Lecture 2 Earth Centered Universe

7/30/2019 Lecture 2 Earth Centered Universe

1/39

Lecture 2

The Scientific Method

Scientific Models

Planetary Motions The Greek Geocentric Model

Aristarchus' Sun-Centred Model

Measurements of Earth, Moon, Sun sizes &distances.


2/39

Don't forget to:

1. Register clickers using UTORid athttp://iclicker.com/registration

Re-register if you used student number or

not your official name as in ROSI.

2. Ensure your utoronto.ca e-mail address is

your e-mail address on ROSI.

3. Bring clickers on Wednesday! (even if not

yet registered at iclicker.com).


3/39

Scientific Method

First introduced ~16th Century:

1. Recognize a problem

2. Make a guess (i.e. construct hypothesis) re

solution.

3. Predict consequences of hypothesis.

4. Perform experiments (or observations) to testhypothesis.

5. Find simplest general rule which organizes

(2),(3) & (4) into a theory.


4/39

Scientific Models

1. A scientific modelis a theory that accounts for aset of observations in nature.

2. The idea that stars reside on a giant celestial

sphere is a model.

3. A scientific model is not necessarily a physical

model.

4. The Suns motion along the ecliptic can beexplained by a geocentric model.


5/39

The Greek Geocentric Model

1. There is a fundamental difference between thecontributions to astronomy made by the ancientGreeks and those made by other ancientcivilizations. The Greeks were interested in

astronomy because of a pure philosophicaldesire to understand how the universe works.They believed in, and looked for, a sense ofsymmetry, order, and unity in the cosmos. Theytook the first steps in creating a unified model of

the universe.Other civilizations were more interested, for

example, in astrology for agricultural predictions,although several had excellent observations.


6/39

Models of the Universe over 4000 years.


7/39

Thales of Miletus ( ~ 600 BCE )Pythagoras ( ~ 530 BCE )

Rational thought can lead to understanding of Universe.

Suggested Sun and stars are balls of fire, not gods. Taught Anaximander, who in turn taught Pythagoras.

Pythagoras considered that Nature can be described withmathematics.

Recognised orbit of moon inclined to Earth's equator,that Earth is spherical, and that Venus the Morning Staris same planet as the Evening Star.

Travelled and studied in various places, especially Egypt.Founded a cult-like society of Pythagoreans, who

postulated a spherical universe with central firecontaining force controlling all motions. The Earth,Moon, Sun and 5 naked-eye planets all move around it.

Roundness of Earth's shadow on moon ==> Earthspherical.

Plato (~380 BCE). Planets = spheres moving in circularorbits.


8/39

The Greek Geocentric Model (cont.)

2. Aristotle argued that the absence of parallax forthe stars in the sky implied that the Earth must be

at the center of the solar system. This is a validscientific argument.

3. Parallaxis the apparent shifting of nearby objects

with respect to distant ones as the position of theobserver changes


9/39


10/39

Fig. 1-19


11/39


4. Stellar parallax was not observed until 1838; thegreatest annual shift observed for any star is only1.5 arcseconds.

5. Even though Aristotle used a correct logicalargument, the conclusion was wrong because itwas based on incomplete data. Parallax is hard toobserve because stars are at great distancesfrom us.

6. Aristotle used very good arguments to concludethat the Moon and Earth are spherical and thatthe Sun is farther away from earth than the Moon

is.


12/39


7. Aristotle saw a difference in the naturalbehavior of Earthly objects compared to heavenlyobjects. He believed that two different sets ofrules existed, one for Earthly objects and one for

celestial objects.

8. The Greeks love of geometry led them toconstruct a model of the heavens based onspheres, with the Earth at the center. To account

for the Suns apparent motion in the sky, the Sunwas located on a sphere around the Earth, insidethe celestial sphere of the stars. The axes of thetwo spheres were tilted with respect to one

another.


13/39

Aristotle's Conclusions

Stationary Earth at centre of the solar system.

Moon spherical: line between lit and unlit side changescurvature with phase of moon.

Sun further away than Moon: Moon's crescent phaseshows that it passes between Earth and Sun.

Earth spherical because:

Only on a sphere do all falling bodies seek the centre.

As one travels North, more of the Northern sky is exposed

while southern stars disappear below the horizon

During lunar eclipses, the Earth's shadow on the Moon is

always circular.

On earth, things fall down toward the centre and stop.

In the heavens, things move in circles, and keep onmoving.


14/39

The Greeks' concentric spheres.


15/39


9. Ptolemy (150 AD) presented the mostcomprehensive geocentric model, called thePtolemaic model. Presented in his book called the

Almagest, it held sway for more than 1,300 years.10. Because the heavens were viewed as perfect, the

use in the Ptolemaic model of the symmetricalcircle to model the motions of celestial objects was

thought to be the most reasonable choice.


16/39

Observations of Planetary Motion1. Five planets are visible to the naked eye:

Mercury, Venus, Mars, Jupiter, Saturn.2. The planets lack the simple, uniform motion of

the Sun and Moon. They sometimes stop theireastward motion among the stars and movewestward for a while. This is called retrograde

motion.


17/39

Retrogrademotion of

Mars.

Similarly

Saturn,Jupiter.


18/39

Retrogrademotion of

Venus


19/39

Observations of Planetary Motion (cont.)3. The planets always stay near the ecliptic. Mercury

and Venus never appear very far from theposition of the Sun in the sky. Thus theirelongation(the angle in the sky from an object tothe Sun) is small.

4. Any model for the planets must explain theseobservations.


20/39

A Model of Planetary Motion: Epicycles1. Ptolemys geocentric model explained the

planetary motions using epicycles. An epicycle isthe circular orbit of a planet, the center of whichrevolves around the Earth in another circle.

2. The model retained the idea of perfect heavenly

circles and uniform speeds. The model explainedwhy the planets never move far from the ecliptic,

but treated Mercury and Venus as special casesin order to explain their small elongations.


21/39

Ptolemy's Epicyclic Model for Mars' Motions


22/39

Mars' Motion in Epicyclic Model


23/39

Ptolemy's kludge for Venus and Mercury


24/39

Criteria for Scientific Models

1. The following three criteria are applied to modernmodels.

(a) The model must fit the data.

(b) The model must make predictions that can betested and be of such nature that it would bepossible to disprove it.

(c) The model should be aesthetically pleasing

simple, neat, and elegant.


25/39

Criteria for Scientific Models (cont.)

2. Ptolemys model meets the first two criteria fairlywell but it is much less successful with the third.

3. Occams razoris the principle that the best

explanation is the one that requires the fewestunverifiable assumptions.

William of Okham (1285-1347?): Ran into trouble withPope John XXII, perhaps due to conflict with

followers of Thomas Aquinas (an Aristotelian).4. The Ptolemaic model did fit the data, so we mustjudge it as an acceptable model even though itlacked that certain neatness we would like.


26/39

Model, Theory, and Hypothesis

1. In science a scheme is not usually called a theoryuntil its ideas are shown to fit observed datasuccessfully. In every-day language, however, the

word theory is often used to refer to ideas thatare much more fanciful and less secure.2. A hypothesis is a guess, generally an intelligent

one, a tentative explanation awaiting further

development and testing.


27/39

Aristarchuss Heliocentric Model

1. 400 years before Ptolemy, around 280 BC, theGreek philosopher Aristarchus proposed amoving-Earth solution to explain celestialmotions. He introduced the concept of a spinningEarth and the first heliocentric model, 1800 years

before Copernicus.

2. Even though Aristarchus could not explain thelack of observable parallax (Aristotles argument),

he believed that the Sun was at the center of thesolar system because it was much bigger in sizethan the Earth.


28/39

Aristarchuss Heliocentric

Model (cont.)

3. Based on observations, he concluded the Sunwas about 20 times farther from the Earth thanthe Moon is. He showed that the Earth is 3 timeslarger than the Moon in diameter, and the Sun isabout 20 times larger than the Moon in diameter.This implies the Sun is about 7 times larger thanthe Earth in diameter.

4. Aristarchus was the first to create a map of thesolar system. He simply did not have the scale forit.


29/39

Aristarchus and relative distances


30/39

Aristarchus: Relative distances of Moon and Sun


31/39

Aristarchus and relative sizes of Earth and Moon


32/39

Aristarchus and relative sizes of Moon & Earth


33/39

Aristarchus and relative sizes of Moon & Sun


34/39

Measuring the Size of the Earth

1. Eratosthenes (276 - 195 BC) was the first person

to clearly understand the shape and approximatesize of the Earth.

2. By comparing shadows at noon during summersolstice at two different locations he understoodthat the Sun must be directly overhead (at thezenith) in Syene but that the Suns direction was

off the vertical by 7 in Alexandria.


35/39

Eratosthenes and the Size of the Earth


36/39

Method of

Eratosthenes to

measure size of the

Earth.

NB: The Sun is

assumed to be MUCH

further away than the

radius of the Earth.

[NOAA Ocean Service

Education]

S


37/39

Measuring the Size of the Earth (cont.)3. He realized that the 7 difference was due to the

Earths curvature and therefore the Earthscircumference was about 360/7 50 times thedistance between the two cities. Knowing thisdistance he was able to find the Earths diameter.His calculation was very close to the correctvalue.

4. Combining the calculations of Aristarchus andEratosthenes, the ancient Greeks had for the firsttime measurements of the radii of Earth, Moon,and Sun and their relative distances. We had towait until 1769 AD to observe the actual value ofthe astronomical unit and thus the true

dimensions of the solar system.


38/39

Measuring the Size of the Earth (cont.)5. The important point here is not the accuracy of

the measurements but the power of simplelogical arguments that allowed the ancientGreeks to have a very good sense of the solarsystem more than 2000 years ago.

Why was the Earth-centred Ptolemaic modelaccepted for 1300 years instead of theheliocentric model computed by Aristarchus andEratosthenes?

Because Aristotle's argument held sway and astationary Earth was demanded. No parallaxeswere observed until well after the Copernican andKeplerian revolutions. (Bessel 1838: 61 Cygni).


39/39

Reading for 3rd Lecture

Chapter2: Sections 2-5, 2-6, 2-7.

(The Copernican Revolution)

NB: We start using clickers on Wednesday!

Lecture 2 Earth Centered Universe

Documents

Transcript of Lecture 2 Earth Centered Universe