LECTURE 4: ANCIENT GREEK ASTRONOMY

Key Questions:

• Why did ancient Greek philosophers believe in a spherical Earth?
• Why did most of these philosophers believe in a geocentric (Earth-centered) cosmos?
• What was the Aristotle/Eudoxus model of the cosmos? What were its strengths and weaknesses?
• How did Eratosthenes measure the size of the Earth?
• How did Aristarchus infer the distances and sizes of the Moon and the Sun?
• Why did Aristarchus advocate a heliocentric (Sun-centered) cosmos?

Many ancient cultures carried out extensive astronomical observations, used them for calendar keeping, and incorporated them in religious rituals.

As far as we know, only the ancient Greeks developed sophisticated models to explain what they saw.

SPHERICAL EARTH

Ancient Greek philosophers argued Earth was a sphere, on several grounds:

• Sphere a "perfect" shape.
• Ships disappear over horizon.
• Positions of constellation above horizon change as one goes north or south.
• Earth casts round shadow on Moon during a lunar eclipse.

A GEOCENTRIC COSMOS

Most Greek philosophers believed in a geocentric (Earth-centered) cosmos.

Argument against daily ("diurnal") Earth rotation:

• If Earth rotated once per day, surface would be moving very fast.
• Dropped objects should fly backwards.
• Maybe heavy winds as well.

• Don't see constellations get bigger and smaller as Earth gets closer and further away.
• More generally, don't see effects of parallax, apparent change of position caused by moving observer.

ARISTOTLE'S LAWS OF MOTION

Aristotle (4th Century BC) was the most influential philosopher advocating a geocentric cosmos.
Part of comprehensive view of how nature works.

• On Earth, material objects naturally move towards Earth's center.
• Moving objects come to rest unless a force is applied. Force produces motion.
• In heavens (Moon and further), natural form of motion is unchanging, uniform, circular motion.
• Laws of heavenly motion fundamentally different from those of motion on Earth.

NESTED SPHERES

Eudoxus and Aristotle (4th century BC), both students of Plato, developed cosmology of nested, rotating, crystalline spheres.

• Stars on outer, celestial sphere, rotating once per day.
• Sun's sphere attached to celestial sphere, additional rotation once per year to produce motion along ecliptic.
• Similar for Moon, rotating once per month.
• Extra spheres for planets to produce retrograde motion.
• "Grinding" produces "music of the spheres."

• Based on an elegant, universal principle: uniform circular motion.
• Explains a lot.
• Complicated (lots of spheres).
• Not very accurate in predicting planetary positions.

SIZE OF THE EARTH

Measurement of Earth's circumference, by Eratosthenes of Cyrene in 3rd Century BC, a major accomplishment of Ancient Greek science.

• Heard that, in Syene, Sun shone to bottom of wells at noon on Summer Solstice. Thus, directly overhead.
• Not true at Alexandria, 5000 stadia (~800 km ~ 500 miles) north of Syene.
• Angle of Sun 7.5 degrees, measured from shadow of vertical pole.
• 7.5 degrees = 7.5/360 of a circle.
• 5000 stadia must be 7.5/360 of Earth's circumference.
• Inferred circumference: 39,300 km, very close to modern value of 40,000 km.

DIAMETER AND DISTANCE OF MOON

Method devised by Aristarchus of Samos (2nd century BC).

• Moon moves (relative to stars) at 360 degrees/month ~ 0.5 degrees/hour.
• From duration of lunar eclipse, can infer angular size of Earth as seen from Moon.
• Compare to angular size of Moon as seen from Earth (0.5 degrees).
• Aristarchus concluded: Earth diameter = 3 x Moon diameter (close to true value).
• Combine with Eratosthenes measurement of Earth diameter to get Moon diameter in stadia (or km).
• Knowing angular size of Moon (0.5 degrees) and physical size of Moon, get distance to Moon from a = d x \theta.

DISTANCE AND DIAMETER OF SUN

Aristarchus again.

Distance:

• At quarter Moon, exactly half of Moon's face illuminated, Sun-Moon-Earth angle (Moon at apex) must be exactly 90 degrees.
• Measure Sun-Earth-Moon angle (Earth at apex).
• Two angles determine shape of triangle, hence relative length of sides.
• Measurement is hard, since Sun-Earth-Moon angle also close to 90 degrees.
• Aristarchus measured 87 degrees, implying d_Sun=19 x d_Moon.

• Sun and Moon have same angular diameter, 0.5 degrees, and a = d x \theta.
• Sun diameter must be 19 times Moon diameter, a_Sun=19 x a_Moon.
• Combined with a_Earth=3 x a_Moon from eclipse measurement, implies a_Sun ~ 6 x a_Earth.

Qualitative conclusion is correct: Sun bigger than Earth, Earth bigger than Moon. But

• True Sun-Earth-Moon angle at quarter Moon is 87.85 degrees, not 87 degrees.
• Implies d_Sun=400 x d_Moon, hence a_Sun=400 x a_Moon,
• Sun is really much bigger than Earth.
• Note that Aristarchus' methods work regardless of whether Earth goes around the Sun or Sun goes around the Earth.

A HELIOCENTRIC COSMOS

Aristarchus reasoned: Sun bigger than Earth, harder to move.
This led him to propose a heliocentric model of the cosmos:

• Sun is the center of the universe.
• Earth and planets orbit Sun.
• Daily motions produced by rotation of Earth.
• See different stars at different times of year because Earth orbits Sun, can't see stars during the day.
• Retrograde motion occurs when planets overtake each other.
• Planets are brightest when moving retrograde because that's when they are closest.

• Arguments against Earth rotation and motion seemed convincing?
• Authority of Aristotle?
• Not developed into a quantitatively accurate theory (until Copernicus and Kepler).