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()(li sunsetgh tl y). different ti me
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 = 1 80° 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 var ies as s hown by anal emma Sidereal Time à the position of E wrt the ob server 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 pa th 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 no t 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 Sty le & New Styl e 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 EEharth 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 (i(motion 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 sol sti ces, (i(motion 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 sol listices & equi noxes 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 Equi nox
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 9/18Maximum 12/17 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. 55
50 True & mean sun aligned
at solstices & equinoxes 45
(rate of change maximum) est ast EE
40 WW Maximum difference
at cross-quarter days 35 ((g)direction of change switches)
30
25
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. 55
50 True & mean sun aligned
at solstices & equinoxes 45
(rate of change maximum) est ast EE
40 WW Maximum difference 35 at cross-quarter days (direc tion of change sw itc hes ) 30
25 But it’s not this simple … 20 -3 -2 -1 0 1 2 3 Earth’s Orbit Earth’s speed varies in orbit à area swept out in a given time stays equal à perihelion (~ January 4) d Earth moves fastest (February is shortest month!) à aphelion (~ July 4) d Earth moves slowest
Orbital Motion Area at aphelion Area at perihelion
Aaphelion = Aperihelion
Orbital speed changes to keep swept areas equal The Analemma PihliPerihelion, EEtharth movi ng ffststastest
~1°
> 1° along orbit
EtExtra rotttiation to put sun on meridian puts true sun behind mean sun
rperihelion = 91.4 million miles, vperihelion = 67,754 mph The Analemma Ap he lion, Earth movi ng slowest < 1° along orbit
~1°
< 1° along orbit
Less rotation to put sun on meridian puts true sun ahead of mean sun raphelion = 94.5 million miles, vaphelion = 65,527 mph Orbit Analemma Position of true sun through the year for Earth in an elliptical orbit just due to orbital speed vari ation
Maximum rate of 2.0 changgpe at perihelion True sun west of & aphelion mean sun 1.0
Maximum difference
0.0 at orbital mid-points 12/22 3/22 6/20 9/18 12/17 (direction of change ssitchs)witches)
-1.0 True sun east of mean sun -2.0 Orbit Analemma 70 Position of true sun 65 through the year for Earth in an ellipt ica l 60 orbit just due to 55
orbital speed variation 50
45 2.0 est ast 40 True sun west of EE WW mean sun 1.0 35
0.0 30 12/22 3/22 6/20 9/18 12/17
25 -1.0 True sun east of mean sun 20 -2.0 -3 -2 -1 0 1 2 3 Total Analemma Tilt and Orbit effects add
3
2
1 5 0 12/22 3/22 6/20 9/18 12/17 Tilt Effect 4 -1 Orblbital Effect -2 3
-3 Sum 2
1
0 2.0 12/21 1/20 2/19 3/21 4/20 5/20 6/19 7/19 8/18 9/17 10/17 11/16 12/16 -1
1.0 -2
0.0 12/22 3/22 6/20 9/18 12/17 -3
-4 -1.0
-2.0 Total Analemma Tilt and Orbit 70
effects add 65
70 60 70
65 65 55
60 60
55 55 50
50 50 45 45 45 st st st st
40 ee ee aa aa 40
E 40 E W W 35
35
30 35 30
25 25 30 20 20 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 25
20 -4-2024 Potsdam’s Analemma 70 65
60
5 55
4 est ast EE 3 50 WW
2
1 45
0 12/21 1/20 2/19 3/21 4/20 5/20 6/19 7/19 8/18 9/17 10/17 11/16 12/16 -1 40
-2
-3 35
-4
30
25
20 -20 -15 -10 -5 0 5 10 15 20 Why is the earliest sunset on December 7, 2009?
Sun position at 3:30 pm EST through the year 7/7/10 6/7/10
8/7/10 5/7/10
4/7/10 9/7/10
3/7/10
10/7/10 2/7/10
Analemma closest to horizon in 1/7/10 11/7/10 early December 12/7/9 The Analemma Varies time of sunrise & sunset à Earliest sunset on about December 8 à Latest sunrise on about January 3 The Analemma Solar noon was 5 minutes before clock noon Position of sun Position at clock noon of sun at thhhroughout year clock At clock noon on
Variation in the nn tttt
noon sun’ s 9/16 oooo length of the Solar declination Equator EasEas
is +3° stst dayyy as measured by ck Nock No eeee oooo ClCl clocks WW
Solar noon Clock noon to solar to4 c°lock 3° 2° 1° 0° ≠ At clock noon sun is 1.25° noon noon West of the meridian 4° 3° 2° 1° 0° 1° 2° 3° 4°