GREEK COSMOLOGY

Ancient Greeks were the first to develop a scientific view of the world. They realized that

• it was possible to observe a natural phenomenon and to seek an explanation for it;
• it was possible to express this explanation in precise, mathematical terms

For the Greeks mathematics = geometry.

For the Greeks geometry = Euclidean geometry, which is a geometry of a flat space.

The Greek world is made of straight lines, circles, and spheres.

However, the Greeks knew that:

• the Earth was a sphere;
• the diameter of the Earth was 250,000 roman stadia;

The Greeks considered pure mathematical thought to be supreme over the observations. The modern science is based on the opposite relationship (well, almost).

Main contributers:

• Eudoxus, a student of Plato.
• Aristotle, another student of Plato (384-322 BC).
• Aristarchus, the first heliocentric model (310-230 BC).
• Ptolemy (100-170 AD).

Eudoxus was the first to introduce the geocentric model (the Earth is at the center). His model had 27 celestial spheres altogether: the number was required to fit observations.

Main assumptions:

• Unmovable Earth is at the center of the world.
• The Sun, planets, and stars go on circles.
• All stars are at the same distance from the Earth.

ARISTOTLE TEACHING

Plato (Aristotle's academic advisor) thought that the observations are not important, perhaps even misleading. The pure geometry is the ultimate reality.

Aristotle took observations seriously (but still he considered them inferior to the pure thought, more like servants of the theory).

Aristotle was the first to introduce the theory of motion, i.e. mechanics, even if we now consider his mechanics to be wrong.

According to Aristotle:

• All earthly things consist of 4 elements: earth, water, air, and fire. They all move differently: earth goes down (i.e. to the center of Earth), fire goes up, water and air stay in between. Air bubbles go up in the water, and rocks sink. Thus, the composition of an object determines the way the object moves.
• An object at rest will remain at rest unless is acted upon by a force.
• To keep an earthly object moving, a force has to be applied to it constantly.
• A celestial motion is perfect, it continues indefinitely without any force.
• All celestial objects are made out of ether, the fifth element. Ether exists only in the cosmos, it is not present on earth.

Aristotle's world consisted of 55 celestial spheres: he had to increase the number of spheres because observations became better, and the 27-sphere model of Eudoxus did not fit the observations.

Nature of time:

The Greeks knew that the history did not stretch back to infinity, i.e. that human society changes with time. What does it tell us about the nature of the time?

A:

The time had a beginning. The world did not exist before the beginning of the time.

B:

The time and the world always were and always will be. It is the Earth that changes, the heavens are eternal and unchangeable.

C:

The time and the world always were and always will be, but the whole world is changing all the time: the past is not like today, and the future will also be different.

Aristarchus

He was well ahead of his time. By comparing the shadow of the Earth with the angular size of the Moon during a total lunar eclipse, he was able to measure: the size of the Moon

$$R_\oplus \approx 3 \times R_{\rm m} \ \ \left(\mbox{truth:}\ 3.67\right),$$

and the Moon-Earth distance:

$$D_{\rm m-\oplus} \approx 60 \times R_\oplus. \ \ \left(\mbox{truth:}\ 60.35\right).$$

Not bad at all!!!

He also measured the Sun-Earth distance:

$$D_{\odot-\oplus} \approx 20 \times D_{\rm m-\oplus}. \ \ \left(\mbox{truth:}\ 389\right).$$

Oops, here he missed a lot!

Nevertheless, since the Moon is only 3 times smaller than the Earth, but the Sun and the Moon have the same size on the sky, Aristarchus concluded that the Sun was times larger than the Earth.

Since the Sun was about 7 times larger than the Earth, the Aristarchus put it at the center! Thus, he created the first heliocentric model.

Others did not accept it, because:

• the Earth was not the center of the universe.
• the Earth then had to move, contrary to observations.
• there should be stellar parallax (i.e. apparent positions of stars on the sky should change as the Earth moves around).

The parallax was not observed, because:

A:

the Earth does not move;

B:

stars move in unison with the Earth;

C:

the parallax exists, but it is so small (because the stars are so far away), that it can only be observed with a good telescope.

Ptolemy (100-170 AD)

He put the final touch on the Aristotelian world system. By this time astronomical observations improved so much that it became clear that the original Aristotelian system does not agree with them. He had to introduce even more spheres, called epicycles.

Alfonso, the king of Castile and Leon (XV century), about the Ptolemaic system:
``If the Lord Almighty had consulted me before embarking upon Creation, I should have recommended something simpler.''

The Ptolemaic model was successful in that it used to calculate the positions of planets for 15 centuries. By the end of XV century, the orbit of Mercury alone had 11 epicycles.

Ptolemaic/Aristotelian physics

• All earthly things consist of 4 elements: earth (rocks), water, air, and fire. They all move differently: earth goes down (i.e. to the center of Earth), fire goes up, water and air stay in between. Air bubbles go up in the water, and rocks sink. Thus, the composition of an object determines the way the object moves.
• If let go, an object will move to the position in the world order predefined by its composition.
• Earthly objects move in a straight line toward or away from the center of the world, which is the center of the Earth.
• Objects move along this line with different speeds, depending on their composition.
• An object at rest (i.e. in its natural, predefined place in the world) will remain at rest unless is acted upon by a force.
• To keep an earthly object moving, a force has to be applied to it constantly.
• A celestial motion is perfect, it continues indefinitely without any force.
• All celestial objects are made out of ether, the fifth element. Ether exists only in the cosmos, it is not present on earth.
• The time and the world always were and always will be. It is the Earth that changes, the heavens are eternal and unchangeable.
• The Earth is at the center of the world.
• Celestial objects move on epicycles which in turn move on other epicycles, and the center of the last epicycle moves in a circle around the center of the motion called equant, which is different from the center of the Earth.