General Astronomy Friday Aug 25 Announcements

1
General AstronomyFriday Aug 25Announcements

• MathCAD
• Tutorial Friday 4pm - 5pm, Room 666.
• Student quantity purchase 61 if 25 students
  agree to purchase
• PRS
• Will start using next week
• Optional, but strongly recommended
• Used PRS units available (typically 20-25) at
• http//groups.yahoo.com/group/prs_exchange/

2
Todays lecture Outline

• Angular Measurements, Powers of ten
• Astronomical Distances
• Night sky
• Constellations
• Ursa Major (Big Dipper)
• Definitions zodiac, ecliptic, Celestial sphere
• Suns motion in sky
• Cause of seasons
• Precession of Earths axis
• Historical evidence alignment of Pyramids
• Calendars (Julian, Gregorian)

3
Astronomers use angles to denote the positions
and apparent sizes of objects in the sky.
4
Angular Measure

• Basic unit of angular measure is the degree º
• Full circle measures 360º
• Right angle measures 90º
• Angular distance is the number of degrees across
  the sky between two points.
• Angular diameter or angular size is the number of
  degrees from one side of an object to the other
  side.
• The angular size of the Moon is 0.5º (1/2º )
• The angular size of the Sun is also 0.5º (1/2º )

5
Big Dipper (Ursa Major)
6
(No Transcript)
7
Try this What is the angular size of this sphere
in degrees as you see it? (Answers will vary from
front to back of room)
8
Angular Measure for Small Angles

• 1º 60 arcminutes 60'
• 1' 60 arcseconds 60''
• So 1º 60x60 3,600 arcseconds 3,600''

Test question What is the angular size of the
Moon ( 0.5) expressed in arcseconds? Answer
1,800''
9
(No Transcript)
10
Example On November 28, 2000, the planet Jupiter
was 609 million kilometers from Earth and had an
angular diameter of 48.6''. Using the
small-angle formula, determine Jupiters diameter
in kilometers (km).
Convert from arcsec to radians 1 radian 57.296
x 60 x 60 206,265 arcsec

• D 48.6'' x 609,000,000 km / 206265 143,000 km

11
Powers-of-ten notation is a useful shorthand
system of writing very large numbers.
100 1 101 10 102 100 103 1,000 104
10,000 106 1,000,000 109 1,000,000,000
One Ten (deca-) Hundred (centa-) Thousand
(kilo-) Ten thousand Million (mega-) Billion
(giga-)
12
Powers-of-ten notation is a useful shorthand
system of writing very small numbers.
100 1 10-1 0.10 10-2 0.01 10-3 0.001 10-4
0.0001 10-6 0.000001 10-9 0.000000001
One One-tenth (deci-) One-hundredth
(centi-) One-thousandth (milli-) One-ten-thousandt
h One-millionth (micro-) One-billionth (nano-)
13
Test your knowledge

• 10-6 109 ?
• 100
• 0.01
• 1,000
• 0.001
• 10

• 2106 /4109 ?
• 510-4
• 8104
• 210-3
• 4103
• 5104

14
(No Transcript)
15
Astronomical distances are often measured in
astronomical units, parsecs, or light years.
Astronomical Unit (AU) One AU is the average
distance between Earth and the Sun (1.496 X 108
km or 92.96 million miles). Light Year (l.y.)
One l.y. is the distance light can travel in one
year at a speed of about 3 x 105 km/s or 186,000
miles/s (9.46 X 1012 km or 63,240 AU). Parsec
(pc) One pc is the distance from which Earth
would appear to be one arcsecond from the Sun.
(3.24 l.y., or 3.1 x 1013 km).
16
Subjects for today

• Observing focus Big Dipper
• Constellations
• Zodiac (12 constellation on the ecliptic)
• Position of Sun throughout the year
• Cause of the seasons
• Harvard commencement video
• Precession slow motion of celestial poles in sky
• Calendars Julian , Gregorian, leap years

17
Observing Focus Ursa Major (Big Bear, Big
Dipper)
18
Finding stars Polaris, Arcturus, Spica using big
dipper
Take arc to Arcturus
Then spike Spica
Pole Star (Polaris)
19
Ursa Major 9pm tonight looking NW
Polaris
20
Eighty-eight constellations cover the entire sky.
21
Eighty-eight constellations cover the entire sky.
22
Constellations

• About 6,000 stars are visible to unaided eye
  (about half above the horizon 3,000).
• 88 semi-rectangular groups of stars called
  constellations entire sky is covered
• Hence, all stars are members of a constellation
• Some stars in the constellations are (relatively)
  close while others are very far away.
• Hence, There is no physical connection between
  stars in a given constellation

23
Constellation names are derived from the myths
and legends of antiquity.
Sword of Orion
24
Winter constellations
25
As Earth orbits our Sun, different constellations
are visible at different times of the year.
The circumpolar constellations are always the
same because they are visible no matter where
Earth is in its orbit.
26
Note that the constellations at sunset
change about 1 constellation/month (i.e. 12
forms) e.g. Virgo, Libra, Scorpius, etc gt
ZODIAC
27
The Zodiac
28
The Zodiac is the set of constellations through
which the Sun appears to pass during one year
(because of the Earths motion around the Sun,
though!)
29
Ecliptic the path of the Sun (and planets) in
the sky complicated by the fact that Earth is
tilted on its own axis by 23.5 degrees
Note Constellations of the zodiac lie on the
path of the ecliptic, since they are behind the
Suns path.
30
Observer at North PoleWhere is Suns position on
Summer Solstice (June 21) ?
North Pole Sun is 23.5? above the horizon all
day on June 21
31
Observer at Equator (e.g Quito) Where is Sun on
March 21 (Vernal equinox)?
Zenith at noon
Mach 21
Observer at equator on March 21 (or Sept 21) Sun
rises in E, at zenith at noon, sets in W)
32
Ecliptic, Celestial Planes and the Path of the
Sun
33
Path of Sun from March 21 to Sept 21
June 21
March 21
Sept 21
Sun today
34
As the Earth moves in its orbit, The path of the
Sun (and planets) changes because of the tilt of
the rotation axis Note Since rotation axis is
fixed with respect to the stars, star paths do
NOT change!
35
Northern Hemisphere Winter
Northern Hemisphere Summer
36
What dates correspond to each figure?
4
1
3
2
37
Cause of seasons
38
(No Transcript)
39
Azimuth of sunrise changes with season
East
Northeast
Southeast
Dawn
40
Stonehenge Ancient astronomical site aligned to
solar azimuth
41
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)
42
PrecessionThe Sun and Moon cause precession, a
slow, conical motion of Earths axis of rotation.
The precession period is 26,000 yrs.
43
12,000 years from now, the bright star Vega will
be the new North Star because of precession.
Current position
44
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!
45
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.

46
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.

47
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.

48
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.

49
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.