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) = 12.5x10-1+3 =12.5x10+2 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 Earth’s 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 Earth’s 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 Earth’s 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 Earth’s 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 (Sun’s path) but are NOT in step w/ stars: faster, slower, sometimes even backwards (retrograde loops) • Planets (usually) don’t TWINKLE like stars do. • Stars are so far away that they appear like points: atmospheric fluctuations (“seeing”) makes their location jump around -- our eye’s 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 Moon’s 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 dec=+38O44’ and RA=18h35.2m

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,  > (90-L) deg. • At latitude L, stars with Declinations, , satisfying: • (90-L) > > (L-90) are equatorial, • Stars with  < (L-90) are "south-polar”: never seen.

23. Sky Looks Different from Different Latitudes Exploring the Celestial Sphere

24. Seasonal/Annual Variations • Seasons: Earth’s 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 Earth’s 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 Earth’s 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 we’ve 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 top’s spin energy and angular momentum and eventually it falls over. Earth’s 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 isn’t 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 19x12=228 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 Gregory’s 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 11:59 PM on Chapter 2 (Night Sky) • 2/7 at 11:59 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 < 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 • What’s 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 Earth’s 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.