Announcements

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• Announcements
• Wednesday Aug 30

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Analemma Solar Position at Noon throughout year
Sun does not transit prime meridian at 1200 noon!
Expected position at along prime meridian at noon
(mean Sun)
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Why the Analemma? Because the Earth orbit around
the Sun is not perfectly circular Equation of
Time

• This effect is caused by
• Obliquity ( tilt of Earths axis)
• Ellipticity of Earths orbit (Earth moves more
  slowly when farther away from Sun)

Maximum difference from uniform motion (Sun
transits at noon daily) is 16 min
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Check your knowledge--
An observer at the equator (Quito) sees a star
at the zenith at midnight on June 21. Which of
the following is true?
(a) The next night, the same star is north of the
zenith.
(b) The star sets in the west near dawn.
(c) Exactly 24 hours later, the star is east of
the zenith.
(d) The star is on the celestial equator.
(e) At this time, the star is on the horizon as
viewed from the South Pole
(f) On Sept 21 at midnight, the same star is on
the eastern horizon.
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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.