 Aristotle makes no improvements to the astronomy, but thinks hard about the cosmology. He wants a mechanical
model of the heavens. He conceives of each of the spheres of Eudoxus and Calippus as being real and made out of
the fifth element, aether. These spheres are considered to be next to each other with no space between, a sort of
Russian doll, or onion conception of the heavens. Because the spheres are physical and next to each other, they
transmit motion to each other, such that the motion of each planet can be complex. So that the motions of one planet
do not interfere with the next one down, Aristotle suggests that there are some „reacting‟ spheres moving at the same
speed but in exactly the opposite direction to the driving spheres. Aristotle ends up with a grand total of 56 spheres to
account for the motions of the heavens.

Problems.
Excellent model of the heavens for that time, but there are some difficulties still.
1. Planetary orbits are really elliptical and not circular. This means that planets get nearer and then further away from
the earth, such that apparent size varies. The concentric sphere model has the planets at a constant distance.
2. As a planet goes around its orbit, its speed varies - faster as it is nearer the sun, slower when it is further away. the
concentric sphere model has difficulties in coping with this.
3. The planets have different shapes of retrogressive motion - the hippopede can only give one shape.
Thus a new model needed to be developed, and key names here are Apollonius and Hipparchus.
Aristarchus, on of the few ancients to believe the sun instead of the earth was central to the cosmos warrants a
mention, but he is of little significance because no-one was convinced by him.

Ptolemaic Astronomy.
Building on the work of Apollonius and Hipparchus, Ptolemy (c100 AD - c170 AD) produced a whole new system which
was to last up to around 1600. He gave up the concentric sphere and hippopede model for a system based on a
device known as the epicycle. With this, allied with two more complex devices based on the epicycle known as the
eccentric and the equant, he was able to account for all of the problems that beset the concentric sphere model. His
astronomy/ cosmology lasted throughout the Roman empire, the dark ages, middle ages and Renaissance and was
only displaced during the scientific revolution. Although somewhat complex, it is mathematically very powerful and can
in principle account for virtually every astronomical phenomenon.

Arguments for geocentrism.
Rotation - If the earth has a daily rotation, accounting for the motion of the stars, then why is there not a constant wind
? Orbit - If the earth is in motion around the sun and through the cosmos, why are objects such a ourselves not swept
off the face of the earth ? Integrity of the earth - If the earth is in rapid motion, why doesn‟t it disintegrate ?
At this point there is little notion of gravity, but there is one of natural place and natural motion, which effectively holds
the earth together. Move the earth from its natural place, and there is no reason why it should hold together any more.
Parallax - If the earth orbits the sun, then why do we not observe parallax ? Man and God - If the earth is in motion
and is not at the centre of the universe, what does that imply for mankind‟s conception of itself and relation to God ?