Ecliptic and Annual Motion II. Ecliptic and Annual Motion 2 Dr. Bill Pezzaglia A. The Ecliptic, (Path of the Sun) B. Annual Motion, the Calendar Topic 02 Updated 8/22/2006 C. Daily Path of Sun & Archeoastronomy A. The Ecliptic 3 A. The Ecliptic 4 1. The Zodiac Constellations 2. Ecliptic Coordinates 3. Precession Perhaps 5000 BC people changed from a nomadic culture to agrarian, settling in Sumer. Sumerians needed a calendar to tell them when to plant food. A1. The Zodiac 3000 BC Babylonians in Early Bronze Age start with 4 constellations for 4 seasons Spring started on the first day that Aldebaran could be seen in the morning sky before sunrise. 5 1a. Helical Rise: The first day a star is visible in east rising just before sunrise Season Spring Summer Fall Winter Starts on Helical Constellation Rise of star Aldebaran Taurus Regulus Antares? Leo Scorpio Ibex (Aquarius) 6 1
1b.1 Surviving Babylonian Cuneiform Clay Tablets of astronomical positions of sun & planets 7 1b.2 2000 BC Babylonians refined it to 12 months associated with constellations (each 30 wide) 8 x 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) 1b.3 Zodiac: Circle of Animals 9 10 1c.1 Egyptians got it from Babylon Temple of Hathor at Dendera 11 12 1c.2 Dendera: Zodiac on Roof 1c.3 Dendera: Zodiac on Roof 2
2. Ecliptic Coordinates 13 At first, positions of sun, moon and planets were measured relative to the bright stars in the zodiac constellations. 2a. Hammurabi [1810-1750 BC] school of scribes defines sexagessimal numbers (base 60). 14 The Babylonians invented the method of measuring the sky in degrees 15 2b. The Ecliptic 2b.1 Ecliptic is the dashed line on your Starwheel 16 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 ) 17 2b.3 Obliquity of the Ecliptic 18 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. 3
2b.4 From Earth s point of view 19 2b.5 Ecliptic on Mercator Map Ascending Node of Sun (blue) is start of spring 20 Plane of the Earth s orbit Around the sun Yellow Red is equator Black Blue is ecliptic Fig 1-6, p.24 2c.1 Ecliptic Longitude 21 Ecliptic Longitude is measured eastward along the ecliptic, starting at 0 degrees at the First Point of Aries. Solstitial Colure 270 180 Equinoctial Colure 90 Solstitial Colure Equinoctial Colure 0 2c.2 Ecliptic Longitude on Polar Map 22 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 180 0 90 2c.3 Ecliptic Longitude by Date 23 Each Zodiac Sign was 30 wide in longitude (one month) 3a.1 Precession of Equinoxes 24 Hipparchus 130 BC finds position of ascending solar node moves 1 west in 78 years (more exact 50 per year) 4
3a.2 Precession of Equinoxes 25 26 3a.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. 3b.1 Source of Precession 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. 27 3b.2 Precession Circle The North Star will change! 28 In Egyptian times it was Thuban in Draco! Center of circle is the Ecliptic Pole 3b.3 Precession Circle 29 3c.1 Nodal Precession The zodiac sign associated with spring changes every 2000 years Year Sign Symbol Note 30 4000 BC Taurus Bull Babylonians 2000 BC Aries Ram Rome! 5
3c.2 Nodal Precession Astrologers start with Aries at spring even though its really should be Pisces! Your birthsign is off by one constellation! Year Sign Symbol Note 31 3c.3 Nodal Precession Today we are at the dawning of the Age of Aquarius Year Sign Symbol Note 32 4000 BC Taurus Bull Babylonians 4000 BC Taurus Bull Babylonians 2000 BC Aries Ram Rome! 2000 BC Aries Ram Rome! 0 Pisces Fish Christianity 0 Pisces Fish Christianity 2000 AD Aquarius new age 3c.4 Nodal Precession At the dawn of history is the myth of Atlantis, ruled by Mercurial mentants 33 B. Annual Motion 34 Year 6000 BC 4000 BC Sign Gemini Taurus Symbol Atlantis? Bull Note Babylonians 1. Solar Calendars 2. Definition of the Year 3. Seasons 2000 BC Aries Ram Rome! 0 Pisces Fish Christianity 2000 AD Aquarius new age 1. Solar Calendars Earliest Calendars (Babylonian) are based instead on phases moon (we ll do later) 35 -early calendars continued- 36 4000 BC Egyptian Solar Calendar starts with helical rise of Sirius, as floods come 25 days later. Has 3 seasons (Flood, Plant, Harvest) of 4 lunar months (30 days) long (e.g. 360 days). Every few years, if Sirius is late a leap month has to be added to keep in phase with floods. 2600 BC Egyptians have two calendars. One has 7 day weeks, 4 weeks to the lunar month, but the 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 it slip, knowing that it will be back in phase with seasons in 1 Sothic Cycle of 1461 years. 6
JULIAN CALENDAR 37 2. Definitions of Year 38 700 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: 365.25636 days one orbit of earth about sun, relative to the stars b) Tropical year: 365.2422 days spring equinox to spring equinox you want to base calendar on this c). Gregorian Calendar 365.25 is longer than 365.2422 1582 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=365.2425 39 3a. The Seasons, and what causes them 40 The Earth s axis of rotation is tilted 23 with respect to the Earth s orbital plane. The orientation of the tilted axis remains the same as the Earth revolves around the Sun Fig 3-4, p.64 3a.2 Seasons vs Hemisphere The seasons are opposite in the southern hemisphere. 41 3a.3 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 42 7
3a.4 Winter Solstice Dec 22 43 3b.1 Solar Altitude Angle and Heat 44 Above Arctic Circle have 24 hours of night At tropic of Capricorn sun is directly overhead Below Antarctic Circle has 24 hours of daylight Tropic of Cancer-- Tropic of Capricorn--- 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 3b.2 Why is it hotter in summer 45 3c.1 Seasons Not the Same Length! 430 BC Meton & Euktemon of Athens measure the length of the seasons. 46 The sun is also up longer (more time to heat up earth) Day is also shorter (less time to heat up earth) 94.1 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. 3c.2: Hipparchus (130 BC): The sun is assumed to travel on a perfect circle at constant speed. The earth is eccentric (off-center). From the earth s point of view, the seasons divide the sky into four 90 degree segments. However, because of the eccentric, the path of the sun in each segment is a different length, hence seasons have different length of time. Surprisingly, the Greeks did not verify this theory by trying to measure a change in apparent diameter of the sun (due to distance to sun not being constant!). 47 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. 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? 48 8
3c.4 Precession of Perihelion Elliptical shape does influence climate, and the Position of the Perihelion changes slowly. Today, winter and summer in northern hemisphere are milder than in the southern hemisphere In 10,500 years the opposite will occur, we ll be at perihelion during summer, northern hemisphere seasons will be severe, southern mild. 49 3c.5 Milutin Milankovitch (1879-1958) 50 He proposed that these cyclic changes in the orbit of the earth might cyclical variations in long term climate, i.e. explain periodic ice ages and global warming. 1. Precession of Perihelion (last slide) 2. Obliquity of Earth (tilt of earth) changes by a few degrees over 41000 years. When its tilted more, the seasons will be more severe 3. Orbital Eccentricity: changes with cycle of 100,000 years. When orbit is more eccentric, seasons will be more severe. C. Daily Motion of Sun 51 C.1a The Local Sky looks like a hemisphere 52 1. Local Sky 2. Diurnal Path of the Sun 3. Archeoastronomy Fig 1-1, p.20 C.1b Local Horizon 53 C.1c Local Horizon System 54 Prime Meridian is line from North to South through Zenith Fig 1-1, p.20 9
C.2a Daily Path of Sun 55 C.2b The Equinoctial Sun 56 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 57 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 C.2b The Winter Sun 58 Sun is on Tropic of Capricorn, lowest declination -23.5 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 Tropic of Cancer Tropic of Capricorn 59 2c.2 Transit Times Note Sun transits 12:08 pm on average at Santa Clara, because we are 8 minutes west of the center of the pacific time zone. Equation of Time: Sun is as much as 20 minutes early/late due to elliptical orbit of earth, and obliquity of ecliptic. 60 2c.1 The Analemma Analemma: is the figure 8 plot of declination of sun vs equation of time 10
2c.3 Sun is a poor timekeeper 61 3. Archeoastronomy 62 Sun moves further in Right Ascension near solstices than at equinoxes, makes sun get behind clock after both solstices 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 Stonehenge (2800 1500 B.C.) Fig 3-11, p.70 3a.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 63 3a.2 El Caracol Observatory, Chichen Itza, Yucatan 64 (1000 A.D.) Doors aligned to vernal equinox! Fig 3-12, p.70 3b.1 Stonehenge 3100 BC 65 3b.2 the avenue points towards summer sunrise 66 The stone circle was added 1000 years later! 11
3b.3 Heelstone in the Avenue 67 3b.4 Summer Solstice Sunrise 68 3c.1 Sillbury Hill, England 69 3c.2 Avebury Circle 70 First begun around 2,660 BC. It is 130 feet high with base circumference of 1640 feet (about the size of the smaller Egyptian pyramids). It is just outside of Avebury The large ditch and embankment is clearly visible. Many of the stones have been removed. 3c.3 Avebury Circle 71 3c.4 Avebury Circle In the past 72 12
3c.5 Today there is little left 73 3c.6 Except it s a good tourist attraction 74 75 76 Ring of Brogar of the Orkney Islands Ring of Brogar of the Orkney Islands 77 References 78 http://www.phys.lsu.edu/farnese/ http://www-spof.gsfc.nasa.gov/stargaze/sjewcale.htm Babylonian: http://physics.unr.edu/grad/welser/astro/mesopotamian.html http://www.world-mysteries.com/alignments/mpl_alindx.htm On Avebury: http://www.avebury-web.co.uk/ http://deschutes.gso.uri.edu/~rutherfo/milankovitch.html Ring of Brogar of the Orkney Islands 13
79 Things to do Fix movies (slide 5, 23). 14