THE SKY: Chapters 2 S1

1
THE SKY Chapters 2 S1

• What are the most obvious things and motions one
  sees in the sky?
• What did ancient peoples know about the sky?
• How did they learn about it? (Ch 3 too)
• What misconceptions did they have?
• What misconceptions do YOU have?

2
Your Local Sky

• You see a hemisphere of sky above the horizon
• Zenith is the point directly upwards
• Meridian runs from N to S through Zenith
• Use altitude above horizon and direction (from
  North) as coordinates

3
IDEA QUIZ (not graded)

• 0.25 x (5.0 x 103)

• 1.25
• 2.5x102
• 1250
• 1.3x103
• 1.3x104

Write down the BEST answer (letter) on a piece
of paper. WRITE BIG SO I CAN SEE IT.
4
IDEA QUIZ (answer)

• 0.25 x (5.0 x 103) (2.5x10-1)x(5.0x103)
• 12.5x10-13 12.5x102

• 1.25
• 2.5x102
• 1250 -- this is the same number
• 1.3x103 -- but this is BEST --2 sig. fig.
• 1.3x104

5
The Celestial Sphere

• Extends Earths Equator Poles into Space

6
Bright Stars on the Celestial Sphere
All stars are officially gathered into 88
constellations Only the brightest have names
7
The Night Sky

• DAILY variations due to Earths ROTATION on
  its axis (from West to East).
• Leads to APPARENT MOTIONS of everything else!
• Sun rises (toward E) and sets (toward W)
• Moon rises (toward E) and sets (toward W)
• STARS COME IN CLASSES
• Equatorial Zone stars also rise and set
• Circumpolar Stars move COUNTERCLOCKWISE in
  circles around the NORTH CELESTIAL POLE
• (In the S. Hemisphere they go CLOCKWISE around
  the South Celestial Pole)

8
Effects Due to Earths Rotation

• Earth rotates from West to East, so stars (and
  everything else in the sky) appear to move from E
  to W
• Some stars are always visible at night from your
  position and others rise and set yet others are
  invisible.

9
Apparent Nightly Stellar Motions
10
Positions of Astronomical Objects

• The relative positions of the stars are
  (very nearly) fixed with respect to (w.r.t.) each
  other.
• The Sun, Moon and Planets positions vary w.r.t.
  the fixed stars.
• We measure positions on the sky using projections
  of the Earths features onto the sky.
• Groups of stars that APPEAR nearby on the sky are
  called CONSTELLATIONS. (but they may be at very
  different distances -- sky is 2D, universe is 3D)
• Sun (and planets) appear to move through a group
  of constellations we call the ZODIAC.

11
The Zodiac
12
Planets vs. Stars

• Planets are WANDERERS
• Easily seen Venus, Jupiter, Mars, Saturn
  (Mercury)
• Later discovered Uranus, Neptune (Pluto)
• They stay NEAR the ecliptic plane (Suns path)
  but are NOT in step w/ stars faster, slower,
  sometimes even backwards (retrograde loops)
• Planets (usually) dont TWINKLE like stars do.
• Stars are so far away that they appear like
  points atmospheric fluctuations (seeing) makes
  their location jump around -- our eyes fovea
  loses them
• Planets are actually smaller, but MUCH closer, so
  they appear like little disks
  their image is never
  completely lost in your eye.

13
Locating Things in the Sky

• Constellations are convenient groups of stars in
  particular parts of the sky provide rough
  locations on the CELESTIAL SPHERE .
• BUT they are NOT PHYSICALLY ASSOCIATED GROUPS OF
  STARS --- some in the same constellation are
  much farther away than others.
• Brightest stars in each constellation names from
  the Greek alphabet alpha (?) Orionis
  (Betelgeuse), beta (?) Orionis (Rigel), etc.
• Other very bright stars have their own names
  e.g., Sirius (? Canis Majoris) Vega (?
  Lyrae) Altair (? Aquilae), etc.
• There are now 88 constellations officially
  recognized by the International Astronomical Union

14
Orion Constellation in 3-D
15
Latitude Longitude on Earth
16
Celestial Coordinates Latitutde Longitude
taken to the Sky

• BUT ALL STARS (AND GALAXIES) ARE
• LOCATED IN CELESTIAL COORDINATES.
• Equivalent to LATITUDE is DECLINATION (?)
  degrees (?), minutes (') and seconds(") (of
  arc)
• from 90 deg (NCP) to -90 deg (SCP).
• 1 circle 360 deg(?)
• 1 deg 60 arcmin
• 1 arcmin 60 arcsec, so
• 1 arcsec 1/3600 th of a degree or 1/1,296,000
  th of a circle.
• Sirius has a declination of -16?, 41', 58"

17
Angular Measure
18
Crude Angular Measures You Can Use
Moons angular diameter 0.5o 30 1800
arcsec
19

• Equivalent to LONGITUDE is RIGHT ASCENSION
  (R.A. or ?) Zero spring equinox (where Sun on
  Ecliptic crosses Celestial Equator)
• measured in units of time hours, minutes and
  seconds, from 0 hours to 23 h, 59 m, 59.999 s.

• One hour of RA 15 deg of angle (360 degrees/24
  hr/day)
• Sirius right ascension of 6 h, 45 m, 09 s.
• Vega has dec38O44 and RA18h35.2m

20
Circumpolar Equatorial Stars

• At the POLES, ALL stars are polar N (or S) CP is
  at the ZENITH (directly overhead)
• Other visible stars circle the CPs.
• The same stars are seen all the time that the
  sun is below the horizon (i.e. half the year) and
  the other half are NEVER seen.

21

• At the equator, ALL stars are equatorial.
• They rise and set each night.
• Polaris is always at the northern horizon.
• Half of the stars with DEC 0 will pass
  through the zenith during the course of a night.
  
• Stars with higher RA will rise and set later in
  a particular night.
• Stars just rising at sunset (so visible all
  night long) now will be just setting at sunset
  in six months (thus below the horizon all night
  long).

22

• At positive latitiude L (example is 40 N),
  
• stars within L deg of the NCP will be
  circumpolar and these stars have Declinations, ?
  gt (90-L) deg.
• At latitude L, stars with Declinations, ?,
  satisfying
• (90-L) gt ?gt (L-90) are equatorial,
• Stars with ? lt (L-90) are "south-polar never
  seen.

23
Sky Looks Different from Different Latitudes
Exploring the Celestial Sphere
24
Seasonal/Annual Variations

• Seasons Earths REVOLUTION around the sun
• Sun rises due E and sets due W on the VERNAL
  (Mar 21) and AUTUMNAL EQUINOXES (Sept 22)
• Sun rises most N of E and sets most N of W on the
  Summer Solstice (June 21)
• Sun rises most S of E and sets most S of W
  Winter Solstice (Dec 21)
• Earth is closest to Sun in January -- it is the
  tilt of Earths axis from perpendicular to
  orbital plane, not distance from Sun, that
  determines seasons.
• The SAME CIRCUMPOLAR stars are seen year-round,
  BUT different groups of EQUATORIAL zone stars
  rise and set at different times of year.

25
Tilt of Earths Axis ? Seasonal Variations

• Reason for Seasons

26
Annual Solar Path Changes

• Local noon is when Sun crosses meridian.
• Height varies throughout the year (analemma), but
  never directly above (at zenith) unless latitude
  between -23.5 and 23.5 degrees (Tropics of
  Capricorn Cancer)
• Sun rises and sets due E and W only on equinoxes

27
The Night Sky More Motions

• Many ancient peoples understood most of what
  weve discussed so far though they thought the
  sky, not earth moved.
• Egyptians
• Polynesians
• Chinese
• Indians
• Amerindians
• Mayans
• Greeks

28
Slow Sky Change PRECESSION

• PRECESSION caused by gravitational torques by
  Sun, Moon ( planets) on the Earth's
  non-spherical shape.
• Angle between the Earth's axis and the
  perpendicular to the ecliptic stays around 23.5?,
  but direction changes.
• The total period of precession is about 26,000
  years.
• POLARIS is the POLE STAR NOW (very close to NCP),
  but 5000 years ago it was THUBAN, and
  12,000 years in the future it will be VEGA.
• There is no Southern Pole star right now.
• Precession implies a star's RA and DEC change
  about 20 arcmin per year.
• There is also nodding'' or NUTATION the Moon
  changes the Earth's tilt angle by less than 20"
  over an 18.6 year period.

29
Precession of Non-Spherical Bodies
Friction slows the tops spin energy and angular
momentum and eventually it falls over. Earths
spin slowed by tides.
30
Lunar Motions

• The MOON shows different PHASES depending on
  its location in orbit around the earth.
• NEW (basically between Earth and Sun), then
• WAXING CRESCENT,
• FIRST QUARTER,
• WAXING GIBBOUS
• FULL (basically on other side of Earth from
  Sun), then
• WANING GIBBOUS,
• THIRD QUARTER,
• WANING CRESCENT
• Lunar Phases in Motion

31
Lunar Phases and Approximate Time
32
The Dark Side of the Moon (sic)

• We (basically) see only one face of the Moon.
• This is because of SYNCHRONICITY between its
  ROTATIONAL and ORBITAL PERIODS.
• If the moon rotated faster (or slower) we could
  see all of it over the course of several months.
• (Earth slowly forced the Moon into this and Moon
  is trying to do the same to Earth).
• One can tell the approximate time from the phase
  of the moon and its location in the sky.
• A full moon rises around 6PM in the east, is
  highest at midnight and sets around 6AM in the
  west.
• So a full moon seen about 45 deg above the
  western horizon indicates a time of roughly 3
  AM.
• But a first quarter moon, seen 45 deg above the
  western horizon indicates a time of roughly 9
  PM.

33
Sidereal (27.32d) vs Synodic (29.53d) Month
The sidereal period is the one seen from someone
out in space who isnt moving the synodic period
is as seen from the moving earth.
34
Calendars Lunar vs Solar

• LUNAR CALENDARS
  (e.g., Hindu, Muslim) are easier to
  keep track of, but can't stay in phase with SOLAR
  CALENDARS, since
• 365.25 d/yr / 29.53 d/mo 12.37 lunar months per
  year
• Therefore, either months are forced to have 30
  days instead (and new moon shifts from first of
  month, and even then still have 5 extra days --
  often a big holiday)
  or else
  months must have unequal numbers of days -- as
  in the Julian and our Gregorian calendar.
• Jewish calendar is Metonic, adding a 13th month
  in 7 of 19 years (since 19x12228 but almost
  exactly 235 synodic months 19 years) (Explains
  Easter too.)
• Chinese calendar adds 13th month to 22 out of 60
  years

35
Years and Other Years and Leap Years

• LEAP DAYS account for difference between
• 365.2422 days per TROPICAL YEAR (equinox to
  equinox)
• and 365.0000 days (noon to noon).
• The SIDEREAL YEAR is 365.2564 days
• Julian year has 365.25000 (not quite good enough
  for astronomers but good enough for this class).
• WHEN DO WE HAVE LEAP YEARS?
  Since Pope Gregorys time the system has been
• Add one day to February if the year is divisible
  by 4 (1992, 1996, 2004, 2008, 2112,
  2116)
• EXCEPT in every year divisible by 100 (NOT 1900,
  2100)
• BUT include every year divisible by 400 (2000,
  2400)

36
Reminders

• Your next graded Mastering Astronomy assignments
  are due
• 1/31 at 1159 PM on Chapter 2 (Night Sky)
• 2/7 at 1159 PM on Chapter 3 (Astronomical
  History)
• You should do the Introduction to Mastering
  Astronomy assignment prior to doing those
  assignments.
• In the future I will probably not remind you of
  due dates in class as they will be posted on MA
  and usually on the course web-site
  www.chara.gsu.edu/wiita/a1010s10.html CHECK
  THESE FREQUENTLY!

37
Eclipses

• An ECLIPSE occurs when one astronomical object
  casts a shadow on another.
• LUNAR ECLIPSES
• Moon moves into the shadow the Earth casts
• Only occurs at FULL MOON but NOT each month.
• Lunar orbit around Earth is inclined by about
  5.2 degrees from Earth's orbit around Sun
  (ECLIPTIC).
• Therefore only 2 times per year are the
  alignments to be close enough for lunar eclipses
  to occur.

38
Eclipse Geometry
39
Lunar Eclipse
40
Lunar Eclipses

• FAVORABLE FOR ECLIPSE WHEN LINE OF NODES
  (intersection of those two planes) POINTS AT
  THE SUN
• PARTIAL eclipses occur more often than TOTAL
  LUNAR ECLIPSES roughly only every 18 months.
• Total lunar eclipses last no more than about
  100 minutes.
• During total lunar eclipses, moon often looks
  red.
• --- due to the small amount of red light
  refracted through the earth's atmosphere.
• Eclipse Seasons and Alignments

41
Solar Eclipses

• Moon casts a shadow on the Earth.
• Can only occur at NEW MOON but NOT each month
  (same reason as lunar).
• Partial shadow PENUMBRA.
  Complete shadow UMBRA.
• PARTIAL ECLIPSE Moon only covers up part of
  Sun (imperfect alignment)
• ANNULAR ECLIPSE Perfect alignment, but Moon
  too small to cover entire Sun (near apogee).
• TOTAL ECLIPSE Perfect alignment and Moon big
  enough to cover entire Sun (near perigee).
• Evolution of a Partial Solar Eclipse

42
Solar Eclipse Geometry
43

• As Earth rotates, shadow races for 1,000s of km
  across surface (at 1700 km/h), but totality
  rarely more than 100 km wide and lasts lt 7.5
  minutes.
• Astronomers study the CORONA --- the outermost
  layer of Sun's atmosphere --- during a total
  Solar eclipse.

44
Solar Eclipse Paths

• Paths of totality between 2006 and 2030 much
  wider areas see partial solar eclipses

45
First Pop Quiz

• Print your name neatly (1 pt)
• Print my name neatly (2 pts)
• Lunar eclipses can only occur at what lunar
  phase? (4 pts)
• If you are at latitude 80o N, a star with
  declination, ?20o will be a (circumpolar,
  equatorial zone, never seen) star for you. (4
  pts)
• All quizzes will be returned with the next exam.
• If you are not sure of your grade need it
  sooner they should be available at the end of the
  next class.

46
Distances and Sizes

• Angular diameter Diameter/distance
• ? D/d
• Theta (angular diameter) is measured in RADIANS,
  with 2? radians 360 degrees or 1 rad 57.296?
  
• Example We know the distance to the Sun and the
  Diameter of the Sun.
• What is the angular size of the Sun?
• ?? 2 R? / 1 AU 1.392 x 106 km / 1.496 x 108
  km
• 9.305 x 10-3 rad 0.5331 deg 31.99 arcmin
• QUESTION If the distance to the Moon is about
  400,000 km, what is its diameter?
  

47
Sizes and Distances

• Total solar eclipse ? ?Moon ? ??
• Therefore, DMoon ?Moon x dMoon
• 9.3x10-3 x 4.0x105 km
  3.7x103km
• Or Rmoon 1.9x103 km
• Correct is 1738 km
• Whats wrong?
• More exactly, R d tan(?/2) but for small angles
  (in rad), tan(?) ? ?3/3 2?5/15 , so
• tan(?) ??

48
Distances from Parallax

• Key tool in measuring distances to nearby stars.
• Apparent shift in position due to Earths orbit
  around the Sun.
• One PARSEC (PARallax SECond) distance at which
  a star would subtend a 1 arcsec angle from a 1 AU
  baseline.
• As there are 206,265/rad, 1 pc 206,265 AU
• 1 pc 3.26 ly 3.085678 x 1016m
• Always a SMALL angle, so
• d (pc) 1/p(arcsec),
• so if p 0.1, d 10 pc, or if d 50 pc, then
  p 0.02

49
Parallax Illustrated
50
Parallax, concluded

• One can also measure distances to planets,
  comets, asteroids etc. in the solar system
• Use two telescopes widely separated on earth to
  see shifts in apparent position w.r.t. distant
  stars.
• The simplest example comes from looking through
  your left and right eyes alternately -- the
  finger held at arms' length "moves" less than one
  held out at half that distance.

51
Different Days and Star Risings

• Time it takes the earth to spin once on its axis
  SIDEREAL DAY -- stars appear in the exact same
  location.
• 23 hours, 56 minutes and 4 seconds long.
• SOLAR DAY is the (average) time between local
  noons (when a shadow of a vertical stick is
  shortest).
• 24 hours, 0 minutes and 0 seconds long.
• Difference earth has moved 0.986 degrees around
  the Sun in its orbit. Therefore, for the sun to
  be overhead again the earth must spin another 3
  minutes and 56 seconds.
• This implies stars RISE about 4 MINUTES EARLIER
  EACH NIGHT as measured by our clocks and watches,
  which are set to solar time in a PARTICULAR TIME
  ZONE

52
(No Transcript)
53
Local Time vs Time Zones

• SINCE THE MID-19th CENTURY CLOCKS ARE NOT SET TO
  LOCAL TIME, which depends on one's exact
  LONGITUDE. I.e. local noon-- when the sun
  is highest in the sky.
• Railroad timetables demanded uniform times
  throughout a large area
• Local noon is earlier in Boston (long71o2 W)
  than in Atlanta (long 84o26 W) according to a
  clock set to the Eastern Standard time (and
  closest to 12 EST in Philadelphia, which is very
  near the center of the time zone at long75o W )

54
Idea Test

• Astronomer N lives at the North Pole and
  Astronomer E lives on the Equator.
• 1) During a 12 hour dark period in January, N
  sees _____ different stars than E.
• 2) During the entire year, N sees ____ different
  stars than E.
• A) substantially fewer
• B) about the same number of
• C) substantially more
• D) there is no way of telling without information
  about Es longitude

55
Idea Test Answers

• Astronomer N lives at the North Pole and
  Astronomer E lives on the Equator.
• 1) During a 12 hour dark period in January, N
  sees _____ different stars than E.
• 2) During the entire year, N sees ____ different
  stars than E.
• In both cases E sees (nearly) all stars but N
  sees almost exactly 1/2 of all stars, so
• A) substantially fewer FOR BOTH 1) and 2)
• B) about the same number of
• C) substantially more
• D) there is no way of telling without information
  about Es longitude