PowerPoint Presentation Astronomy 112

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Astronomy 112
Dr. Steve Desch Arizona State University Spring
2009
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• RecapWe have now discussed the motions of the
  Sun and Moon and planets in the sky, and the
  Ptolemaic model to explain them.
• Besides their daily cycle (rise in east,
  culminate in south, set in west), Sun and Moon
  and planets each move through the constellations
  of the zodiac. The Sun takes a year, the Moon
  takes a month, the planets take different times.
• Venus and Mercury stay close to the Sun. Mars,
  Jupiter and Saturn sometimes are close to the
  Sun, but sometimes can be in opposition to the
  Sun.
• We discussed how all the Ptolemaic model is
  consistent with all of these cycles (to the
  accuracy of the ancients' observations)

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Ptolemy hypothesized that planets spun on tiny
spheres, which themselves spun around the Earth
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These tiny spheres are "epicycles"
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Hypothesis Sky-bowl model 3.0, the Ptolemaic
model
Epicycles of Mars, Jupiter and Saturn and Moon
are like this
Epicycles of Mercury and Venus are centered on
the line to the Sun.
Earth a little off center ("eccentric")
All of the epicycles can be a little tilted, too
VERY COMPLICATED!
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The Ptolemaic model
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• RecapWe also discussed the motions of the Moon
  relative to the Sun.
• The phases of the Moon have to do with its
  position in the sky relative to the Sun new moon
  when close to the Sun, first quarter when 90
  degrees from the Sun, and full moon when 180
  degrees from Sun, opposite it in the sky.
• Moon's path around sky doesn't exactly line up
  with Sun's path, even though they both go through
  the zodiac but occasionally the Moon does go in
  front of the Sun, producing a solar eclipse.

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1
2
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New
Waxing crescent
Waning crescent
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1st qtr
3rd qtr
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1
Waxing gibbous
Waning gibbous
Full
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Sun in Sagittarius in December / January
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Sun in Capricorn in January / February
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Sun in Aquarius in February / March
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• RecapWe also used Eratosthenes's results to
  test a prediction of the Ptolemaic model, that
  the Earth is round.
• A stick in the ground in Alexandria casts a
  shadow on noon around June 20th, but a stick in
  Syene, at the same time, does not.

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Eratosthenes's experiment
If the Earth is flat, Sun would be 25,000 miles
away
25,000 miles ?
500 miles
Alexandria
Syene
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Eratosthenes's experiment
Alexandria
Syene
Observations more easily explained if Earth is a
sphere with radius 6380 km, and Sun is very far
away (gtgt 25000 miles away)
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Solar Eclipses
Occasionally the Moon crosses in front of the Sun
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The Sun and the Moon happen to appear to be the
same size
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Moon's shadow just touches the Earth, like a
pencil point, draws a line on the Earth's surface.
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From http//eclipse.gsfc.nasa.gov
August 11, 1999
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The Moon's penumbra is large most of the Earth
gets a partial eclipse
The Moon's umbra is only about ten miles across
at Earth's surface. A total eclipse is rare.
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Solar eclipses happen when the Moon is between
the Earth and Sun. Why doesnt this happen every
new moon, every 29.5 days? The Moon's "epicycle"
or orbit around the Earth takes it a little bit
above or below the zodiac
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Ascending node
If nodes are 90º away from Sun, Moon will be high
above or below Sun in sky
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Ecliptic Sun's path in sky
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Descending node
Ascending node
If nodes are 0º (or 180º) away from Sun, Moon
will be either directly in front of Sun, or
directly opposite the Sun in the sky
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Node
Ascending node
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Node
Descending node
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The Moons path is a circle in the sky that more
or less goes through the zodiac. The Sun's path
in the sky goes directly through the
zodiac. These two circles cross at two points in
the sky, called nodes (always on the zodiac, by
definition). The nodes move along the zodiac.
They catch up with the Sun every 346.6 days 1
eclipse year
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Solar eclipses happen when one of the two nodes
catches up with the Sun AND the Moon is at the
node (the Moon will automatically be new) This
happens about 2-4 times per year. Can you
predict an eclipse? Yes! If you know when one
eclipse occurred, you can predict one in the
future.
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The Saros cycle 19 eclipse years 19 x 346.6
days 6585.4 days (the same node has caught up
with the Sun on the zodiac again) 223 months
223 x 29.531 days 6585.3 days (the Moon is a
new moon again) Match to within a few hours.
Eclipses repeat after 6585.3 days 18 years, 11
1/3 days the Saros Example Eclipse in Europe
August 11, 1999 is followed by an eclipse in the
US, August 21, 2017.
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From http//eclipse.gsfc.nasa.gov
August 11, 1999
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From http//eclipse.gsfc.nasa.gov
August 11, 1999
August 21, 2017
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From http//eclipse.gsfc.nasa.gov
May 20, 2012
May 10, 1994
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Not Quite the Saros cycle 20 eclipse years 20
x 346.6 days 6932.0 days (the same node has
caught up with the Sun on the zodiac again) 235
months 235 x 29.531 days 6939.8 days (the
Moon is a new moon again Metonic cycle) Match is
off by a week still, a new moon may be close to
the node again after 6939.8 days 19 years.
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Moon is new again 19 years later, too, but
doesn't quite line up with Sun
May 10, 1994
May 10, 2013
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Predicting eclipses is big business! 585 BC
Thales of Miletus predicts a solar eclipse that
stops a war February 29, 1504 Christopher
Columbus predicts a lunar eclipse that
intimidates native Jamaicans into helping
him 1806 Shawnee political leader Tecumseh
consolidates political power among western tribes
by predicting a solar eclipse In A Connecticut
Yankee in King Arthurs Court by Mark Twain, Hank
Morgan escapes execution by predicting an eclipse.
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Lunar Eclipses
Sometimes the full Moon suddenly is darkened deep
red or black, for an hour or two. This is a
lunar eclipse.
From Tempe Last total lunar eclipse October
28, 2004 Next total lunar eclipse December 21,
2010
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Sunlight can be bent by the Earth's atmosphere
but after passing through so much air, the Sun's
light looks red (exactly like a sunset!)
Sun
Earth's umbra
Earth's penumbra
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Earth's shadow --- it's always round. The
only shape that always casts a round shadow is a
sphere.
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Lunar eclipses occur when the (otherwise Full)
moon enters Earth's shadow. Happens when a node
is exactly opposite the Sun in the sky. Saros
cycles apply to lunar eclipses, too.
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From http//eclipse.gsfc.nasa.gov
Lunar eclipses can be seen from half of the Earth
at a time. There are also more lunar eclipses
because the Earth's shadow is bigger. You'll see
more lunar eclipses than solar eclipses because
of this.
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The next good lunar eclipse to be seen from
Arizona is December 21, 2010, soon after
midnight.
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• So Ptolemy's model works pretty well!
• Do the predicted motions of Sun, Moon and planets
  match observations? Yes
• Do solar and lunar eclipses occur as predicted?
  Yes
• Is the Earth round? Do sticks cast shadows of
  different lengths in different locations? Yes,
  Ptolemy's model works if Earth's radius is 6380
  km and the Sun is far.
• So is Ptolemy's model right? No!
• We should always question our models. What other
  predictions does it make? What other
  observations can we perform? Here's a
  prediction
• Different parts of the Earth should see the Moon
  in front of different stars.

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Two observers looking at the same time but far
apart on Earth will see the Moon in slightly
different (by an angle ?) directions. Measure
that angle, know the radius of the Earth, a
little trig, and voila
?
?
H distance to Moon
?
O radius of the Earth
Distance to Moon 385,000 km
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O radius of the Moon
Measure the apparent size of the Moon, and know
its distance, plus a little trig, and voila
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A distance to Moon
Radius of the Moon 1740 km
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Aristarchus (280 BC)
Moon should appear half full (the quarter moon)
when it is closer to new moon than to full moon,
NOT halfway between them.
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Aristarchus (280 BC)
Moon should appear half full (the quarter moon)
when it is closer to new moon than to full moon,
NOT halfway between them.
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cos ? A / H (Earth-Moon distance) /
(Earth-Sun distance)
distance from Earth to Moon
?
distance from Earth to Sun
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Aristarchuss best estimate of ? 87 degrees
cos 87 about 0.05 1 / 20
distance from Earth to Moon
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distance from Earth to Sun
Aristarchus concluded the Sun was 20 times
farther away than the Moon.
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Modern observations ? 89.85 degrees
cos 89.85 about 0.00258 1 / 390
distance from Earth to Moon
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distance from Earth to Sun
The Sun is 390 times farther away than the Moon,
or 149,000,000 km.
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Lets pause and appreciate the mind-bogglingly
big distances Alexandria to Syene 500 miles
800 km 8 x 102 km The radius of the Earth
6,400 km 6.4 x 103 km The distance to the Moon
385,000 km 3.85 x 105 km The distance to the
Sun 149,000,000 km 1.49 x 108 km The radius
of the Sun 700,000 km 7 x 105 km !!!
And the Greeks mostly got these right!
Sun appears same size as Moon
Its 390 times farther, so 390 times bigger
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• Other predictions of the Ptolemaic model?
• The Earth is round, with the firmaments axis
  fixed to the Earths poles. You can't see all
  the stars from Greece. - Yes! Canopus, for
  example, not visible from Greece.

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North Star
axis
Greece
Earth
Canopus
Firmament of stars
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North Celestial Pole
We keep track of this using "celestial
coordinates"
North Pole
Celestial Equator
Equator
South Pole
SCP
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Latitude 90 degrees Declination
90 degrees
North Celestial Pole
North Pole
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Latitude 0 degrees Declination
0 degrees
Celestial Equator
Equator
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Latitude -90 degrees Declination
-90 degrees
South Pole
SCP
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Right Ascension 180 degrees 12 hours
Right Ascension 270 degrees 18 hours
Right Ascension 90 degrees 6 hours
Right Ascension 0 degrees 0 hours
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Northern stars (Big Dipper, Northern
Cross)
Southern stars (Southern Cross, Centaurus)
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North Star
At the equator (latitude 0 degrees), the North
Star is always right on (0 degrees above) the
northern horizon
At north pole (latitude 90 degrees), the North
Star is directly above (90 degrees above northern
horizon)
North star not visible from southern hemisphere
Height of North Star above horizon your
latitude!
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To North Star, 90
"up"
horizon
equator
l latitude
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To North Star, 90
"up"
We see stars highest in the sky when they are in
the south
horizon
North
d
equator
90 - l
South
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Maximum altitude a 90 - l d
"up"
horizon
d
equator
90 - l
a angle above horizon altitude
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Maximum altitude a 90 - l d
"up"
a 180
a 90
horizon
d
a gt 180
equator
90 - l
a angle above horizon altitude
a 0
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The maximum altitude of a star above the southern
horizon is a 90 - l d The North Star,
Polaris, has d 90, so a 180 - l If l 90
(you are at the North Pole), a 90 (straight
overhead) If l 0 (you are at the equator), a
180 (directly opposite southern horizon, i.e.,
directly on northern horizon) If l lt 0 (you are
south of the equator), a gt 180 (star is below the
northern horizon, cannot be seen)
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The maximum altitude of a star above the southern
horizon is a 90 - l d Spica, in the zodiac
constellation Virgo, has , has d -10, so a
80 - l If l 90 (you are at the North Pole), a
-10 (it is 10 degrees below the southern horizon,
and cannot be seen) If l 0 (you are at the
equator, e.g., Singapore), a 80 (it is 80
degrees above southern horizon, just 10 degrees
to the south of being directly overhead) For l
-10 (e.g., Brazil), a 90 (Spica can be directly
overhead)
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North Celestial Pole
North Pole
Celestial Equator
Equator
South Pole
SCP
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How does this relate to the Suns path in the
sky, the ecliptic? We know that on the summer
solstice, when the Sun is in Gemini, it is
directly overhead at noon in Syene (latitude
23 degrees)... a 90, l 23, so d 23 On
the vernal and autumnal equinoxes, when the Sun
is in Pisces or Virgo, it is directly overhead at
the equator... a 90, l 0, d 0 On the
winter solstice, when the Sun is in Sagittarius,
it is directly overhead at a latitude -23
degrees... a 90, l -23, d -23.
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Gemini
Virgo
Pisces
Sagittarius
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Gemini
Suns declination 0 deg
Suns declination 23 deg
Virgo
Pisces
Suns declination -23
deg
Suns declination 0 deg
Sagittarius
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Sagittarius
Suns declination -23 deg
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Gemini
Suns declination 23 deg
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The Sun's changing declination affects how high
it is in our sky
Latitude of Phoenix 33 Winter d -23. a
90 - l d 34 In winter, Sun can only ever get
34 degrees above southern horizon, even at
noon Spring Fall, d 0. a 90 - l d
57 Summer, d 23. a 90 - l d 80 In
summer, the Sun can be almost overhead at noon
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In Spring and Fall, the Sun rises exactly in the
East and sets exactly in the west. In Winter, the
Sun doesn't get as high above the southern
horizon. It rises in the southeast, and sets in
the southwest. In Summer, the Sun gets far above
the southern horizon. It rises in the northeast
and sets in the northwest.
celestial equator
June
December
March, September
East
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In Spring and Fall, the Sun rises exactly in the
East and sets exactly in the west. In Winter, the
Sun doesn't get as high above the southern
horizon. It rises in the southeast, and sets in
the southwest. In Summer, the Sun gets far above
the southern horizon. It rises in the northeast
and sets in the northwest.
June
March, September
December
celestial equator
West
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As complicated as the Ptolemaic model is, it
successfully predicts all the motions of the
planets and Sun and Moon (and eclipses) to within
the accuracy of the observations made by ancient
astronomers. It passed every test. This is the
model in place when the Roman empire fell. The
model would last gt 1000 years. More detailed
studies of the planets' motions would show flaws,
but this would take until the 1500's. The model
predicted distances to the Sun and Moon and
planets. These couldn't be directly measured
until the 1600's or later. Pretty successful
model! But wrong.