Greek Astronomy

Pythagoras to Ptolemy(and the aftermath)

Much of this is from Arthur Koestler's The Sleepwalkers:Man's Changing Vision of the Universe

Why the Greeks?

They were the first people to use MODELS to explain HOW (but not WHY) the planets moved the way they did, and to PREDICT the future motions of the planets.

Pythagoreans (Pythagoras 530-450 BC?)

• Numbers held the secret to the universe• The universe is harmonious• The Earth and Moon are Round (Spherical)• Planets move on concentric crystal spheres,

and the motion of the spheres produces a sound - “Music (Harmony) of the Spheres”

PROBLEM!!Planetary Retrograde Motion

Evolution into Two “Camps” “Geocentric” and “Heliocentric”

Philolaus

(5th Cent. BC - student of Pythagoras)

Herakleides

(375-310 BC - Student of Plato & Aristotle)

Aristarchus - Part 1Relative Distances of the Sun and Moon

Assume:

A. Circular orbit for the Moon

B. Uniform orbital Speed of the Moon

C. Sun close enough to have divergent rays hitting Moon at 1st & 3rd Quarter phases

Method: Measure time intervals between 1st & 3rd quarters and 3rd & 1st quarters. Use geometry to get ratio of EM to ES.

His Result:ES ~ 20 EM (The true value is closer to 400 EM)

Note: Because the angular sizes are the same, the Sun must be physically about 20 timer larger than the Moon:

Relative Sizes of the Earth, Moon, and Sun

Use:

A. ES ~ 20 EM

B. Moon & Sun both subtend 2 degrees (true value is 1/2 degree)

C. Measured shadow of Earth at distance of Moon is approx. 8/3 Moon’s diameter

Final Results - Sizes and Distances in Units of Earth’s Diameter

Aristarchus Modern Value

Moon’s Distance 10 30

Moon’s Diameter 1/3 0.272

Sun’s Distance 200 11,700

Sun’s Diameter 7 109

Although his numbers were not quite correct, Aristarchus came to the correct and important conclusion that THE SUN IS MUCH LARGER THAN THE EARTH!

Yeah, but how large is THAT?

Eratosthenes (276-195/6 BC) Determined the circumference (X), and hence size of the Earth

Syene - Alexandria ~ 5000 stadia

Syene - Alexandria ~ 7 degrees

7/360 = 5000/X

X = 250,000 stadia

With this information it was possible to get the physical sizes of the Moon and Sun!

Aristarchus - Part 2 HELIOCENTRIC COSMOLOGY

No direct record of the model - only descriptions by Archimedes (287-212 BC) and Plutarch (46-120 AD)

Why HELIOCENTRIC?

(Because Sun is biggest?)

A. The Earth rotates on its axisB. The Earth and planets orbit the Sun

In this model:

Consequence of a Moving Earth - STELLAR PARALLAX

NOT OBSERVED!!!

Need another condition:

C. Stars very far away w.r.t. size of Earth’s orbit.

Aristarchus was highly regarded for his determination of the (relative) sizes and distances of the Sun and Moon, but NOT his cosmology model. WHY?

Possibly:

A. It Violated Aristotelian Physics (more later…)

B. Lack of Parallax combined with a general belief in a smaller cosmos.

Still, his model was known to others centuries after his death (Example - It is mentioned by Macrobius, circa 400 AD, referring to a speech by Cicero).

GEOCENTRIC COSMOLOGYPlato (428-348 BC) - “Let us concentrate on (abstract) problems, said I, in astronomy as in geometry, and dismiss the heavenly bodies, if we are truly to apprehend astronomy” - The Republic

Wanted eternal perfection

Equated change with degradation

Separated physics from mathematics and made it part of theology

Believed that the visible world is only a shadow of reality, to be deduced from reason alone.

Plato deduced by “reasoning” that:

A. The shape of the Earth must be a perfect sphere (all points equidistant from the center, the only solid uniquely specified by a single parameter)

B. All celestial motion must be in perfect circles with uniform speed - “Uniform Circular Motion” [thus incorporating Pythagorean mysticism but not Pythagorean empiricism]

IT WAS THE PERSISTENT, OBSESSIVE, DOGMATIC BELIEF IN POINT B THAT ARRESTED ALL FURTHER PROGRESS IN ASTRONOMY FOR THE NEXT 1500 YEARS…………

Eudoxus 4th Century BC (a student of Plato)

SPHERES OF EUDOXUS (an “Onion Universe”)

• Planets are located on spheres centered on Earth

• Nested spheres with different axes of rotation and rotation rates used for planetary motion

• (Not concerned with physical reality)

Required 27 (or more) spheres to do the job.

Aristotle, who wanted a physical model, made the axes physically connected, requiring more spheres to cancel out those inside.

This model failed to explain the changing brightnesses of the planets, the “different” behavior of Mercury & Venus, etc.

Aristotle (384-322 BC)“The principles of science are derived from experience”

“It is from astronomical observations that we derive the principles of astronomical science”

He was aware of the sphericity of the Earth based on observations”

A. Round shape of lunar eclipses

B. Changes in altitude of the NCP with latitude, visibility of southern constellations, etc.

Unfortunately, he did not always live up to this ideal.

Aristotle’s CosmologyA. The Earth is the center of the

universe. It occupies the “lowest” position, being made up of the 4 “base” materials or elements (“air, earth, fire, and water”)

B. The sky, the Sun, planets, etc., are placed above, and are made of a perfect immutable substance - “quintessence” (the “5th Element”)

Physics of Aristotle

Tended to give inanimate objects very “animistic” qualities

In his physics, TO KEEP AN OBJECT IN MOTION REQUIRED A CONSTANT PUSH OR PULL.

This “blindness” to the fact that moving bodies tend to persist in their movement unless stopped or deflected prevented the emergence of a true science of physics until the time of Galileo.

Apollonius (most work done circa 250-220 BC)

“The Ferris Wheel Universe”

Introduces the deferent and epicycles

• Model is geocentric

• Provides retrograde motion

• Provides varying brightnesses (and sizes)

• Uses Uniform Circular Motion

Hipparchus - most work done about 160-127 BC in Rhodes & Alexandria• Invented or developed Trigonometry• Systematic astronomical observations (star catalog,

discovers precession of equinoxes!)• Correctly measured Earth-Moon Distance• Correctly measured length of year and estimated his

own uncertainty in the value• Measured motions of Sun, Moon, planets; predicted

their future locations & eclipses• Includes lunar parallax for eclipse visibility• Develops cosmological model for motion of the Sun

Claudius Ptolemy - most work done circa 150 AD Compiles “The Almagest”

• Used lunar parallax to get distance to Moon (same value as Hipparchus) ~ 29 1/2 DEarth

• Brought to “completion” the geocentric models of Apolloniun & Hipparchus into a single framework, used for the next 1500 years.

Cosmology of Ptolemy

“We believe that the object which the astronomer must strive to achieve is this: to demonstrate that all phenomena in the sky are produced by uniform and circular motions.”

“Having set ourselves to the task to prove that the apparent irregularities of the five planets, the Sun, and the Moon can be represented by means of uniform circular motion, because only those motions are appropriate to their divine nature… We are entitled to regard the accomplishment of this task as the ultimate aim of mathematical science based on philosophy.”

Full Geocentric Model

Introduces the equant (add to deferent & epicycle) and moves the Earth off-center

Treat Mercury & Venus differently than the Sun, Moon, Mars, Jupiter, and Saturn

Result:• 39-40 wheels needed to make it work

• Fairly accurate predictor of planetary positions

• Agreed with Greek philosophy

BUT:• Assumes infallibility of Plato and absolute correctness of his premises

• STERILE. Can NEVER lead to any new knowledge, because it presumes that its two premises (Uniform Circular Motion) contains all there is to know about planetary motion.

Regression & Collapse of Scientific Thought - 100-1500 AD

“In the year 1500 [AD] Europe knew less than Archimedes, who died in the year 212 BC.” - A.N. Whitehead

• Earth was flat

• Sky was a solid dome over the Earth

• Stars were carried around by angels

•Etc.

(Slow) Resurgence of Scientific Thought after 1000 AD

• Earth’s sphericity re-discovered circa 1000 AD• Aristotle is re-discovered and replaces Plato circa

1100 AD as ultimate authority. Thereafter often referred to simply as “The Philosopher”.

• Dualistic world of philosophers & map-makers• Astronomy:

1. Geocentric2. Uniform Circular Motion3. Divorced from Math & Science4. Crippled by “educated” people’s ability to see

the underlying nature of things (Newton’s 1st Law, for example)

Copernicus

Heliocentric Model and Retrograde Motion

https://www.youtube.com/watch?v=72FrZz_zJFU

But in reality, for it to work (agree with the observations)....