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![Page 1: Announcements Reading Assignment posted for Lecture 1-3 + planetarium Please turn off all electronic devices Please sign attendance sheet.](https://reader037.fdocuments.in/reader037/viewer/2022110321/56649f455503460f94c6736f/html5/thumbnails/1.jpg)
Announcements
Reading Assignment posted for Lecture 1-3 + planetarium
Please turn off all electronic devices
Please sign attendance sheet
![Page 2: Announcements Reading Assignment posted for Lecture 1-3 + planetarium Please turn off all electronic devices Please sign attendance sheet.](https://reader037.fdocuments.in/reader037/viewer/2022110321/56649f455503460f94c6736f/html5/thumbnails/2.jpg)
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
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Lecture 3:Greek Cosmology
Astronomy 1143 – Spring 2014
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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
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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?
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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
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Angular Size
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Angular Distance & Size
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Angular Size Changes with Distance
The angular size of a dime and quarter can be the same, even though their physical sizes are different
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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
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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
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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
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Geometry, Distance and Size
Say you wanted to measure the height of this:
a
Need to know this distance!
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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
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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
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Method of Trigonometric Parallaxes
Distant Stars
p
Earth
ForegroundObject
p = parallax angle
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Parallax decreases with distance
Closer objects have larger parallaxes:
Distant objects have smaller parallaxes:
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Lunar Parallax
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Right Triangles
opposite
hypotenuse
adja
cent
A
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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
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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
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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
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Measuring the Moon’s Size
Step 2: Use the definition of a tangent
a/2YouR
distance
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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
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Mean Distance:384,400 km(~60 REarth)
Perigee(nearest):363,300 km
Moon Appears ~11% larger at Perigee
Apogee(farthest):
405,500 km
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Moon at Perigee Moon at Apogee
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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
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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
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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?
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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
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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
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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.
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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
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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
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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
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In addition, stars always have the same brightness. Earth not getting closer or farther away.
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Lack of Stellar Parallaxes
June
Distant Stars
ForegroundStar
December
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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
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Mars Retrograde MotionAugust 2003
Photo by Turkish amateur astronomer Tunç Tezel
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Earth
Epicycle
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Ptolemy’s Solar System
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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.