Astronomy of the Ancient World – Pre 1500’s Astronomy is the oldest branch of physics. Since the beginning of civilization mankind has looked at the night sky and attempted to answer two fundamental questions: 1) Why are we here? 2) When should we plant crops or hunt for food? (i.e. How to calculate the seasons)

Astronomy Prior to 3000 BC Before 3000 BC, people had observed that the stars in the sky appeared to travel in a series of concentric as they watched through out the night. (See Fig. 1.4)

Egyptians and Babylonians - 3000 BC By 3000 BC, the Egyptians and Babylonians were aware that five objects in the sky besides the Moon and the Sun behaved differently from the other stars. These five objects were the major planets (Mercury, Venus, Mars, Jupiter, and Saturn). Planet is Greek for wanderer. If one watched the sky for many days and recorded the exact location of the stars, they would find that these five objects slowly changed their location in the evening sky during the course of the year.

Greeks (Pythagoras) - 500 BC Pythagoras believed that because mathematical concepts are perfect unlike earthly objects that mathematics was the language of God. Example: The mathematical concept of a circle is exact and everlasting while any circle that you draw will be imperfect to some degree and the material upon which you draw will decay. This caused Pythagoras to develop a mathematical model of the solar system that would explain the observations concerning the planets and stars.

Pythagoras’ Crystal Sphere Model Figure 1.5

Pythagoras’ Crystal Sphere Model - 500 BC 1. Earth was a spherical object at the center of the universe and stationary. 2. The Sun, Moon and five Major Planets were each on their own transparent crystal spheres centered about the Earth. 3. The remaining stars in the sky were all on a single transparent crystal sphere. 4. Each crystal sphere rotated at a constant rate. However, the rotation rate was different for each sphere.

Pythagoras’ Crystal Sphere Model - 500 BC Pythagoras’ model explained all of the observational data up to that time. Pythagoras’ model also made predictions!! 1. The planets might wonder in the sky but they would always travel in the same direction at constant speed. 2. The brightness of all objects in the sky would remain constant over time since none of the objects moved closer or farther from the Earth.

Pythagoras’ Philosophy - 500 BC Student: Dr. Pythagoras, why do the objects in the sky travel in circles instead of some other shape? Pythagoras: Because they are rotating on crystal spheres in the Eather. Student: But, why should the universe be composed of crystal spheres instead of some other shape? Pythagoras: Notice that the objects in the heavens are everlasting unlike objects on Earth that are born and die. This is because the Gods have created the heavens to be perfect and would have only used a perfect form, the sphere, which has no corners or other imperfections.

Pythagoras’ Philosophy - 500 BC This concept of perfection was essential to Pythagoras and his followers. He also claimed that all physical objects had dimensions which were either integers or ratios of integers (i.e. 2, 3, 4/3, etc). This meant that if you used a ruler with sufficiently small markings then all measurements would be integers since the Gods would only use perfect numbers. For example, if we used a ruler whose markings were three times smaller our numbers would be the integers 6, 9, and 4. This is how this type of numbers obtained their name: Rational Numbers!!

Pythagoras’ Philosophy - 500 BC Unfortunately for Pythagoras’ followers, they ran into trouble when they applied their philosophy to triangles using the Pythagorean theorem. The Pythagorean theorem was the discovery by Pythagoras that the three sides of a right triangle are related by the equation: c2 = a2 + b2 c a b

Pythagoras’ Philosophy - 500 BC For some triangles, the results were in agreement with the philosophy of the Pythagoreans. For instance c2 = 32 + 42 = 9 + 16 = 25 c = 5 5 3 4

Pythagoras’ Philosophy - 500 BC However, the following triangle proved a problem since no rational number squared is equal to 2!! The number representing the length of the remaining side is the square root of two and it is a number whose decimal continues for ever!!! The Pythagoreans called this type of number an irrational number and there discovery caused political and social upheaval in Greece. c2 = 12 + 12 = 2 c = 1.414213562373095.... c 1 1

Downfall of Pythagoreans The Pythagoreans were somewhat of a mystical cult. They claimed that only their members truly understood the workings of the universe and that the crystal spheres produced a music that only they could hear (Harmony of the Spheres). For a price, they were willing to teach people to hear this symphony!! This combined with the discovery of irrational numbers led to their becoming outcasts. However, Pythagoras’ great mathematical achievements ensured his idea of perfection would continue to influence the philosophy of later thinkers including Plato, Aristotle, Leonardo de Vinci, and Galileo.

Problem With Crystal Sphere Model Over time, the Greeks noticed that contrary to the crystal sphere model, the planets did not travel across the sky at a constant rate, but that they would sometimes even turn around and start traveling in the opposite direction (retrograde motion). Plato (Socrates' Student) believed strongly in Pythagoras's concept of perfection and tasked his followers with developing a mathematical model scheme to retain the basic ideas of the crystal sphere model.

Multiple Transparent Sphere Model The model developed by Plato’s followers and supported by Aristotle was the multiple transparent sphere model. In this model, each planet is actually attached to a rotating sphere which is connected to collection of concentric inner spheres centered about the Earth instead of just a single sphere. Each inner sphere rotates about its own axis and effects the rotation of the following sphere which rotates about another axis which might point in a different direction.

Multiple Transparent Sphere Model Success: The multiple transparent sphere model could explain the retrograde motion of planets. Problem: Since the distance between a planet and the Earth is constant in the multiple transparent sphere model, the brightness of a planet according to this model should be constant. Eventually, people discovered that the brightness of planets changed over time. Thus, Aristotle’s followers had to devise a new model.

Ptolemaic Solar System One of Aristotle’s followers, Apollonius of Perga, found an ingenious way of solving the problem of the planets. Apollonius’ solution was to use epicycles (i.e. to place the planets on circles that rotated about other circles as shown below). By adjusting the different rates of rotation, the planet can be made to travel in a wide range of complicated paths like a Spiro graph. Epicycle Deferent Earth

Ptolemaic Solar System Ptolemy, the greatest astronomer of the ancient world, perfected this model of the solar system in the Roman province of Egypt by making minor adjustments. He included it in the great encyclopedia (the Almagest) that he wrote and which contained the sum of all Greek knowledge. This model accurately predicted seasons and the locations of objects in the night sky and was the dominant view of the universe until the birth of modern astronomy in the 1500’s. It was also consistent with Aristotle’s view of motion and was successfully used by explorers like Columbus to cross uncharted oceans and lands.

Aristarchus’ Model As an alternative to the Multiple Transparent Sphere Model for explaining retrograde motion of the planets, the Greek, Aristarchus, suggested placing the sun at the center of the universe and placing the Earth and the major planets in orbit around the sun. He also had a spinning spherical Earth rather than a stationary spherical Earth. Aristarchus’ model was not accepted because his model led to several problems which he could not answer.

Problems With Aristarchus’ Model 1. What force (push or pull) could cause such a huge object as the Earth to move. 2. If the Earth spins, why don’t objects fly off into space? 3. If the Earth spins, why does a falling apple land next to the tree instead of several miles away? 4. Doesn’t the motion of heavenly objects differ from earthly objects? (The objects in the heavens keep moving forever while objects on Earth eventually come to rest.) Aristotle developed a comprehensive model of all motion in the universe and not just the objects in the sky. Thus, Aristotle’s ideas won the debate and they reigned for almost 2,000 years.