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SOAR: the Sky in Motion Y SOAR: The Sky in Motion Life on the Tilted Teacup Ride The Day in all its Glory: The Analemma Aileen A. O’Donoghue Priest Associate Professor of Physics Kiva December 1997 – October 27, 2009 Celestial Coordinates Right Ascension NCP à RA or α à From prime meridian (0h) to 23h59m59s Eastward Declination E à Dec or δ à From celestial equator (0º ) to SCP poles N & S 90º Tilted Sky Observers see sky “tilted” due to latitude To NCP To Celestial We see Equator To NCP enith ourselves ZZ “on top” of the Earth, beneath the sky. So we see λ sky motions Observer ’s Latitude tilted Standard Clock Time It’s 6 pm Every Longi tud e at s()(lisunsetgh tl y). different time It’s 9 pm. It’ s 3 pm. It’s It’s midnight. noon. It’s 3 am. It’s 9 am. It’s 6 am (sunrise). The Ecliptic (path of the sun) View from Earth àSun move s ~1º/day eastward across stars àSun moves north and south in dliideclination à Solstices & EiEquinoxes are positions in the sky. This motion is through the YEAR! Moon Phase is lit moon visible Insert is moon as see from Earth Moon Phases New Moon: Elongation = 0° (angle from sun to moon) à Waxing Phases: visible after sunset d Waxing Crescent: 0° < Elongation < 90° E d First Quarter: Elongation = 90° E d Waxing Gibbous: 90° E < Elongation < 180° Full Moon: Elongation = 180° 1st QUARTER transit WAXING WAXING GIBBOUS CRESCENT eastern western sky sky Observer’s meridian Elongation = Angle from Sun FULL NEW SUN rising south setting SETTING Moon Phases Full Moon: Elongation = 180° à Waning Phases: visible before sunrise d Wani ng Gi bbous: 90° W < ElongatElongatonion < 180° d Third Quarter: Elongation = 90° W d Waning Crescent: 0° < Elongation < 90° W New Moon: Elongation = 0° 3rd QUARTER transit WANING WANING CRESCENT GIBBOUS eastern sky western sky Observer’s meridian Elongation = NEW SUN Angle from Sun Full RISING rising south setting Fun with Time & Phase 1st quarter DiDetermine riiising, waxing waxing 6pm transit and gibbous crescent Transiting 9pm setting times of Moon 3pm Setting Observer’s Above Moon to each phase Time West Above Time is the one full mdnt noon new above the Rising Earth Moon to rotation ob’bserver’s hd!head! East 3am 9am waning gibbous 6am waning crescent 3rd quarter Question 1st quarter An observer sees waxing waxing 6pm the moon rise at gibbous crescent midnight. 9pm 3pm What phase is it? full mdnt noon new Observer’s a) First Quarter Time Above b) Full Moon rd Rising c) 3 Quarter Moon to 3am 9am waning East gibbous 6am waning crescent 3rd quarter Time Clock Time à the position of the mean sun at TZ center d eggp. 12 pm = transit of mean sun ( (gavg. of analemma) à Mean Solar Day = 24:00:00 (hours:min:sec of time) Solar Time à the position of the sun wrt the observer eg. Noon = sun transits à SlSolar Day varies as shown by analemma Sidereal Time à the position of E wrt the observer d eg. 0h Local Sidereal Time (LST) = E transits d Sidereal time = R.A. on the meridian à Sidereal Day = 23:56:00 The Sidereal Day Sidereal Day: 360° rotation puts star back on meridian ~1° along orbit The Solar Day Solar Day: 361° rotation puts sun back on meridian ~1° ~1° along orbit The Sun at Noon Noon ⇒ Sun on meridian Sun’s position varies: the Analemma 6/25/07 5/26/07 7/30/07 4/26/07 8/29/06 3/27/07 9/28/06 2/27/07 10/28/06 1/26/07 11/27/06 12/27/06 The Sun at Noon Noon ⇒ Sun on meridian Sun’s position varies: the Analemma The Analemma Position of true sun at clock noon à Clock Noon 6/25/07 5/26/07 Mean Sun d 12:00 pm in a 24:00:00 day 7/30/07 d Position of Mean Sun 4/26/07 8/29/06 at noon 3/27/07 à True Sun’s Position 9/28/06 d varies due to Sun’s 2/27/07 10/28/06 speed along path 1/26/07 11/27/06 E varies due to elliptical path 12/27/06 E varies due to tilted path True sun East True sun West of mean sun of mean sun Mean Sun & True Sun Mean sun on meridian defines clock noon True sun on meridian defines solar noon 6/25/07 5/26/07 Mean Sun 7/30/07 4/26/07 True sun 8/29/06 True sun East of West of 3/27/07 mean sun: 9/28/06 mean sun: Solar Solar 2/27/07 noon is 10/28/06 noon is 1/26/07 late 11/27/06 early “sun slow” 12/27/06 “sun fast” The Calendar The Year à Tropical (equinox to equinox) = 365.242190 d à Sidereal (star to star) = 365.256363 d à Anomalistic (perigee to perigee) = 365.259635 d à Lunar (node to node) = 346.620076 d Julian Calendar (45 BCE) = 365.25 d à Add 1 day every four years d 365.25 – 365.24219 = 0.00781 days/year too many ⇒ Extra day every 128 years The Calendar Gregori an Cal end ar (1582) = 365.2425 d à Council of Trent: want E on March 21 d as it was during Council of Nicaea in 325 CE d Easter is 1st Sunday after 15th day of moon after E E Moon phases tabulated, not observed! à 325 to 1582 (1257 years), 9.8 days ahead d Drop 10 day s: 10/15/1582 foll owed 10/4/1582 E American Colonies 9/14/1752 followed 9/2/1752 J George Washington born 2/22/1732, 2/11/1732 OS http://en.wikipedia.org/wiki/Old_Style_and_New_Style_dates à Century years divisible by 400 have leap days d 1600, 2000 had leap days, 1700, 1800, 1900 did not Doing the Math Adidoption of the Gregori an CldCalendar Leap year for Julian Leap year Leap year for Julian for Julian Leap year Leap year for all for all Dropped Dropped Dropped Dropped 10 days 11 days 12 days 13 days Doing the Math Old Style & New Style dates Marriage certificate from Warsaw (then in Russia) Marriage Dated 3/16/1907 Certificate Dated Nov/Dec 23/6 Doing the Math Mean Sun à Projection of sun onto Celestial Equator d moves 360° in one year (365.242191 days) 360D v = = 0.985647356 D day Mean Sun 365.242191 days True Sun True Sun on Ecliptic à speed varies due to d S’Sun’s chihanging DlitiDeclination d Elliptical orbit Mean Sun on Celestial Equator Speed Variation Due to Tilt Analogy: Aiilrplanes on EhEarth à Both fly at same speed (mph) Airplane at high Airplane at angle latitude covers more covers fewer degrees of longitude. degrees of longitude. Speed Variation Due to Tilt 10° along Ecliptic (motion of true sun in 10 days) 10° along Ecliptic ((imotion of true sun in 10 d)days) 10° along Celestial Equator 10° along Celestial Equator (motion of mean sun in 10 days) (motion of mean sun in 10 days) Speed Variation Due to Tilt 10° along Ecliptic At equinoxes (motion of true sun in 10 days) true sun moves <1° each day ⇒ true sun falls behind mean sun ≈ 12° in right ascension (motion of true sun in sky) 10° along Ecliptic At solsti ces, ((imotion of true sun in 10 d)days) true sun moves > 1° each day ⇒ true sun gets ahead of mean sun ≈ 9° in right ascension (ti(motion of true sun in sk)ky) 10° along Celestial Equator 10° along Celestial Equator (motion of mean sun in 10 days) (motion of mean sun in 10 days) True Sun Speed Variation Solilstices à True sun and mean sun aligned, but … à True sun getting ahead of mean at maximum rate Equinoxes à True sun and mean sun aligned, but à True sun getting behind mean at maximum rate Cross-Quarter Days à Between solstices & equinoxes à True sun farthest from mean à Switching between getting ahead & behind Cross Quarter Days Days ½ way between sollistices & equinoxes à Beltane ~May 1 d ½ way from Vernal Equinox to Summer Solstice à Lughnasa ~ August 2 d ½ way from Summer Solstice to Autumnal Equinox à All Hallows (Samhain) ~November 1 d ½ way from Autumnal Equinox to Winter Solstice à Candlemas (Imbolc) ~ February 2 d ½ way from Wint er So ls tice to Verna l Equ inox If Candlemas Dayyg be fair and bright, If Candlemas Dayyp be damp & black, It Winter will have another flight will carry cold winter away on its back. Speed Variation Due to Tilt Solstices & Equinoxes (June & December) à mean and true sun align, fastest rate of change Cross-Quarter Days à maximum separation of mean and true sun à switchinggg direction of change 3 True sun fthstfarthest west 2 (early, fast) 1 Mean sun 0 & true sun 12/22 3/22 6/20 9/18 12/17 aligned -1 -2 True sun farthest east -3 (late, slow) Speed Variation Due to Tilt 3 Maximum rate of change at solstices & equinoxes 2 1 0 12/22 3/22 6/20 9/18 12/17 Maximum difference at cross-quarter days -1 (direction of change switc hes ) -2 -3 Tilt Analemma 70 PiiPosition of true sun 65 through the year for Earth in a circular 60 orbit. 55 50 3 True sun west of mean sun 45 est 2 ast EE 40 WW 1 35 0 12/22 3/22 6/20 9/18 12/17 -1 30 -2 25 -3 True sun east of mean sun 20 -3 -2 -1 0 1 2 3 Tilt Analemma 70 PiiPosition of true sun 65 through the year for Earth in a circular 60 orbit.
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