A. The Ecliptic. Ecliptic and Annual Motion. A. The Ecliptic. II. Ecliptic and Annual Motion. A. The Ecliptic, (Path of the Sun)

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1 Ecliptic and Annual Motion Dr. Bill Pezzaglia II. Ecliptic and Annual Motion A. The Ecliptic, (Path of the Sun) 2 Topic 02 Part 1 Short version 9/30/2012 B. Annual Motion, the Calendar C. Daily Path of Sun & Archeoastronomy A. The Ecliptic 1. The Zodiac Constellations 2. Ecliptic Coordinates 3. Precession 3 A. The Ecliptic 1. The Zodiac 3000 BC Babylonians in Early Bronze Age start with 4 constellations for 4 seasons 4 Spring started on the first day that Aldebaran could be seen in the morning sky before sunrise. 1a. Helical Rise: The first day a star is visible in east rising just before sunrise 5 1b.1 Surviving Babylonian Cuneiform Clay Tablets of astronomical positions of sun & planets 6 Season Starts on Helical Rise of star Constellation Spring Aldebaran Taurus Summer Regulus Leo Fall Antares Scorpio Winter? Ibex (Aquarius) x 1

2 1b BC Babylonians refined it to 12 months associated with constellations (each 30 wide) 7 1c. Egyptians get it from Babylonians 8 0 Great Bull 30 Great Twins 60 Worker in River Bed (cancer) 90 Great Lion 120 Furrow (Woman holding wheat) 150 Weighing Scales 180 Scorpion 210 Soldier 240 Goat Fish (Capricorn) 270 Great Man of Heavens (Aquarius) 300 Fish Tails 330 Hired Farm Laborer (Aries) 9 2. The Ecliptic 2b.1 Ecliptic is the dashed line on your Starwheel 10 The Babylonians determined the exact path of the sun through the zodiac constellations Its NOT the same as the equator! 2b.2 Obliquity of the Ecliptic The Ecliptic is tilted 23½ to the equator ( obliquity ) 11 2b.3 Obliquity of the Ecliptic 12 This is because the earth s axis of rotation is tilted by 23½ degrees relative to the axis of its orbital revolution around the sun. This is what gives us seasons. 2

3 2c.1 Ecliptic on Mercator Map Spring equinox when sun at ascending node Summer Fall Winter 13 Ascending node of sun First Point of Aries 0 2c.2 Ecliptic Longitude on Polar Map 14 The sun moves about 1 degree east along the ecliptic each day. 0 Spring Equinox 90 Summer Solstice 180 Fall Equinox 270 Winter Solstice North Ecliptic Pole 270 Solstitial Colure Equinoctial Colure c.3 Ecliptic Longitude by Date 15 Each Zodiac Sign was 30 wide in longitude (one month) Around 2000 BC started with Aries 3a.1 Precession of Equinoxes 16 Hipparchus 130 BC finds position of ascending solar node moves 1 west in 78 years (more exact 50 per year) 3a.2 Precession of Equinoxes a.3 Precession of Equinoxes This causes the First Point of Aries (the place where the sun causes Ascending Node of Sun to slide through zodiac constellations crosses the equator) to move relative to the zodiac constellations. 3

4 3b.1 Source of Precession 19 3b.2 Precession Circle The North Star will change! 20 Reason: Moon & Sun tug on equatorial bulge of earth, trying to make it sit up straight. Causes rotating earth to precesses like a top, making one complete cycle every Chaldean Period of 25,800 years. In Egyptian times it was Thuban in Draco! Center of circle is the Ecliptic Pole B. Annual Motion Solar Calendars Solar Calendars 2. Definition of the Year 3. Seasons (a)egyptian: Earliest based upon helical rise of Sirius 2600 BC Egyptians have two calendars. Astronomical has 7 day weeks, 4 weeks to the lunar month Civil calendar has 10 day weeks, 30 day months, 12 months to the year with 5 holidays added, so 365 days. The calendar gets off by ¼ day a year, but they just let JULIAN CALENDAR Definitions of Year BC Roman calendar has 12 months, but wrong length. 46 BC Julius Caesar has to decree the year will have 445 days to reset calendar. Thereafter, it starts on March 1 at the spring equinox (corresponding to Aries) Every 4 th year a leap day will be added to the last day of the year February 29 (month of atonement) a) Sidereal year: days one orbit of earth about sun, relative to the stars b) Tropical year: days spring equinox to spring equinox you want to base calendar on this 4

5 c). Gregorian Calendar is longer than Pope Gregory drops 11 days from year to reset calendar Leap Century Rule: centuries are NOT leap years, unless divisible by 400 (1900 was not a leap year!) This calendar is off by 1 day in 2500 years 365+1/4-3/400= a.1 Seasons vs Hemisphere The Earth s axis of rotation is tilted 23 with respect to the Earth s orbital plane, but keeps pointed towards the North Star during the orbit The seasons are opposite in the southern hemisphere. 26 3a.2 Summer Solstice June 22 Above Arctic Circle have 24 hours of sunlight At tropic of Cancer sun is directly overhead Below Antarctic Circle has 24 hours of night 27 3a.3 Winter Solstice Dec 22 Above Arctic Circle have 24 hours of night At tropic of Capricorn sun is directly overhead Below Antarctic Circle has 24 hours of daylight 28 Tropic of Cancer-- Tropic of Capricorn--- 3b.1 Solar Altitude Angle and Heat 29 3b.2 Why is it hotter in summer 30 Lambert s Law (1760) Intensity is reduced by cosine of angle of incidence Sunlight coming in at a low altitude angle will have its energy spread out over more area. Summer in Northern Hemisphere Winter in Southern Hemisphere The sun is also up longer (more time to heat up earth) Day is also shorter (less time to heat up earth) 5

6 3c.1 Seasons Not the Same Length! 430 BC Meton & Euktemon of Athens measure the length of the seasons. 31 3c.3 Earth s Orbit is Elliptical 2000 years later Copernicus will realize the earth goes around the sun, and Kepler will show that the orbit is an ellipse with varying speed days Spring 92.3 days Summer 88.6 days Fall 90.4 days Winter 330 BC: Callippus of Cyzicus develops a complicated theory of spheres within spheres to explain why the sun would speed up and slow down. Aphelion (furthest) is around July 3, moves slower Perihelion (closest) is around Jan 3, moves faster DANGER: common misconception is that this is the reason for the seasons. Why is this wrong? C. Daily Motion of Sun 33 C.1a The Local Sky looks like a hemisphere Local Sky 2. Diurnal Path of the Sun 3. Archeoastronomy Fig 1-1, p.20 C.1b Local Horizon System 35 C.2a Daily Path of Sun 36 Prime Meridian is line from North to South through Zenith 6

7 C.2b The Equinoctial Sun 37 Spring (and Fall) Equinox, the sun is on the equator Sunrise is due East Sunset is due West Transit is when sun crosses prime meridian Sun Transits at local noon, at 52 above the horizon C.2b The Summer Sun 38 Sun is on Tropic of Cancer, highest declination 23.5 Sunrise is in North-East Sunset is in the North-West Transit is at 52+23=75 altitude angle (above horizon) Length of day is around 15 hours Tropic of Cancer C.2b The Winter Sun 39 Sun is on Tropic of Capricorn, lowest declination Sunrise is in South-East Sunset is in South-West Transit is at 52-23=29 altitude angle (above horizon) Length of day is about 9 hours 40 Tropic of Capricorn 2c.1 The Analemma 2c.2 Transit Times Note Sun transits 12:08 pm on average at Hayward, because we are 8 minutes west of the center of the pacific time zone. 41 2c.3 Sun is a poor timekeeper Sun moves further in Right Ascension near solstices than at equinoxes, makes sun get behind clock after both solstices 42 Equation of Time: Sun is as much as 20 minutes early/late due to elliptical orbit of earth, and obliquity of ecliptic. Analemma: is the figure 8 plot of declination of sun vs equation of time Also the day is longer than 24 hours when we are near the perihelion (sun moves faster on ecliptic). This is why the lower loop of the figure 8 is bigger in the analemma 7

8 3. Archeoastronomy Stonehenge ( B.C.) Fig 3-11, p a.1 Rising and Setting Points Ancient astronomers would naturally put a rock on the ground to mark the extreme points on the horizon where the sun rises/sets each summer and winter 44 3b.1 Stonehenge 3100 BC The stone circle was added 1000 years later! 45 3b.2 the avenue points towards summer sunrise 46 3b.3 Heelstone in the Avenue 47 3b.4 Summer Solstice Sunrise 48 8