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 REarthR^{Earth} \rightarrow RMoonR^{Moon} and RSunR^{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: PΛ2=aΛ3.P^{\Lambda }2 = a^{\Lambda }3.
  • Kepler discovered PΛ2=aΛ3P^{\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((518)Λ3).\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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