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- 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.

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