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What is one piece of evidence that the Earth is round?

a) North Star always same height above horizon

b) Constellations always have the same orientation

c) Shadow of Earth on Moon during lunar eclipse is rabbit-shaped

d) Everyone on Earth sees same constellations

e) North Star not always visible

Lecture 3:Greek Cosmology

Astronomy 1143 – Spring 2014

Key Ideas:Greeks -- geocentric (Earth-centered)

Universe

Parallax – • apparent shift in position of object viewed

from different locations• Geometric measure of distance

Measuring the Moon’s Diameter• Angular Diameter and Distance Needed

Size of Moon & Sun relative to Earth measured – depth in heavens seen

Key Ideas:

Evidence for Geocentric Universe• High speeds not needed for Earth• Stars do not change appearance over course

of year• No parallaxes seen for stars

Ptolemy’s geocentric model• Complicated by need to explain observations• Retrograde motion explained by epicycles• Model matched observations and made

predictions – did it represent reality?

Describing the SkyWe do not “see” a 3-dimensional night sky

We can describe brightnesses and colors and motions

Stars appear as single points of light

Planets are close to points of light (at least to the naked eye)

Sun and Moon appear as actual extended objects

Describe separation of stars on the sky and the apparent size of objects by angular distance and angular size

Angular Size

Angular Distance & Size

Angular Size Changes with Distance

The angular size of a dime and quarter can be the same, even though their physical sizes are different

Measuring big distances

Measuring distances and physical sizes in astronomy is very difficult

Obvious methods such as meter sticks are out (there’s that whole lack of oxygen thing)

We don’t usually have reference objects here on Earth to help us out

Answer: Use geometry

The Moon’s Size and Distance The first step to understanding the nature of the Moon is to measure how big it is and how far away it is.

Measuring these quantities requires geometry.

We again want to measure distances/sizes that are very, very big

Measuring the Size of the Moon

The further away an object is, the smaller its apparent angular size.

If two objects have the same angular size, the more distant object has a larger radius.

We must know the distance to calculate the actual physical size of an object by geometry.

True for things on Earth and in the sky

Geometry, Distance and Size

Say you wanted to measure the height of this:

a

Need to know this distance!

The height of Mount EverestThe height of Mount Everest (aka

Chomoloangma or Sagarmatha) was very difficult to determine because its distance from surveyors was poorly known.

Named after Sir George Everest, the surveyor-general of India

1808: Great Trigonometric Survey of India began

1852: Mt. Everest identified as the highest peak by Radhanath Sikdar

Definition of Parallax

Parallax is the apparent shift in the position of an object when it is viewed at different positions

The size of the shift depends on• Distance to the object• Distance between viewing points

If you measure the angular size of the shift and the distance between the observation points, you can calculate the distance

Method of Trigonometric Parallaxes

Distant Stars

p

Earth

ForegroundObject

p = parallax angle

Parallax decreases with distance

Closer objects have larger parallaxes:

Distant objects have smaller parallaxes:

Lunar Parallax

Right Triangles

opposite

hypotenuse

adja

cent

A

Right Triangles

opposite

hypotenuse

adja

cent A

If you have a right triangle, the length of one side and the angle, you can get the length of the other side

Measuring the Moon’s Size

Unlike parallax, we can do this from one place

Step 1: Measure the angular size of an object on the sky and divide by 2

aYou

Measuring the Moon’s Size

Unlike parallax, we can do this from one place

Step 1: Measure the angular size of an object on the sky and divide by 2

a/2You R

distance

If we know a and distance, we can get R

Measuring the Moon’s Size

Step 2: Use the definition of a tangent

a/2YouR

distance

Measuring the Moon’s Size

Step 3: Put numbers into your calculator

Distance of Moon: 384,400 km

Angular size of Moon: 31’ (arcminutes)

about ¼ of the Earth’s radius

Mean Distance:384,400 km(~60 REarth)

Perigee(nearest):363,300 km

Moon Appears ~11% larger at Perigee

Apogee(farthest):

405,500 km

Moon at Perigee Moon at Apogee

How does the Sun compare to the Earth and Moon?Measuring the parallax of the Sun is much

more difficult

Measurement of the Earth-Sun distance relies on more indirect methods

However, a few facts about the relation between the Earth, Moon and Sun can be figured out from observations that ancient cultures could make

What can we learn from solar eclipses?

The Sun is more distant than the Moon

The Sun has the same angular size as the Moon

Therefore, the Sun has a bigger radius than the Moon

Sun vs. EarthGreek astronomers calculated the size of the Sun

as well as the Earth & Moon

Aristarchus, using the angle between Earth-Moon-Sun at quarter moon (see EC problem), argued that the Sun was ~5 times larger than Earth

Ptolemy, using other geometric arguments, found a similar value

Aristarchus argued that the larger Sun should be stationary rather than the smaller Earth

Ptolemy (and vast majority of other astronomer) thought that the Earth did not move. Why not?

Greek Cosmology

Greek thinkers sought to:• Explain observations with a model of the solar

system• Apply model to observations of Sun, Moon,

planets & stars

Scientific Method in operation!

Geocentric Hypothesis• Earth is at the center of the Universe, and

everything orbits around the Earth

Aristotle-Greek,384-322 BCE

Hypothesized a geocentric system

(Earth at the center)

Hypothesis: The Earth is at the center of the Universe, and the planets orbit around the Earth

Claudius Ptolemais(Ptolemy - c. 150 CE)Great Astronomer & Geographer of the late classical age.

Wrote the Mathematical Syntaxis• Compilation of Mathematical &

Astronomical knowledge of the time.• Known to us as the Arabic “Al Magest”

Argued for the geocentric model based on observational evidence.

Scientific ArgumentsFor thousands of years, the consensus (but not the

only view) was that the Universe was geocentric

This was not because no one was making observations or testing hypotheses in a scientific manner

Ancient astronomers discussed several reasons why observations were in agreement with a geocentric model

Basic problems: did not conceive of the true distances to stars & incomplete knowledge of physics

The Need for Speed

A major conceptual barrier was the enormous speed.

Rotation at the Equator:• Circumference of Earth:

40,000 km• Time for One Rotation:

24 hours• Speed = Distance Time

= 40,000 km 24 hr

= 1670 km/hr

Ptolemy’s argument: you always see half the sky, so the Earth has to be at the center & very small compared to the size of the heavens

In addition, stars always have the same brightness. Earth not getting closer or farther away.

Lack of Stellar Parallaxes

June

Distant Stars

ForegroundStar

December

Simple Geocentric Model of Universe

However, model does not explain all observations

• Variable speed of Sun and Moon across the sky – different angular distances covered night to night

• RETROGRADE MOTION

Mars Retrograde MotionAugust 2003

Photo by Turkish amateur astronomer Tunç Tezel

Earth

Epicycle

Ptolemy’s Solar System

The Ultimate Geocentric SystemPtolemy’s Universe

• Geocentric• Sun larger than Earth larger than Moon• Heavens have depth and are distant from Earth

Ptolemy’s final geocentric system was quite complex:• 40 epicycles & deferents required.• Equants & eccentrics for all planets, the Moon, & the

Sun• It agreed with the available observations and predicted

the motions of the planets, Sun, and Moon.

It was to prevail virtually unchallenged for nearly 1500 years.