Download The Ptolemaic Geocentric Universe

The Ptolemaic Geocentric Universe
The Ptolemaic universe is based on the assumption that all celestial objects can only move with
perfect uniform circular motion. The Earth is at the center of the universe. Everything else
orbits the Earth on epicycles orbiting on deferents centered on a point near the Earth. In order
of increasing distance from the Earth, they are the Moon, Mercury, Venus, Sun, Mars, Jupiter,
and Saturn. The celestial sphere with the fixed stars surrounded everything else. The other
planets we know of today (Uranus, Neptune, and Pluto) cannot be seen with the naked eye,
and were not known to Ptolemy. He overlooked that the use of equants violates the notion of
uniform circular motion.
Ptolemy explained various motions as follows:
1. The daily motion of the celestial sphere (westward) which carried the other spheres with it
was caused by the natural circular motion of celestial spheres (view of Plato and Aristotle).
2. The annual motion of the sun through the constellations is explained by the sun's sphere
moving eastward about 1o per day with respect to the celestial sphere. The non-uniform motion
is explained because the sun's deferent is eccentric to the position of the earth and the motion is
uniform with respect to the equant.
3. The moon's monthly motion is from the eastward motion of the moon's sphere with respect
to the celestial sphere (about 12o per day).
4. The eastward motion of the planets is due to the eastward motion of the epicycle on the
deferent with respect to the celestial sphere. The retrograde motion occurs when the planet is
on the inner part of the epicycle. The period of the epicycles is the time between successive
retrograde motions. Mars, Jupiter, and Saturn are retrograde when in opposition because the
radius of the epicycle is always in the same direction as the Earth - Sun radius. The nonuniformity of the motion is because of the eccentrics and equants.
Mercury and Venus always stay near the sun (are seen as morning or evening stars) because
their epicycle centers are constrained to stay on a line between the Earth and the Sun. The
epicycle of Venuw (46o) is bigger than that for Mercury (23o).
The universe as described by Ptolemy yields no information on the distances to the planets. His
model was used for about 1400 years to predict the positions of the planets. It worked to an
accuracy of about 5o.
The Copernican Heliocentric Universe
The Copernican universe is still based on the assumption of uniform circular motion for all
celestial objects. The major difference between the Ptolemaic and Copernican universes is that
the Copernican universe puts the Sun at the center rather than the Earth. Although Copernicus
does away with the equant, he still uses epicycles and eccentrics, and his system is still just as
complicated as Ptolemy's and no more accurate! The order of the spheres is similar to the
modern view of the solar system with the Sun at the center followed by Mercury, Venus, Earth
(with the Moon still orbiting the Earth), Mars, Jupiter, and Saturn. Copernicus then puts the
sphere of the fixed stars around all else at a very large distance (to explain why there is no
parallax).
Copernicus explained the observations as follows:
1. All the daily motions can now be explained by the eastward rotation of the Earth on its axis.
This appears as a westward motion in the sky. Thus, instead of the whole universe rotating
around a still Earth, the universe can sit still while the Earth turns.
2. The annual motion of the sun with respect to the stars can be explained by the revolution of
the Earth around the Sun in an eastward direction. The non-uniformity of this motion is
explained by having the center of the Earth's orbit be offset from the Sun (ie. the eccentric orbits
remain). The distance of the stars must be very large to prevent seeing parallax.
3. The monthly motion of the moon is due to the eastward revolution of the moon around the
Earth. Its non-uniformity is explained with epicycles and an eccentric orbit.
4. The non-uniform eastward motion of the planets can be explained by their eastward
revolution around the sun using eccentric orbits and epicycles. The retrograde motion is a
natural effect of the Earth passing by the outer planets which naturally happens at opposition and
of Mercury and Venus passing by the Earth. Mercury and Venus always appear near the Sun
because their orbits around the Sun are smaller than that of the Earth.
Copernicus has no explanation of the force behind the motions. The errors in predicting the
positions of the planets are still up to about 5o. However, with the Copernican model, the
relative distances to the planets can be calculated.
The true sidereal periods of the planets (the period with respect to the stars as seen from the
sun) can be derived from the synodic period (when the planet appears to be in the same
position relative to the sun) with the equation 1/S = 1/Pi - 1/P o.