PowerPoint Presentation Astronomy 112

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Astronomy 112
Dr. Steve Desch Arizona State University Spring
2009
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• RecapWe have discussed the Ptolemaic model.
• Earth is a sphere floating in space. Consistent
  with observations that of shadow lengths in
  different locations, with fact that some stars
  invisible from Phoenix, and the shape of Earth's
  shadow during lunar eclipses.
• Sun, Moon and Planets orbit around Earth in
  complicated series of circular motions.
  Consistent with (inaccurate) observations of
  planets' positions, including the retrograde
  motion of planets (especially Mars) consistent
  with eclipses consistent with phases of the Moon.

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North Star
axis
Phoenix
Earth
Canopus
Firmament of stars
horizon
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• RecapWe have discussed the Ptolemaic model.
• Earth is a sphere floating in space. Consistent
  with observations that of shadow lengths in
  different locations, with fact that some stars
  invisible from Phoenix, and the shape of Earth's
  shadow during lunar eclipses.
• Sun, Moon and Planets orbit around Earth in
  complicated series of circular motions.
  Consistent with (inaccurate) observations of
  planets' positions, including the retrograde
  motion of planets (especially Mars) consistent
  with eclipses consistent with phases of the Moon.

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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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• RecapThe Ptolemaic model makes predictions
  about distances to the Sun, Moon and planets.
• Size of the Earth determined by Eratosthenes's
  experiment. Radius of Earth 6380 km.

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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.
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• RecapThe Ptolemaic model makes predictions
  about distances to the Sun, Moon and planets.
• Size of the Earth determined by Eratosthenes's
  experiment. Radius of Earth 6380 km.
• Distance to Moon determined by simultaneous
  observations from different locations. Distance
  to Moon 385,000 km.

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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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• RecapThe Ptolemaic model makes predictions
  about distances to the Sun, Moon and planets.
• Size of the Earth determined by Eratosthenes's
  experiment. Radius of Earth 6380 km.
• Distance to Moon determined by simultaneous
  observations from different locations. Distance
  to Moon 385,000 km.
• Size of Moon determined by apparent size in sky
  and distance to Moon. Radius of Moon 1740 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
?
A distance to Moon
Radius of the Moon 1740 km
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• RecapThe Ptolemaic model makes predictions
  about distances to the Sun, Moon and planets.
• Size of the Earth determined by Eratosthenes's
  experiment. Radius of Earth 6380 km.
• Distance to Moon determined by simultaneous
  observations from different locations. Distance
  to Moon 385,000 km.
• Size of Moon determined by apparent size in sky
  and distance to Moon. Radius of Moon 1740 km.
• Distance to Sun might be determined by
  Aristarchus's experiment observing the Moon's
  phases (this turns out to be too difficult).
  Distance to the Sun 149,000,000 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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Modern observations ? 89.85 degrees
cos 89.85 about 0.00258 1 / 390
distance from Earth to Moon
?
distance from Earth to Sun
The Sun is 390 times farther away than the Moon,
or 149,000,000 km.
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• RecapThe Ptolemaic model makes predictions
  about distances to the Sun, Moon and planets.
• Size of the Earth determined by Eratosthenes's
  experiment. Radius of Earth 6380 km.
• Distance to Moon determined by simultaneous
  observations from different locations. Distance
  to Moon 385,000 km.
• Size of Moon determined by apparent size in sky
  and distance to Moon. Radius of Moon 1740 km.
• Distance to Sun might be determined by
  Aristarchus's experiment observing the Moon's
  phases (this turns out to be too difficult).
  Distance to the Sun 149,000,000 km.
• Size of Sun determined by apparent size in sky
  and its distance. Radius of Sun 696,000 km.

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Sun appears same size as Moon
Its 390 times farther, so 390 times bigger
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North Star
Let's go back to that prediction that some stars
aren't visible from Phoenix.
axis
Phoenix
Earth
Canopus
Firmament of stars
horizon
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North Celestial Pole
We can keep track of where stars are, 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
a lt 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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Cancer
Gemini
Suns declination 0 deg
Leo
Suns declination 23 deg
Virgo
Taurus
Libra
Aries
Scorpius
Pisces
Suns declination -23
deg
Suns declination 0 deg
Sagittarius
Capricorn
Aquarius
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March Sun's declination is 0 degrees. Sun is
directly overhead the Earth's equator. This is
where the ecliptic (Sun's path) crosses the
celestial equator. Sun rises exactly east, sets
exactly west. Sun is above the horizon (day) 12
hours, is below horizon (night) 12 hours,
therefore is "equinox" (equal night). It's
Spring, so we call where the Sun is at this time
the "Vernal Equinox". Vernal equinox currently
is in Pisces. Used to be (2000 years ago) in
Aries. Aries ram symbol of spring.
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Cancer
Gemini
Suns declination 0 deg
Leo
Suns declination 23 deg
Virgo
Taurus
Libra
Aries
Scorpius
Pisces
Suns declination -23
deg
Suns declination 0 deg
Sagittarius
Capricorn
Aquarius
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June Sun's declination is 23 degrees. Sun is
directly above latitude 23 North. March through
June, Sun's declination is more and more North
then June through September it's less and less
north. In June Sun seems to stop moving north in
sky, and "turns" to the south. We call this
latitude on Earth (23 North) a "turning"
latitude, or "tropic" (Greek for "turning").
In June Sun is in Gemini, but it used to be
(2000 years ago) at maximum north declination in
June in Cancer. Latitudes 23 North called
"Tropic of Cancer". Cancer crab walks
sideways (like Sun reversing its northward
movement).
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June Sun's declination is 23 degrees. Sun
rises north of east and sets north of west. Sun
is above horizon (day) more than 12 hours in
Northern hemisphere summer. Day lasts less
than 12 hours in Southern hemisphere winter.
Sun stops moving north in the sky, standing
still, so this is a "solstice". It's summer, so
we call where the Sun is in the sky the "Summer
Solstice". Summer solstice is now in Gemini,
but used to be in Cancer.
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Cancer
Gemini
Suns declination 0 deg
Leo
Suns declination 23 deg
Virgo
Taurus
Libra
Aries
Scorpius
Pisces
Suns declination -23
deg
Suns declination 0 deg
Sagittarius
Capricorn
Aquarius
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September Sun's declination is 0 degrees. Sun
is directly overhead the Earth's equator. This
is where the ecliptic (Sun's path) crosses the
celestial equator. Sun rises exactly east, sets
exactly west. Sun is above the horizon (day) 12
hours, is below horizon (night) 12 hours,
therefore is "equinox" (equal night). It's Fall,
so we call where the Sun is at this time the
"Autumnal Equinox". Autumnal equinox currently
is in Virgo. Used to be (2000 years ago) in
Libra. Libra scales balance equal day and
night.
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Cancer
Gemini
Suns declination 0 deg
Leo
Suns declination 23 deg
Virgo
Taurus
Libra
Aries
Scorpius
Pisces
Suns declination -23
deg
Suns declination 0 deg
Sagittarius
Capricorn
Aquarius
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December Sun's declination is -23 degrees. Sun
is directly above latitude -23 South. September
through December, Sun's declination is more and
more South then December through March it's less
and less South. In December Sun seems to stop
moving south in sky, and "turns" to the north. We
call this latitude on Earth (23 South) a
"turning" latitude, or "tropic" (Greek for
"turning"). In December Sun is in
Sagittarius, but it used to be (2000 years ago)
at maximum south declination in December in
Capricorn. Latitudes 23 South called "Tropic of
Capricorn". Capricorn invented more than 2000
years ago.
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December Sun's declination is -23 degrees. Sun
rises south of east and sets south of west. Sun
is above horizon (day) less than 12 hours in
Northern hemisphere winter. Day lasts more
than 12 hours in Southern hemisphere summer.
Sun stops moving north in the sky, standing
still, so this is a "solstice". It's winter, so
we call where the Sun is in the sky the "Winter
Solstice". Winter solstice is now in
Sagittarius, but used to be in Capricorn.
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Knowing as we do now that the Earth goes around
the Sun, we can visualize the seasons like this
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Why are the solstices and equinoxes changing
positions in the sky? First noticed (?) by
Hipparchus (190 - 120 BC) in 128 BC. Hipparchus
noticed things like The Sun used to be in front
of certain stars at the beginning of Spring but
now was far from them at the beginning of Spring.
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North Ecliptic Pole
North Celestial Pole
vernal equinox
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Sky is spinning around Earth's poles / Earth is
spinning like a top But the Earth's axis is
wobbling like a top.
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North Ecliptic Pole
North Celestial Pole
vernal equinox
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Earth's north pole traces a circle in the sky
centered on "North Ecliptic Pole"
Celestial Equator
Ecliptic Plane
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Earth's north pole traces a circle in the sky
centered on "North Ecliptic Pole"
Ecliptic Plane
Celestial Equator
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2800 BC
15,000 AD
2000 AD
Entire cycle takes 26,000
years. Equinoxes move or "precess" 1 zodiac
constellation per 2000 years
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Precession of the Equinoxes
4000 BC 2000 BC 1 AD 2000 AD 4000 AD
Vernal Equinox Summer Solstice Autumnal
Equinox Winter Solstice
Gemini Taurus Aries Pisces
Aquarius
Virgo Leo Cancer Gemini
Taurus
SagittariusScorpius Libra Virgo
Leo
Pisces Aquarius CapricornSagittarius Scorpius

These constellations invented 4000 BC?
These constellations invented 1 AD
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Horoscopes Aries Taurus Gemini
Cancer Leo Virgo Libra
Scorpius Sagittarius Capricorn
Aquarius Pisces
Actual Pisces Aries Taurus Gemini Cancer Leo Virgo
Libra Scorpius Sagittarius Capricorn Aquarius
Month Mar / Apr Apr / May May / Jun
Jun / Jul Jul / Aug Aug / Sep Sep / Oct
Oct / Nov Nov / Dec Dec / Jan Jan /
Feb Feb / Mar
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In the Ptolemaic model, the Earth is still, so
the sky must be shifting. An entire religion
(Mithraism) was based on this.
Slaying of the Bull ( Taurus) because the Vernal
Equinox now in Aries
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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. Precession of
the Equinoxes not fully understood except as a
shifting of the "sky-bowl" in Ptolemaic
model. This is the model in place when the Roman
empire fell. The model would last over 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.