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!!!

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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.

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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”).

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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!