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Home , Analemma, Declination, Position of the Sun

SOAR: The in Motion Life on the Tilted Teacup Ride

The

Aileen A. O’Donoghue Priest Associate Professor of Physics Celestial Coordinates  NCP  RA or   From prime (0h) to 23h59m59s Eastward

  Dec or   From celestial (0º) to SCP poles N & S 90º Tilted Sky  Observers see sky “tilted” due to To NCP Our view is tilted with respect to ’s due to our latitude.

 Observer’s Latitude Tilted Sky  Observers see sky “tilted” due to latitude To NCP Meridian To We see Celestial To NCP ourselves Equator “on top” of the Earth,  beneath the 90 -  sky.

So we see  sky motions Observer’s Latitude tilted Coordinate System

to to observer’s celestial zenith pole

to  = observer’s latitude  90 -  to observer’s to observer’s northern southern horizon horizon Diurnal Circles  Each celestial Observer sees full object diurnal circle circles the observer

each day Observer sees  half of the Observer diurnal circle sees part of each circle Observer sees none of the diurnal circle View of Observers  Diurnal circles are parallel to CE  rise and set at CE’s angle from horizon

Celestial Equator

Stars rise parallel to celestial equator 90° - 

Stars set parallel to celestial equator Paths  Each travels a diurnal circle  Portion of diurnal circle above horizon determines object is “up”

All paths parallel up for to celestial 19 hours Summer equator up for 15 hours up for 8 hours

North , …  Everything in the sky (sun, , stars, etc.)  Rises in the each day 00°hr 15°1hr  Sets in the 30°2hr Measuring Circles: 45°3hr 60°4hr ° 360 = 24 hr 75°5hr 15° = 1 hr 270°18hr 90°6hr Each hour, the sun moves 15 degrees in the sky 1° = 4 min or 15’ = 1 min Every 4 minutes, the sun moves 180°12hr 1 = 60’ in the sky Time = Position of Sol It’s 6 pm  Observers move through (sunset).

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). vs. Clock Time  Solar time varies across time zones Time Zone’s Solar Noon Clock Noon FOR ALL Sun’s path seen from time zone center

Eastern Observer’s Western Observer’s Solar Noon Solar Noon

Time East Zone West Rising side side Setting Solar Time vs. Clock Time  Solar time varies across time zones Time Zone’s Solar Noon Clock Noon FOR ALL

Solar noon is Solar noon is (Degrees)(4 minutes/degree) (Degrees)(4 minutes/degree) earlier than clock noon later than clock noon

Degrees Degrees Eastern East of TZ West of Western Observer’s center TZ center Observer’s Solar Noon Solar Noon Time East Zone West Rising side side Setting Celestial  Finding Latitude & from  Altitude of (NCP)  Transit time of star  Looked up in an (eg. Field Guide)

to observer’s zenith to celestial equator

to north

NNSS Observer at 20° N Star Transit Time Gives position of star with respect to the sun eg. transits at 11 6 pm 5 pm Standard pm on December 15 for 4 pm every time zone Time 9 pm 3 pm

2 pm

11 pm 1 pm Aldebaran’s Position on 12 am 12 pm 12/15 nearly opposite Sol!

3 am 9 am

6 am Clicker Question  What’s your longitude if you see transit at 1 am on September first and your watch is set for Pacific time? On 9/1 Altair transits Observer sees Altair at 10 pm PDT transit at 1 am PDT At 10 pm Altair  transits TZ Late West center at 120° W of TZ center

Longitude difference from clock’s time zone center = (3 hours)(15°/hour) = 45° West

Observer’s Longitude = TZ center + Latitude difference = 120° W + 45° = 165 ° W Models of Earth Why are tilted? Earth’s Earth’s Orbit  UMi  with sun at one focus  perihelion – closest to sun  aphelion – farthest from sun  N Pole toward Polaris

Aphelion Perihelion July 3, 2017 Other January 4, 2017 focus Earth’s Orbit  Rotation Axis tilted 23.5° from  23.5° Earth’s Orbit  Axis always points at Polaris The Home World  The Earth in space  360° in 365 days  ~1°/day  Rotation axis tilted 23.5° from orbit axis  Declination of sun varies through year  subsolar latitude varies through year &  Declination () of the sun

: Sun crossing celestial equator Sol = 0°  Vernal Equinox: sun moving north  Autumnal Equinox: sun moving south

: Sun at N/S extreme Sol = ± 23.5°  (N) : sun at northernmost point  (N) solstice: sun at southernmost point Right Ascension () of the sun  0h = Vernal Equinox ()  6h = Summer Solstice ()  12h = Autumnal Equinox ()  18h = ()  Equinox – sun on Celestial Equator  Vernal ():  = 0°,  = 0h  Sun crossing equator moving north  Autumnal (fall):  = 0°,  = 12h  Sun crossing equator moving south Seasons Solstice – sun farthest north or south  Northern Summer  = +23.5°,  = 6h  Sun over Tropic of (23.5ºN)  Northern Winter  = -23.5°,  = 18h  Sun over (23.5ºS) Seasons  Due to changing angle of sunlight  At low angles, sunlight spreads out  less energy falls on any piece of ground

45° 30°

1.41 m2 1.15 m2 1 m2 Sun 45º from Sun 30º from Sun directly vertical vertical overhead Sun angle Path length through atmosphere

Seasons: Due to changing insolation. Seasons  Vary with latitude NCP Sun in the sky The View from Earth  Rotate to Earth’s equatorial plane  Center on Earth  Project sun onto sky  Vernal Equinox SCP The Ecliptic (path of the sun) View from Earth Sun moves ~1º/day eastward across stars Sun moves north and south in declination  Solstices & Equinoxes are positions in the sky.

This motion is through the YEAR! Sun’s path on a winter day Sun’s path on a winter day

Winter Altitude of Declination of Celestial Equator: Sol: -23.5° 90 – 44.6 = 45.4° Winter Altitude of Sol: 21.9° Sun’s path on a fall/spring day Sun’s path on a summer day Sun’s path on a summer day Summer Declination of Sol: +23.5°

Altitude of Summer Celestial Equator: Altitude of 90 – 44.6 = 45.4° Sol: 68.9° Clicker Question At noon on the summer solstice, the sun’s maximum altitude in Key West (24.6°N) is

A. 41.9° B. 65.4° C. 88.9° Hint: 90° – 24.6° = 65.4° Hint: What is 65.4° + 23.5? Sun in the sky View from Earth  Sun moves ~1º/day eastward across stars  Sun moves north and south in declination

h 18h, 12h, 6 , 0h, ―23.5º 0º +23.5º 0º

Celestial Equator

Winter Solstice Autumnal Summer Solstice Vernal Equinox in Sagittarius Equinox in in in Stars in the sky  Midnight view from Earth  Stars opposite sun’s position  see opposite ’s ,  eg. is a winter sky constellation, summer  Midnight “window” shifts 1° eastward/day

Celestial Equator

Winter Solstice Autumnal Summer Solstice Vernal Equinox in Sagittarius Equinox in Virgo in Taurus in Pisces Time  Clock Time  the position of the mean sun at TZ center  eg. 12 pm = transit of mean sun (avg. of )  Mean Solar Day = 24:00:00 (hours:min:sec of time)  Solar Time  the wrt the observer eg. Noon = sun transits  Solar Day varies as shown by analemma   the position of  wrt the observer  eg. 0h Local Sidereal Time (LST) =  transits  Sidereal time = R.A. on the meridian  Sidereal Day = 23:56:00 The Sidereal Day  Earth turns 360° with respect to stars  eg. Vega transit to Vega Transit  23:56:00

Next Day Solar Noon ~ 1° Solar Noon One Day The Sidereal Day  Earth turns 360° with respect to stars  eg. Vega transit to Vega Transit  23:56:00

Earth takes Next 4 minutes to Day turn extra 1° Solar Noon ~ 1° Solar Noon One Day The Sidereal Day  Earth turns 360° with respect to stars  eg. transit to Capella Transit  23:56:00

Transit of Capella occurs 4 Next minutes earlier Night Stars rise, transit & set four minutes earlier each

One day! Night Transit 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  Clock Noon 6/25/07  5/26/07 Mean Sun 12:00 pm in a 7/30/07

24:00:00 day 4/26/07  Position of Mean Sun 8/29/06 at noon 3/27/07 9/28/06  True Sun’s Position 2/27/07  varies due to Sun’s 10/28/06 1/26/07 speed along path 11/27/06 12/27/06  varies due to elliptical True sun East True sun West path of mean sun of mean sun  varies due to tilted path 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” Solar Noon Today (9/12/17)  Potsdam (44° 40’ N, 75° 00 W)  Standard time of solar noon = 11:56:13 am  Daylight time of solar noon = 12:56:13  Canton (44° 36’ N, 75° 10 W)  Standard time of solar noon = 11:56:53 am  Daylight time of solar noon = 12:56:53  40 seconds later than Potsdam  Earth turns 1° in 4 minutes  Earth turns 15’ in 1 minute  Earth turns 10’ in 40 seconds!!  Celestial events in Canton 40 seconds later than in Potsdam!! Doing the Math  Mean Sun  Projection of sun onto Celestial Equator  moves 360° in one year (365.242191 days) 360 v   0.985647356  day Mean Sun 365.242191 days

 True Sun True Sun on Ecliptic  speed varies due to  Sun’s changing Declination  Elliptical orbit

Mean Sun on Celestial Equator Position of Sunrise & Sunset  of rising depends on 

1 sin Arise  cos degrees cos   Sunrise appears to move along horizon  original calendar! eg. Stonehenge, Machu Pichu, Woodhenge (Illinois) Position of Sunset

9/9/9 6:42 pm EDT 12/9/9 3:4011/9/9 pm EST 3:59 pm EST10/9/9 5:46 pm EDT 40 minutes before 40 minutes40 before minutes before 40 minutes before sunset sunset sunset sunset Precession  Earth’s axis wobbles over 26,000

RA and Dec grid wobbles with pole, ecliptic does not wobble so solstices & equinoxes change position

©1996-2001 Scott R. Anderson http://www.opencourse.info/astronomy/introduction/03.motion_earth/ Raymo’s 365 Starry Nights

Precession Circle

View from the Pyramids Raymo’s 365 Starry Nights Position of the winter solstice in 1000 BCE

Tropic of Capricorn name origin Capricorn, the Mergoat Raymo’s 365 Starry Nights

Position of the Vernal Equinox now

Motion of the Vernal Equinox to the “Age of ” Raymo’s 365 Starry Nights

When the moon is in the Seventh HousePosition of And aligns with Then peace will guide the planets the Vernal And love will steer the stars Equinox now

This is the dawning of the Age of Aquarius Aquarius! Aquarius!

Harmony and understanding MotionSympathy of and the trust Vernal abounding NoEquinox more falsehoods to the or derisions Golden living dreams of visions Mystic“Age crystal of Aquarius” revelation And the mind’s true liberation Aquarius! Aquarius!