Class Announcements Wednesday, September 1

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Class AnnouncementsWednesday, September 1

• Student Pictures J-Z at 1110 am today
• Course goals email Will summarize Friday, please
  email if you havent
• Observing/ Clear Sky patrol
• Started Tuesday night.
• East elevator, 7th floor VAN Door next to
  elevator

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What dates correspond to each figure?
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2
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Cause of seasons
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Azimuth of sunrise changes with season
East
Northeast
Southeast
Dawn
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Stonehenge Ancient astronomical site aligned to
solar azimuth
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Seasons Summary

• Due to the Earths 23.5º tilt on its axis

N. Summer Northern Hemisphere tilted toward
Sun N. Winter Southern Hemisphere tilted toward
Sun

• 4 important dates
• 1. Summer solstice (June 21) sun most northerly
  on ecliptic
• 2. Autumnal equinox (Sep 21) sun crosses
  celestial equator
• 3. Winter solstice (Dec 21) sun most southerly
  on ecliptic
• 4. Vernal (spring) equinox (Mar 21) sun crosses
  c. equator

• Myth The Earth is closer to Sun in summer

Wrong! The suns rays reach (N. hemisphere) of
the Earth more DIRECTLY in (Northern H.) summer,
less DIRECTLY in winter (doesnt have to do with
sun-earth distance)
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PrecessionThe Sun and Moon cause precession, a
slow, conical motion of Earths axis of rotation.
The precession period is 26,000 yrs.
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12,000 years from now, the bright star Vega will
be the new North Star because of precession.
Current position
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Precession and the mystery of the Egyptian
pyramids

• The sides of the great (Middle Kingdom, c.2550
  BCE) pyramids are very accurately aligned to true
  north, but there was no bright star within 2 of
  the North Celestial Pole in 2550BCE because of
  precession. How did the ancient Egyptians do this?

Sides are aligned within 4 arcmin (0.07 deg) of
true north!
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Solution?

• In 2000, Kate Spence (Cambridge Univ.)
  suggested the Egyptians used the bright stars
  Kochab and Mizar in the Big dipper.
• A plumb line was used, and when the 2 stars
  aligned with the plumb line, that was the
  direction of true north.
• This would only work for a few decades near
  2,480 BCE, dating the pyramids very accurately.

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A (Very) Brief History of the Calendar

• The Earth takes 365.24220 days to orbit around
  the Sun once (one year). This period is called a
  tropical year. Note that it is not an even number
  of days!
• 0.24220 fractional days is 5 hours, 48 minutes,
  and 46 seconds a fraction that has caused
  endless headaches for calendar makers who would
  rather the year was exactly 365 days long!
• If all years were 365 days, after 4 years the
  calendar would be in error (not in accord with
  the Suns position) by
• 4 x 5.81hr 23¼ h 1 day.
• In 45 BCE Julius Caesar decreed that years are
  365 days long with one extra day added in
  February, every four years (accurate to one day
  in 128 years). This is the Julian calendar, and
  was used in Europe from 45 BCE to 1582 AD.
• This worked OK for centuries, but it meant that
  by 1580 AD the calendar was off by about 10
  days. In other words, the Sun no longer was at
  the Vernal Equinox on March 21, but rather about
  March 11. This interfered with agricultural
  planting times, religious feast days, etc.
• Aside The synodic period of moon (time from new
  to new moon) is 29.52 days, so 12 lunar months
  are 29.5212 354.24 days. This is one day short
  of a tropical year, so lunar calendars (e.g.
  Islamic) slowly migrate w.r.t solar (i.e. Julian,
  Gregorian) calendars.

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Gregorian Calendar

• In 1582 AD, Pope Gregory XIII introduced the
  currently used Gregorian calendar.
• To fix the Julian calendar, Gregory decreed
• There would be no Mar 10-20, 1582. (skipped 10
  days)
• Do not allow leap years in Centuries unless the
  year is evenly divisible by 400 (good to one day
  in 3300 years).
• This means 1900, 2100 were leap years, but 2000
  was not.
• Although the U.S. does not have a legal
  calendar, it unofficially has adopted the
  Gregorian calendar, based on Act of Parliament of
  the United Kingdom in 1751, which specified use
  of the Gregorian calendar in England and its
  colonies.

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Other calendars currently in use

• Hebrew calendar (official calendar of Israel)
  12 or 13 months, each month 29 or 30 days, era
  mundi starts at 3760 BCE (i.e. this is year
  5,763). A year is 50 weeks plus 3, 4, or 5 or
  days leap year has 54 weeks.
• Islamic calendar (first described in Koran)
  Strictly lunar. Months start at first sighting of
  lunar crescent. Calendar starts from Era of the
  Hijra, commemorating the migration of the Prophet
  and his followers from Mecca to Medina in 622 AD
  1 A.H. (Anno Higerae). There are 11 leap years
  in 30 year cycle. Ramadan (month 9) is month of
  fasting, starts at lunar crescent sighting. Since
  this is a lunar calendar, the (Gregorian) dates
  of Ramadan vary.
• Chinese calendar. 12 months(29 or 30 days),
  cycles of 60 years with 12-yr periods for Earthly
  cycles (year of dragon, snake, ox, etc).
  Occasional a 13th intercalary month is added.
  No specific year 0, but the calendar is at least
  2,500 yrs old. Chinese government and businesses
  use Gregorian calendar.

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Some interesting calendar factoids

• What date is Easter? Why does it change every
  year?
• Part of Pope Gregory XIIIs calendar reform
  stated Easter Day is the first Sunday after the
  first full moon that occurs after the vernal
  equinox.
• For Example next spring (2005), the first full
  Moon after March 21 is Friday March 25, so Easter
  2005 is Sunday, March 27, 2005.
• What are leap-seconds? When and why are they
  used?
• The Earth does not rotate exactly with a fixed
  period (recall sidereal period is 23h 56m 4s
  appx).
• It is slowing, largely because of tides.
• The length of the mean solar day has increased by
  roughly 2 milliseconds since it was exactly
  86,400 seconds of atomic time about 184 years ago
  (i.e. the 184 year difference between 2004 and
  1820).  
• That is, the length of the mean solar day is at
  present about 86,400.002 seconds instead of
  exactly 86,400 seconds. (The second is defined by
  an atomic clock).
• They are inserted as needed, on Jan 1 and/or July
  1). There have been 25 leap seconds inserted
  since 1972.

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Review Quiz

• The Sun is viewed at noon at the zenith on June
  21. What is the observers latitude?
• 0 (equator)
• -23.5
• 23.5
• 90
• The star Sirius rises tonight at 930pm. One week
  from tonight, Sirius will rise at
• 930pm
• 902pm
• 926pm
• 958pm
• Suppose the Earths rotation axis were
  perpendicular (90) to the ecliptic plane. How
  would this change affect the seasons?
• No effect (seasons are caused by changing
  Earth-Sun distance)
• The length of the seasons would double in
  duration
• The length of the seasons would be noticeably
  shorter
• There would be no seasons

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• At the summer solstice, an observer at the North
  pole sees the Sun at midnight at what altitude?
• Below the horizon
• On the horizon
• Above the horizon at 23.5 altitude
• At the zenith
• When the Sun is on the celestial equator, what
  day is it?
• June 21
• Mar 21
• Sep 21
• Could be either Mar 21 or Sep 21
• The constellations of the zodiac are all located
  on
• The celestial equator
• The ecliptic
• The central meridian
• The vernal equinox

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• Approximately how many stars can be seen in a
  dark location using only the naked eye?
• 3,000
• 300
• 30,000
• At least 100,000
• Why couldnt the ancient Egyptians have used the
  North star (Polaris) to align the pyramids along
  the north-south direction?
• The north star is not visible from Egypt at that
  time.
• The north star sets at night in Africa and cannot
  be seen
• The Egyptians religion worshiped the Sun, so
  stars could not be used.
• The direction of north was not same direction as
  Polaris because of precession of the Earths
  axis.
• Why are leap years needed in our calendar?
• Because the sidereal day and solar day are
  slightly different
• Because the Earths orbital period around the Sun
  isnt exactly 365 days
• Because the Earths axis is tilted 23.5 to the
  ecliptic plane.
• Because the Earths orbit is elliptical, not
  circular.

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• How long does the Earth take to rotate once on
  its own axis?
• 23h 56m 3s
• 24h 0m 0s
• 24h 3m 56s
• Varies throughout the year, longest in winter.

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• Mesopotamian Astronomy
• Data long-term written records from as early as
  4,000 BC
• Application predictions of planetary motions
  based on patterns by 500 BC also found 18.6 year
  lunar eclipse cycle (Saros cycle).
• Context relatively stable, large scale,
  river-based society. (Egyptian record is similar)
  

Ziggurat of Ur-Nammu Astronomical Observatory?
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Ancient Greek Astronomers
Aristarchus (310 230 BCE)
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• Ancient Greek Astronomy
• (a very brief summary!)
• Aristotle (c. 340BCE)
• Idealist (ideas more important than observation).
  Celestial shapes and orbits must be perfect
  circles
• Argued for geocentric Unverse (stationary Earth)
  based on lack of observed annual parallax of
  stars
• Aristarchus (c. 240BCE)
• Determined Earth-Moon distance, Earth-Sun
  distance using trigonometry
• Proposed heliocentric (Sun centered) Model
• Correctly surmised that lack of stellar parallax
  was because stars were extremely far away (cf.
  Aristotle)
• Erastosthenes (c. 200 BCE)
• Determined size of Earth from shadows at Syene,
  Alexandria at Summer solstice
• Ptolemy (c. 140 AD)
• Comprehensive star catalog
• Developed geocentric model based on epicycles to
  explain retrograde motion of planets

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• Aristotle (384-322 BC)
• Introduced a physical theory of dynamics.
  Considered math and logic more important than
  observation.
• Theory (essences associated with intrinsic
  motions
• 3 Motions up, down, around
• 5 Essences earth, water, air, fire, and ether
• Other details circular motion is eternal
  celestial objects are spherical, perfect,
  unchanging
• Evaluation comprehensive, elegant

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Aristotles Arguments for a stationary, spherical
Earth Expected from theory Shape of Earth's
shadow in lunar eclipse Latitude dependence of
stellar motion Arguments against motion There
would be an enormous wind (since the atmosphere
is not attached) One should see stellar
parallax (but does not) Implications one could
in principle sail west in order to go east
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An Objection to the Revolution of the
Earth Aristotle mis-judged stellar distances,
which are much larger than Earth-Sun distance!
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• Status following Aristotle
• We have a theory, within which to frame
  questions.
• The planetary question What compound of circular
  motions accounts for retrograde behavior?
• The problem of comets not spheres, not circular
  motion maybe meteorological?
• General issue raised How does one decide which
  data are important, which ignorable?
• Quantitative followup
• Aristarchus (310-230 BC) Applied geometry to get
  relative sizes. Determined linear size of moon
  from comparison with Earth's shadow
• Small angle equation q (") 206,265 d/D

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Aristarchus Relative size of Earth and Moon

• During total Lunar eclipses, the Moon is
  completely immersed in the Earths shadow.
• Total lunar eclipse takes 3 ½ hours, so Moon has
  moved appx. 1 Earth diameter in 3 ½ hrs
• Moons orbital period is 27.3 days 655 hr
• Hence the circumference of the Moons orbit must
  be
• So the radius of the Moons orbit is

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Eratostheness Method for Finding the
Circumference of the Earth
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Retrograde Motion of planets

• All planets generally move eastward with repsect
  to the background of stars. This is called
  prograde motion
• Near opposition or inferior conjunction, planets
  reverse direction and move westward wr.t. stars
  this is retrograde motion
• Ancient astronomers (since Ptolemy, 150 AD)
  explained retrograde motion as caused by
  epicycles in a geocentric (Earth-centered) model
  of the solar system
• Since Copernicus (1580 CE) and Kepler (c. 1600
  CE), retrograde motion can be explained in
  heliocentric (Sun-centered) model as due to
  varying orbital speeds of planets in nearly
  circular orbits

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Planetary orbits and retrograde motion

• All planets display retrograde motion, including
  inferior planets
• Retorgrade motion typically lasts a few months
• For inferior planets (Mercury, Venus),
  retrograde motion occurs near inferior
  conjunction
• For superior planets (Mars, Jupiter, Saturn,
  Neptune, Uranus) retrograde motion occurs near
  opposition
• Web site animation of Mars retrograde motion

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Claudius Ptolemy (127-151 AD)

• Worked at library in Alexandria, wrote "Almagest"
  
• Model of planetary motion epicycle carried by a
  deferent. This explains retrograde motion,
  brightness variation.
• Elaboration Earth and motion centers offset
  (equant). This explains the variable angular
  velocity.

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Ptolemys Model of Motion of a Planet (explains
retrograde motion)
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The Complete Geocentric Model of Ptolemy
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Ptolemaic Geocentric Model

• Successes
• First model with predictive power
• In use for 1500 years!
• Shortcomings
• relative sizes of planet orbits arbitrary
• due to the equant, the model was not quite
  geocentric
• likewise it was not quite uniform circular motion
  
• extensions of the model for motion perpendicular
  to the ecliptic was independent of the model for
  motion along the ecliptic.
• The model contains unexplained coincidences

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Claudius Ptolemy (c. 85-165 AD)

• Greatest ancient astronomer
• Worked in Alexandria at the great library
• Ptolemy published the Almagest, an encyclopedia
  in which he used centuries of Babylonian
  observations of the motions of the planets to
  justify a geocentric (Earth centered) model of
  the universe.
• The ideas of the Ptolemaic system ruled the
  world of astronomy for 1,500 years, until
  Copernicus and Galileo (c. 1600)

9th cent. Greek MSS of the Almagest (Vatican
Library)
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Ptolemy devised the longest used geocentric model
to explain retrograde loops by putting planets on
epicycles and deferents.
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Epicycles explain retrograde motion in geocentric
models
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Footnote The great library at Alexandria, Egypt

• Greatest library in ancient world, containing at
  least 400,000 books
• Aristarchus was librarian c. 150 BCE
• Note Lighthouse at Alexandria harbor was one of
  the 7 wonders of ancient world
• Original collection from Aristotles personal
  collection (c.350 BCE)
• All visitors to Alexandria were required to
  surrender their books for copying (by Royal
  decree)
• Destruction of the library
• Possibly (partly?) destroyed by the army of
  Julius Caesar (47 BCE) who burned the harbor
  during invasion of Egypt
• But there is evidence that library still existed
  in 56 CE (e.g. inscription at right)
• In 391 CE Roman Emporor Theodosuis ordered
  descruction of all pagan temples. This likely
  included the library
• Modern library completed 2002 AD

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Nicolaus Copernicus (c. 1580) devised the first
comprehensive heliocentric (Sun-centered) model

• Copernicus imagined a universe where the Sun was
  at the center instead of Earth.
• He suggested that Earths motion around the Sun
  provided a more natural explanation for
  retrograde loops as Earth passed the other
  planets.

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Heliocentric planetary position terminology is
stated relative to Earth
Opposition Inferior conjunction Superior
conjunction Greatest eastern elongation (appears
east of the Sun in the sky) Greatest western
elongation (appears west of the Sun in the sky)
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In this heliocentric model, the planets just
appear to move backwards as the faster moving
Earth laps the more distant planet once each
year when it is at opposition.