Download Angular sizes, moon phases, Ptolemy

1
Lecture 3
Angular Sizes,
Moon Phases, and
Ptolemy
September 14, 2015
2
Measuring Angles
• Apparent distances in the sky are determined by
measuring the angle between two objects.
• There are 360 degrees in a circle.
• Each degree is split into 60 arcminutes
3
Angular Size
q
As distance increases, angular size decreases
q
4
Linear Size from Angular Size
D
 rq
180
rq

57.3
5
The Sun and the Moon have roughly the same angular
size. However, the Sun is 400 times more distant than
the Moon. What is the linear size of the Sun compared
to that of the Moon?
100%
A.
B.
C.
D.
400 times greater
400 times smaller
200 times greater
200 times smaller
0%
A.
B.
0%
C.
0%
D.
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The Sun and the Moon have roughly the same angular
size. However, the Sun is 400 times more distant than
the Moon. What is the linear size of the Sun compared
to that of the Moon?
 rSunq Sun
A. 400 times greater
DSun
rSun
180


B. 400 times smaller
DMoon  rMoonq Moon rMoon
C. 200 times greater
180
D. 200 times smaller
400rMoon

 400
rMoon
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Phases of the Moon
• The Moon orbits the Earth ~ every month.
• The Moon appears to have different phases
because we see more or less of the lighted side of
the Moon depending on where it is with respect to
the Sun.
• Sidereal period: time to complete one revolution
with respect to the stars (27.3 days)
• Synodic period: time to return to same phase as
seen from Earth (29.5 days)
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Sidereal and Synodic Month
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First Quarter
Phases of the Moon
Waxing
Gibbous
Waxing
Crescent
Full Moon
New Moon
Flash Applet
Waning
Gibbous
Waning
Crescent
Last Quarter
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Phases - Photos
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Changes in the Full Moon
Laurent Laveder of Quimper, Bretagne, France photographed 12 full Moons of
2005-2006 and stitched the pictures together to make this movie.
The Moon swells and shrinks, it rocks back and forth and up and down. This is a
result of the Moon's motion around its tilted, elliptical orbit. Each full Moon occurs
at a different point in that orbit, and so we see it from a slightly different distance
and angle. The rocking motions are called libration; because of them we can see
59% of the Moon's surface rather than the 50% you might have learned in school.
Spaceweather.com 5/15/06
When does the third quarter moon rise?
A.
B.
C.
D.
About 6 AM
About noon
About 6 PM
About midnight
51%
38%
10%
1%
A.
B.
C.
D.
When does the third quarter moon rise?
About 6 AM
About noon
About 6 PM
About midnight
E
A.
B.
C.
D.
W
first quarter
third quarter
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Shape of the Earth –
Aristotle ( 384-322 BC)
• Earth’s shadow was curved during a lunar eclipse.
• Ships appeared to sink below the horizon.
• View of stars differs from different locations.
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The Geocentric Universe
• Ancient people (Aristotle) “knew” from
observations that
– The stars appear fixed on the sky relative to each
other.
– Planets, moon and Sun change position with respect
to the stars.
– Mercury and Venus only seen near Sun.
• These observations led them to theorize that the
Earth is at the center and all objects move
around it.
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Basic Geocentric View
• Order of planets somewhat arbitrary.
• Mercury and Venus always orbit at a velocity that
keeps them near the Sun.
Celestial Sphere
Saturn
Mars
E
Mercury
Jupiter
Venus
Moon
Sun
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Retrograde Motion
• Direct Motion: Planets usually move from west-to-east
in the sky with respect to the stars over long periods of
time.
• Retrograde Motion: Planets sometimes change direction
and go east-to-west with respect to the stars
East
West
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Ptolemy (140 AD)
• Planets move on “epicycles”
• Epicycles moved on deferent that was
centered not on the Earth, but on an equant
point.
• All motions were on
circles (“perfect
shape”)
epicycle
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Ptolemy (140 AD)
• Size and rates of motion on epicycles was
calculated using tabulated data
• Predicted positions of
planets very
accurately.
• Accepted theory for
~15 centuries!
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Epicycles
Animation
(Figure 3.11 p.61)
In Ptolemy’s model, when is a planet closest to
Earth?
A. When the planet crosses
the deferent.
B. During its retrograde
westward motion.
C. When it is closest to the
equant point.
D. There is no specific time in
its orbit when the planet is
closest to Earth.
10%
86%
3%
A.
B.
C.
1%
D.