Hipparchus of Rhodes

Hipparchus of Rhodes
• Hipparchus worked
from about 160 to
130 B.C.
• He was a
mathematician who
used geometry to try
to solve the problem
of retrograde motion.
http://universe-review.ca/I08-18-Hipparchus.jpg
A Clockwork Cosmos
• Hipparchus extended the idea of the
crystalline spheres. The main path or orbit
of the planet was termed the deferent.
• Attached to and centered on the deferent
was a second, smaller orbit called the
epicycle. The planet revolved as the
deferent and epicycle both revolved.
http://faculty.uml.edu/awalters/43.311/lecturesf2k2/Slide9.GIF
Real backward motion
• As the deferent and epicycle both turned
independently, the planet would actually
move backward during the retrograde
(westward) portion of its motion.
• With a correctly sized deferent and
epicycle, the predicted positions of the
planets would match the actual positions
within naked-eye accuracy limits!!!
http://pl.wikipedia.org/wiki/Grafika:Epicycle_et_deferent.png
Attacking problem #2
• To try to solve the problem of the sun and
planets traveling faster at some times of
the year than others, Hipparchus proposed
the eccentric.
• Despite the requirement that the earth be
at the center of the cosmos, Hipparchus
placed the earth off-center by a small
distance.
The Eccentric
• The off-center placement allowed the sun
and planets to appear to speed up when
they were closer to the earth and appear
to slow down when they were farther
away. (The angular velocity no longer
appears to be uniform.)
The Eccentric
• Imagine standing in
the exact center of
the infield of a race
track. Walk towards
the track’s inner edge
and the cars appear
to be moving faster
on the side you’re
closer to, and slower
on the opposite side.
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit3/Images/epicycle.gif
The 3rd Problem
• The last problem to be solved was that of
different shape & duration planetary
retrograde motions from one year to the
next.
http://www.xtec.es/recursos/astronom/articulos/retro/indexe.htm
http://jcboulay.free.fr/astro/sommaire/astronomie/univers/galaxie/etoile/systeme_solaire/mars/page_mars3.htm
Ptolemy
• Hipparchus never
solved this last
problem. It had to
wait for a Greek
astronomer
working in
Alexandria, Egypt
around 125 A.D.
Claudius Ptolemy
http://www.livius.org/a/1/greeks/ptolemy.jpg
The Equant
• Ptolemy proposed
a point in space
opposite the
eccentric point,
called the
equant, where
the angular
speeds of the sun
and planets would
appear to be
uniform. http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit3/Images/equant.gif
The Equant (2)
• While this helped solve the problem of
differently shaped retrograde loops, it also
violated the premise that the crystalline
spheres turned with uniform speeds. Now
they were required to actually speed up
and slow down.
• How does this happen when no force or
engine drives the crystalline spheres?
A Special Problem - Epicycles
of Venus & Mercury
• Ptolemy also realized that Hipparchus’
model had another problem – with
Mercury, Venus, and the Sun all revolving
around the earth, Mercury and Venus
should sometimes appear in opposition to
the sun (180o from the sun in our sky).
• However this never happened. Venus
was never more than 46o from the sun,
and Mercury never more than 28o.
The Solution for Mercury &
Venus
• Ptolemy proposed that the epicycles of
Mercury & Venus be “pinned” to a line
drawn between the Sun and the Earth.
• In this way, those two planets could
oscillate from one side of the sun to the
other, yet continue orbiting the earth.
The Epicycles of Venus and Mercury, “pinned” to a line drawn from
the Sun to the Earth.
A Prediction
• Ptolemy’s setup for the epicycles of
Mercury and Venus makes a prediction:
each planet should be able to show
crescent and new phases as seen from
the earth, but never a full phase.
• Later, we’ll see that we actually do see full
phases for Mercury and nearly-full phases
for Venus.
Ptolemy’s 2 other accomplishments
• Ptolemy calculated what he believed to be
the size of the cosmos: 20,000 earth radii
or 134,000,000 kilometers (radius).
• Ptolemy wrote the first astronomy
textbook, the Almagest (the “Majestic
Book”).
http://www.er.uqam.ca/nobel/r14310/Ptolemy/Images/Regiomontanus/1496.g.jpg
The Almagest
Why does an idea persist?
• Because these
ideas were now in
print and were
published at then
Great Library in
Alexandria, these
ideas became
institutionalized.
http://ils.unc.edu/dpr/path/alexandria/
Here’s the kicker!
• Despite the complex geometry and logical
inconsistencies, this model worked well
enough to accurately predict the positions
of the planets to within a few minutes of
arc!
• The Ptolemaic model works well enough
that the planetarium projector mechanism
is based on it!
• It’s no wonder that this system wasn’t
seriously challenged for 1400 years!