# Chapter 2: Classical Astronomy

• Every ancient culture observed the night sky and tried to understand it.
• Ancient Greek astronomers established the foundation of modern astronomy.
• Studying the sky systematically.
• Using logic (as in their philosophy).
• Using geometry (that they invented).
• Created the foundation of the Scientific Method that we still use.

#### What is Earth’s Shape?

• Earth looks flat to us.
• Aristotle argued that Earth is a really huge sphere. The part we see is so small that it looks flat. His evidence included:
• During lunar eclipses, Earth’s shadow is always curved.
• Merchants traveling from Greece to other regions reported seeing new stars or not being able to see familiar stars.
• This is not possible if Earth is flat.
• This is possible if Earth is a sphere.

#### Relative Distances

• NOTE: Relative distance is like a ration
• Aristarchus of Samos determined relative distances - NOTE - he used numbers to prove his thinking.
• Measuring the angle between the directions to the Moon and the direction to the Sun sets up a triangle.
• Drawing the triangle to scale, his measured the relative distances of the Moon and Sun.
• He derived that the Sun was 20x farther from Earth than the Moon - it is really 400x farther away.

### Angular Sizes

• Observations in astronomy measure angles
• The angle we see/measure depends on:
• The physical size of the object.
• The distance of the object from us.

### Relative Sizes

• We observe that he Sun and Moon are almost the same angular size, which is about 0.5 degrees.
• Aristarchus derived that the Sun was 20x farther from Earth than the Moon - it is really 400 x farther away
• Therefore, the Sun must be 20x (really 400x) larger than the moon.
• During a lunar eclipse, we observed that Earth’s shadow is about 4x larger than the Moon.
• Combine this with the relative size of the Sun and Moon:
• Sun’s size = 400 x Moon’s size.
• Sun’s size = 400 x 0.25 x Earth’s size
• Sun’s size = 100x Earth’s size.

#### Model of the Solar System

• If the Sun is 100x larger than Earth, then its logical for the Sun to be the centre of the solar system = heliocentric model, with smaller Earth orbiting the Sun.
• How can we test this idea? - as required by the Scientific Method.

#### Testing the Heliocentric Model

• If we observe from different locations, nearer objects shift directions compared to more distant objects - parallax.
• If Earth orbits the Sun, we should observe nearer stars in different directions from opposite sides of Earth’s orbit.
• Greek astronomers searched for parallax of the brighter (nearer?) stars compared to the fainter (more distant?) stars.
• No stellar parallax was seen ﻿$\rightarrow$﻿ rejected the heliocentric model and accepted the model with Earth at the centre of the solar system - geocentric model.
• Conclusion is wrong, but the scientific method is correct.

#### How Big is Earth?

• The Greek astronomer Eratosthenes developed a method to measure the absolute size of Earth. He built on:
• Aristotle’s argument.
• On the same day at noon the Sun is observed from Alexandria and the city of Syene (now called Aswan).
• In Alexandria the Sun is ~7 degrees south of zenith.
• In Syene the Sun is at the zenith.
• For a spherical Earth and a very distant Sun this gives an angle of ~7 degrees at the centre of Earth between the two cities.
• Travelers between Alexandria and Syene had estimated the distance to be 5000 stadia, but the length of a stadium unit was not well defined.
• Using these values leads to an equation:
• (5000 stadia)/(circumference = 2*PI*r) = (7 degrees)/(360 degrees)
• R = (360 degrees/7 degrees) (5000 stadia/(2*PI)) is about (41000 stadia)
• Depending on the value of the stadium, this might have been very close to Earth’s correct radius.
• NOTE: Eratosthenes could not have used algebra because that had not yet been invented, but he could solve for the Earth’s radius using other methods.
• Knowing ﻿$R^{Earth}$﻿ ﻿$\rightarrow$﻿ ﻿$R^{Moon}$﻿ and ﻿$R^{Sun}$﻿

#### The Planets

• The word “planet” means “wanderer” because they move across the celestial sphere.
• The paths of the planets are very close to the Sun’s path across the celestial sphere = the ecliptic.
• The orbit planes of the planets are very close to Earth’s orbit plane.
• The movement of the planets
• The planets move across the celestial sphere in a MUCH more complicated way than the Moon or the Sun.
• Some time the planets move “forward” = toward the East across the celestial sphere = “prograde” motion - like the Moon and Sun.

#### Explaining Retrograde Motion

• Greek astronomer Claudius Ptolemy developed an explanation of retrograde motion.
• Because stellar parallax could not be detected, he used the geocentric model.

#### Ptolemy’s Retrograde Model

• Ptolemy had to use two orbits for each planet to produce retrograde:
• Large orbit - deferent with Earth at its centre.
• Small orbit - epicycle that moves along the deferent and the planet orbits along the epicycle.
• Prograde motion = outer side of epicycle.
• Retrograde motion = inner side of epicycle.
• Ptolemy developed his model about the year 150.
• Over the following centuries it had to match many more observations, which required modifications that greatly increased its complexity.

#### Ockham’s Razor

• In the 1300s the philosopher William of Ockham developed the idea known today as “Ockham’s razor”.
• “Entities must not be unnecessarily multiplied”.
• Means: “The simplest explanation is likely the true explanation.”.
• Is Ptolemy’s model correct?
• It is getting more and more complicated.

### European Renaissance Astronomy

• European astronomy was dormant after Ptolemy (~150) until ~1500, but there were advances in Arabic and Asian cultures.
• The European Renaissance revived the study of astronomy began in ancient Greece.
• Applying Ockham’s razor to Ptolemy’s geocentric model ﻿$\rightarrow$﻿ heliocentric model.

#### Nicolaus Copernicus

• Copernicus (1473-1543) learned about the heliocentric model when he studied in Italy.
• He saw that he heliocentric model can explain retrograde motion in a simple way.
• Planets orbit the Sun, not the Earth.
• The orbit speeds decrease moving away from the Sun.
• When a faster inner planet passes a slower outer planet ﻿$\rightarrow$﻿ retrograde motion.
• Heliocentric model also explains why Venus and Mercury are always close to the Sun.

#### Model of Copernicus

• The heliocentric model that Copernicus revived was revolutionary in two ways:
• Earth revolves around the Sun.
• It violated the teaching of the Catholic church.
• It was much simpler, but was NOT more accurate than the model of Ptolemy.
• Problem: the model of Copernicus contains assumptions that are not correct.

#### Tycho Brahe

• Tycho (1546-1601) was a Danish nobleman.
• He built an “observatory” where he observed the planets for decades.
• His observations were the most accurate made before the telescope was invented.

#### Johannes Kepler

• Kepler began as Tycho’s assistant.
• Using Tycho’s decades of observations he discovered three laws of planetary motion:
• Planetary orbits are elliptical NOT circular.
• Major axis (or semimajor axis “a”).
• Minor axis (or semiminor axis “b”).
• Two focus positions instead of a centre, with the Sun at one focus, the other focus is empty.
• Eccentricity 0 < e < 1.
• Planets do NOT orbit at a constant speed.
• Each planet has its highest orbit speed when it is closest to the Sun.
• Each planet has its lowest orbit speed when it is farthest from the Sun.
• The variable orbit speed makes the line between a planet and the Sun sweep out equal areas in equal lengths of time - a quantitative way of representing the variation
• There is a numerical relationship between the orbit period (P) and the semimajor axis (a) of the elliptical orbit: ﻿$P^{\Lambda }2 = a^{\Lambda }3.$﻿
• Kepler discovered ﻿$P^{\Lambda }2 = a^{\Lambda }3$﻿ in 1619, and we still use it today.
• Ex. In 2003, a new dwarf planet, Sedna, was discovered 518 AU from the Sun.
• Its orbit period was found by calculating P = sqroot﻿$\left ( (518)^{\Lambda }3\right ).$﻿
• Summarizing Kepler’s Findings
• Tycho’s observations have numerical relationships.
• Observations agree with the heliocentric model.

#### Galileo Galilei

• Galileo (1564-1642) lived at the same time as Tycho and Kepler, but in Italy.
• He studied motion in general.
• He built the first astronomical telescope and made major discoveries that supported the heliocentric model.
• Galileo’s telescope discoveries.
• The Moon’s surface is covered with craters, not a smooth surface.
• The Sun has spots, not heavenly perfect.
• Jupiter has moons that orbit it, not only Earth.
• Venus has all the phases our Moon has.
• Space is huge and is filled with stars.