# Aileen A. O Donoghue Priest Associate Professor of Physics

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1 SOAR: The Sky in Motion Life on the Tilted Teacup Ride The Year Aileen A. O Donoghue Priest Associate Professor of Physics

2 Celestial Coordinates Right Ascension RA or From prime meridian (0 h ) to 23 h 59 m 59 s Eastward NCP Declination Dec or From celestial equator (0º) to poles N & S 90º SCP

3 Tilted Sky Observers see sky tilted due to latitude Our view is tilted with respect to Earth s due to our latitude. To NCP Observer s Latitude

4 Tilted Sky Observers see sky tilted due to latitude We see ourselves on top of the Earth, beneath the sky. To NCP To NCP Zenith Meridian 90 - To Celestial Equator So we see sky motions tilted Observer s Latitude

5 Horizon Coordinate System to north celestial pole to observer s zenith = observer s latitude to observer s northern horizon 90 - to celestial equator to observer s southern horizon

6 Diurnal Circles Each celestial object circles the observer each day Observer sees part of each circle Observer sees full diurnal circle Observer sees half of the diurnal circle Observer sees none of the diurnal circle

7 View of Observers Diurnal circles are parallel to CE Stars rise and set at CE s angle from horizon Celestial Equator Stars rise parallel to celestial equator 90 - Stars set parallel to celestial equator

8 Star Paths Each travels a diurnal circle Portion of diurnal circle above horizon determines time object is up All paths parallel to celestial equator Vega up for 19 hours Summer sun up for 15 hours Antares up for 8 hours North South

9 Sunrise, Sunset Everything in the sky (sun, moon, stars, etc.) Rises in the east Sets in the west Measuring Circles: 360 = 24 hr 15 = 1 hr Each hour, the sun moves 15 degrees in the sky 1 = 4 min or each day 15 = 1 min Every 4 minutes, the sun moves 1 degree = 60 in the sky 0 0 hr 15 1 hr 30 2 hr 45 3 hr 60 4 hr 75 5 hr hr 90 6 hr hr 5 hr

10 Clock Time = Position of Sol Observers move through times It s 9 pm. It s 6 pm (sunset). It s 3 pm. It s midnight. It s noon. It s 3 am. It s 9 am. It s 6 am (sunrise).

11 Solar Time vs. Clock Time Solar time varies across time zones Sun s path seen from time zone center Time Zone s Solar Noon Clock Noon FOR ALL Eastern Observer s Solar Noon Western Observer s Solar Noon Rising East side Time Zone West side Setting

12 Solar Time vs. Clock Time Solar time varies across time zones Time Zone s Solar Noon Clock Noon FOR ALL Solar noon is (Degrees) (4 minutes/degree) earlier than clock noon Solar noon is (Degrees) (4 minutes/degree) later than clock noon Eastern Observer s Solar Noon Degrees East of TZ center Degrees West of TZ center Western Observer s Solar Noon Rising East side Time Zone West side Setting

13 Celestial Navigation Finding Latitude & Longitude from Altitude of Polaris (NCP) Transit time of star Looked up in an ephemeris (eg. Field Guide) to observer s zenith to celestial equator to north celestial pole N Observer at 20 N S

14 Star Transit Time Gives position of star with respect to the sun eg. Aldebaran transits at 11 pm on December 15 for every time zone 9 pm 6 pm 5 pm 4 pm 3 pm 2 pm Standard Time 11 pm Aldebaran s Position on 12 am 12/15 nearly opposite Sol! 1 pm 12 pm 3 am 9 am 6 am

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

16 Models of Earth Why are globes tilted?

17 Earth s Orbit

18 Earth s Orbit UMi Ellipse with sun at one focus perihelion closest to sun aphelion farthest from sun N Pole toward Polaris Aphelion July 3, 2017 Other focus Perihelion January 4, 2017

19 Earth s Orbit Rotation Axis tilted 23.5 from 23.5

20 Earth s Orbit Axis always points at Polaris

21 The Earth in space The Home World 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

22 Solstices & Equinoxes Declination ( ) of the sun Equinox: Sun crossing celestial equator Sol = 0 Vernal Equinox: sun moving north Autumnal Equinox: sun moving south Solstice: Sun at N/S extreme Sol = ± 23.5 (N) Summer solstice: sun at northernmost point (N) Winter solstice: sun at southernmost point Right Ascension ( ) of the sun 0 h = Vernal Equinox ( ) 6 h = Summer Solstice ( ) 12 h = Autumnal Equinox ( ) 18 h = Winter Solstice ( )

23 Seasons Equinox sun on Celestial Equator Vernal (spring): = 0, = 0 h Sun crossing equator moving north Autumnal (fall): = 0, = 12 h Sun crossing equator moving south

24 Seasons Solstice sun farthest north or south Northern Summer = +23.5, = 6 h Sun over Tropic of Cancer (23.5ºN) Northern Winter = -23.5, = 18 h Sun over Tropic of Capricorn (23.5ºS)

25 Seasons Due to changing angle of sunlight At low angles, sunlight spreads out less energy falls on any piece of ground m 2 Sun 45º from vertical 1.15 m 2 Sun 30º from vertical 1 m 2 Sun directly overhead

26 Sun angle Path length through atmosphere Seasons: Due to changing insolation.

27 Seasons Vary with latitude

28 Sun in the sky View from Earth Rotate to Earth s equatorial plane Center on Earth Project sun onto sky The Ecliptic NCP Vernal Equinox SCP

29 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!

30 Sun s path on a winter day

31 Sun s path on a winter day Altitude of Celestial Equator: = 45.4 Winter Declination of Sol: Winter Altitude of Sol: 21.9

32 Sun s path on a fall/spring day

33 Sun s path on a summer day

34 Sun s path on a summer day Summer Declination of Sol: Altitude of Celestial Equator: = 45.4 Summer Altitude of Sol: 68.9

35 Clicker Question At noon on the summer solstice, the sun s maximum altitude in Key West (24.6 N) is A B C Hint: = 65.4 Hint: What is ?

36 View from Earth Sun in the sky Sun moves ~1º/day eastward across stars Sun moves north and south in declination 18 h, 23.5º 12 h, 0º 6 h, +23.5º 0 h, 0º Celestial Equator Winter Solstice in Sagittarius Autumnal Equinox in Virgo Summer Solstice in Taurus Vernal Equinox in Pisces

37 Stars in the sky Midnight view from Earth Stars opposite sun s position see opposite season s constellations, eg. Gemini is a winter sky constellation, Scorpius summer Midnight window shifts 1 eastward/day Celestial Equator Winter Solstice in Sagittarius Autumnal Equinox in Virgo Summer Solstice in Taurus Vernal Equinox in Pisces

38 Clock Time Time the position of the mean sun at TZ center eg. 12 pm = transit of mean sun (avg. of analemma) Mean Solar Day = 24:00:00 (hours:min:sec of time) Solar Time the position of the sun wrt the observer eg. Noon = sun transits Solar Day varies as shown by analemma Sidereal Time the position of wrt the observer eg. 0 h Local Sidereal Time (LST) = transits Sidereal time = R.A. on the meridian Sidereal Day = 23:56:00

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

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

41 Earth turns 360 with respect to stars eg. Capella transit to Capella Transit 23:56:00 The Sidereal Day Next Night Transit of Capella occurs 4 minutes earlier Stars rise, transit & set four minutes earlier each One Night day! Transit

42 The Sidereal Day Sidereal Day: 360 rotation puts star back on meridian ~1 along orbit

43 The Solar Day Solar Day: 361 rotation puts sun back on meridian ~1 ~1 along orbit

44 The Sun at Noon Noon Sun on meridian Sun s position varies: the Analemma 6/25/07 7/30/07 5/26/07 4/26/07 8/29/06 3/27/07 9/28/06 2/27/07 1/26/07 12/27/06 10/28/06 11/27/06

45 The Sun at Noon Noon Sun on meridian Sun s position varies: the Analemma

46 Clock Noon 12:00 pm in a 24:00:00 day Position of Mean Sun at noon True Sun s Position varies due to Sun s speed along path varies due to elliptical path varies due to tilted path The Analemma Position of true sun at clock noon 6/25/07 7/30/07 3/27/07 2/27/07 1/26/07 12/27/06 True sun East of mean sun 5/26/07 4/26/07 8/29/06 9/28/06 10/28/06 11/27/06 Mean Sun True sun West of mean sun

47 Mean Sun & True Sun Mean sun on meridian defines clock noon True sun on meridian defines solar noon 6/25/07 7/30/07 5/26/07 Mean Sun True sun East of mean sun: Solar noon is late sun slow 3/27/07 2/27/07 1/26/07 12/27/06 4/26/07 8/29/06 9/28/06 10/28/06 11/27/06 True sun West of mean sun: Solar noon is early sun fast

48 Solar Noon Today (9/12/17) Potsdam (44 40 N, W) Standard time of solar noon = 11:56:13 am Daylight time of solar noon = 12:56:13 Canton (44 36 N, 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!!

49 Mean Sun Doing the Math Projection of sun onto Celestial Equator v moves 360 in one year ( days) Mean Sun days day True Sun speed varies due to Sun s changing Declination Elliptical orbit True Sun on Ecliptic Mean Sun on Celestial Equator

50 Position of Sunrise & Sunset Azimuth of rising depends on 1 sin A rise cos degrees cos Sunrise appears to move along horizon original calendar! eg. Stonehenge, Machu Pichu, Woodhenge (Illinois)

51 Position of Sunset 9/9/9 6:42 pm EDT 12/9/9 3:40 11/9/9 pm EST 3:59 pm EST 10/9/9 5:46 pm EDT 40 minutes before 40 minutes before 40 minutes before 40 minutes before sunset sunset sunset sunset

52 Precession Earth s axis wobbles over 26,000 years RA and Dec grid wobbles with pole, ecliptic does not wobble so solstices & equinoxes change position Scott R. Anderson

53 Raymo s 365 Starry Nights Precession Circle View from the Pyramids

54 Raymo s 365 Starry Nights Position of the winter solstice in 1000 BCE Capricorn, the Mergoat Tropic of Capricorn name origin

55 Raymo s 365 Starry Nights Position of the Vernal Equinox now Motion of the Vernal Equinox to the Age of Aquarius

56 Raymo s 365 Starry Nights When the moon is in the Seventh House And Jupiter aligns with Mars Then peace will guide the planets And love will steer the stars This is the dawning of the Age of Aquarius Aquarius! Aquarius! Harmony and understanding Sympathy and trust abounding No more falsehoods or derisions Golden living dreams of visions Mystic crystal revelation And the mind s true liberation Aquarius! Aquarius! Motion of the Vernal Equinox to the Age of Aquarius Position of the Vernal Equinox now

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