Transcript A Sun-Centered Universe - Sierra College Astronomy Home Page

Pick up 3rd hour stuff!
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3rd hour stuff will first appear in the center of
the room before lecture.
It will then be moved to the box labeled “3400”
outside the planetarium
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All 3rd hours will collect there until the end of the
semester
Scores posted just outside the planetarium
(listed by 4-digit ID number)
Answers posted online
Third Hour This week: Star Charts! Bring Star
Charts!
Lecture 3a: An Earth-Centered Universe
Terms
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Observer coordinates: altitude, azimuth,
zenith, horizon, meridian
Earth coordinates: latitude, longitude,
north pole, equator
Celestial coordinates: declination, right
ascension, north celestial pole,
celestial equator
Angles: degree, minute of arc, second
of arc, angular separation
Earth
in CS
Lecture 3a: An Earth-Centered Universe
Ancient Astronomy
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There are many ancient artifacts of
astronomy
 Aztec
Templo Mayor
 Chaco Canyon of the Anasazi
Aztec
Chaco
– Includes sun dagger
 Machu
Picchu in Peru
 Stonehenge in England
© Sierra College Astronomy Department
Sun dagger
Machu
Stonehenge
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Lecture 3a: An Earth-Centered Universe
Mesopotamian/Babylonian Astronomy
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Made the first long term records of astronomy
Created the 12 zodiacal constellations
Developed the angle measuring system we use
Used leap months in calendar
Discovered patterns of planetary motions by
keeping track of synodic periods
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Interest in planetary positions was due to their
interest in astrology, the belief that the positions of
celestial objects influence events on the Earth
They developed mathematical description of
planetary motions and could make crude
predictions
© Sierra College Astronomy Department
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Lecture 3a: An Earth-Centered Universe
Pythagoras (c.582-c.500 BC) and his Students
It was Pythagoras (or his students) who
rejected the notion of a flat Earth and
embraced the idea of a spherical Earth
 His model of the universe had Earth
revolving around a “central fire” which
could not be seen because it was
blocked by a “counter Earth”. The moon
and Sun around traveled around the
central fire.
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Pythag
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Lecture 3a: An Earth-Centered Universe
Eudoxus (408-355 BC)
He proposed that planetary motions were
a combination of circular motions
 He put the earth in center and planets
were attached to spheres which moved
at the appropriate rates to roughly
reproduce their motions.
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Exodus
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Lecture 3a: An Earth-Centered Universe
Aristotle (384-322 BC)
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Physical theory of dynamics
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We have a comprehensive theory, a framework for
questions.
Applications:
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motions: up, down, around
essences: earth, water, air, fire, ether
simple vs. compound
circular motion: complete, unchanging
Comets: clearly changeable, must be meteorological
Planets: compound circular motion
Spherical
Earth
Also made cogent arguments about the spherical
shape of Earth
© Sierra College Astronomy Department
7Spherical
Earth2
Lecture 3a: An Earth-Centered Universe
Aristarchus (310-230 BC)
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Dimensions of the Moon
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Angular size (0.5 degrees)
Linear size (inferred from lunar eclipses)
Distance (Small Angle Formula relates distance to
angular and linear size)
An example of a geometric approach to
astronomy
Made first estimate of Earth-Sun distance
(relative to Earth-Moon distance)
Also suggested a Sun-centered universe
© Sierra College Astronomy Department
eclipse
F8
Geometry
Small angle
Formula
(Don’t use)
8
D
q
d
So, what is the angular
size of the Moon?
© Sierra College Astronomy Department
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Lecture 3a: An Earth-Centered Universe
Eratosthenes (276-195 B.C.)
Measuring the Size of Earth
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Alexandria
Eratosthenes devised a clever way to
measure the Earth’s size. He observed that
when the Sun was overhead (at the zenith)
at Syene, it was 7° from overhead at
Alexandria.
Since 7° is about 1/50 of a full circle (360°),
the circumference of the Earth should be 50
times the distance from Syene to Alexandria,
or 50 x 5,000 stadia = 250,000 stadia.
© Sierra College Astronomy Department
Erato
Erato2
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Lecture 3a: An Earth-Centered Universe
Eratosthenes
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250,000 stadia roughly translates into
45,000 km, based on our best guess as to
the size of a stadium. The Earth’s actual
circumference is about 40,000 km, so
Eratosthenes calculation is 12% too big. But
his geometrical method is correct.
Earth’s circumference of 40,000 km gives a
diameter of about 13,000 km (~ 8,000 mi).
© Sierra College Astronomy Department
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Lecture 3a: An Earth-Centered Universe
Hipparchus
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Hipparchus
A discovery of a “new” star in 134 B.C.
prompted him to make a catalogue of the
brighter stars
 This led to another discovery: precession of
the poles
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– Hipparchus noticed the vernal equinox drifted
westward 1° every 78 years implying it would
take 26,000 years to travel the full cycle of 360°
along the ecliptic
– This was due to the earth’s poles slow movement
on the celestial sphere, completing a loop in
about 26,000© years
Sierra College Astronomy Department
precess
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Lecture 3a: An Earth-Centered Universe
Claudius Ptolemy (127-151 AD)
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Claudius Ptolemy
Worked in at the Great Library at Alexandria
 Invented the latitude and longitude system
 Wrote a book on astronomy – megisth
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– Often referred to as Almagest = “the Greatest”
– Contained improved methods to find distance to the
Sun and Moon
– May have taken some ideas from Hipparchus
© Sierra College Astronomy Department
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Lecture 3a: An Earth-Centered Universe
Claudius Ptolemy (127-151 AD)
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Claudius Ptolemy is credited for devising
the first predictive model of the universe,
the Ptolemaic model (A.D. 150)
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Discredited Aristarchus’s Sun-centered model with
incorrect assumptions
Philosophical keys: use circles, have uniform
circular motion
The Sun, Moon and each planet moved
upon an epicycle, the center of which
revolved around a deferent circle
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Compound circular motion allowed planets to
have retrograde motion
© Sierra College Astronomy Department
01-20C
Retrograde
Ptolemaic
Model
01-22
Ptolemy, Mars
01-23C
Ptolemy,
Mercury and
Venus
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Lecture 3a: An Earth-Centered Universe
Claudius Ptolemy
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01-20C
Retrograde
To improve accuracy, Ptolemy had to offset
the Earth from the center of the deferent
Ptolemaic
and make the uniform circular motion
Model
relative to another point, equally offset from
center called the equant
It is difficult to know whether Ptolemy
believed the universe actually worked this
way, or was this simply a model that gave
fairly accurate predictions.
D-7
01-22
Ptolemy, Mars
01-23C
Ptolemy,
Mercury and
Venus
© Sierra College Astronomy Department
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Lecture 3a: An Earth-Centered Universe
Criteria for Scientific Models
(Slide from Lecture 1b in Handbook)
 Three modern criteria of scientific models:
– Model must fit the data
– Model must make predictions that can be
tested and be of such a nature that it
would be possible to disprove it
– Model should be aesthetically pleasing simple, neat, and elegant (Occam’s razor)
Lecture 3a: An Earth-Centered Universe
Criteria for Scientific Models
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Ptolemy’s model meets the first two
criterion for a good scientific model fairly
well but it is much less successful with
the third (aesthetically pleasing).
 Earth
not quite in the center
 Scale of deferents and epicycles arbitrary
 Not quite uniform circular motion
© Sierra College Astronomy Department
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See Chapter S1, p 93
Lecture 3: Patterns in the Sky
Observation: The Planets
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Inferior
The early observers noted several planetary
configurations
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Opposition: when a planet and Sun appear in the
opposite part of the sky (Elongation = 180°)
Superior
– Only happens for Mars, Jupiter, Saturn
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Conjunction: when the planet and Sun appear together
in the sky (Elongation = 0°)
Greatest Elongation: when Mercury or Venus reaches a
maximum elongation angle during a particular apparition
The time it took a planet to return to a particular
configuration (e.g. conjunction, opposition) was
called the synodic period.
Plan.
© Sierra College Astronomy Department
Config.
(Space)
Plan.
18 Config.
Other Slides
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Lecture 3a: An Earth-Centered Universe
Small Angle Formula
angular diameter(q ) 
linear diameter(D )
distance(d )
 206, 265"
Solved for d:
distance(d ) 
linear diameter(D )
angular diameter(q )
 206, 265"
For the moon:
F8
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Linear diameter = 3476 km
 Distance from Earth = 384,000 km
Therefore the angular diameter is 1870”  0.5o
See Text
© Sierra College Astronomy Department
Geometry
Small angle
formula
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Lecture 3a: An Earth-Centered Universe
Small Angle Formula
angular diameter(q ) 
linear diameter(D )
distance(d )
 206, 265"
Solved for d:
distance(d ) 
linear diameter(D )
angular diameter(q )
For the moon:
Angular diameter = 0.5o = 1800”
 Linear diameter = 3/8 Earth’s diameter
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 206, 265"
F8
Geometry
Small angle
formula
Therefore the distance to the moon is calculated to be
42 Earth diameters, though the actual answer must
be smaller
See Text 21
© Sierra College Astronomy Department