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Ecliptic and 2 Annual Motion II. and Annual Motion

Dr. Bill Pezzaglia A. The Ecliptic, (Path of the )

Topic 02 B. Annual Motion, the Calendar

Part 1 C. Daily Path of Sun & Updated Aug 27, 2009 Archeoastronomy

3 4 A. The Ecliptic A. The Ecliptic

• 1. The Zodiac • 2. Ecliptic Coordinates • 3.

Perhaps 5000 BC people changed from a nomadic culture to agrarian, settling in . Sumerians needed a calendar to tell them when to plant food.

A1. The Zodiac 5 1a. Helical Rise: The first a is 6 visible in east rising just before sunrise • 3000 BC Babylonians in Early Bronze Age start with 4 constellations for 4 seasons Season Starts on Helical Rise of star • Spring started on the Spring first day that Summer Aldebaran could be seen in the morning Fall sky before sunrise. Winter ? Ibex ()

1 1b.2 2000 BC Babylonians refined it to 12 1b.1 Surviving Babylonian “Cuneiform” Clay 7 8 associated with constellations (each 30° wide) Tablets of astronomical positions of sun &

0° Great Bull 180° 30° Great Twins 210° Soldier 60° Worker in River Bed () 240° ()

90° Great 270° Great Man of Heavens (Aquarius)

120° Furrow (Woman holding wheat) 300° Fish Tails x 150° Weighing Scales 330° Hired Farm Laborer ()

1b.3 Zodiac: “Circle of Animals” 9 1c.1 Egyptians got it from Babylon 10

Temple of Hathor at Dendera

1c.2 Dendera: Zodiac on Roof 11 1c.3 Dendera: Zodiac on Roof 12

2 2. Ecliptic Coordinates 13 2a. Hammurabi [1810-1750 BC] 14 •At first, positions of sun, and planets • school of scribes defines were measured relative to the bright in sexagessimal numbers the zodiac constellations. (base 60).

•The Babylonians invented the method of measuring the sky in degrees

2b. The Ecliptic 15 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 !

2b.2 Obliquity of the Ecliptic 17 2b.3 Obliquity of the Ecliptic 18 This is because the earth’s axis of rotation is tilted The Ecliptic is tilted by 23½ degrees relative to the axis of its orbital 23½° to the equator revolution around the sun. (“obliquity”) This is what gives us seasons.

3 2b.4 From Earth’s point of view 19 2b.5 Ecliptic on Mercator Map 20 Ascending Node of Sun (blue) is start of spring

Plane of the Earth’s orbit

Around the sun

YellowRed is equator BlackBlue is ecliptic

Fig 1-6, p.24

2c.1 Ecliptic Longitude 21 2c.2 Ecliptic Longitude on Polar Map 22 Ecliptic Longitude is measured eastward along the ecliptic, starting at 0 degrees at the . The sun moves about 1 degree east along the 0° ecliptic each day.

90° 0° Spring

Solstitial Colure 90° Summer 270° 90° 0° 180° Fall Equinox Solstitial Colure 180° 270° Winter Solstice 270°

North Ecliptic Pole 180° Solstitial Colure Equinoctial Colure Equinoctial Colure Equinoctial Colure

2c.3 Ecliptic Longitude by Date 23 3a.1 Precession of 24

Each Zodiac Sign was 30° wide in longitude (one ) 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 3a.3 Precession of Equinoxes 26 This causes the First Point of Aries (the place where the sun crosses the equator) to move relative to the zodiac causes Ascending Node of Sun to slide through zodiac constellations constellations.

3b.1 Source of 27 3b.2 Precession Circle 28 Precession The North Star will change!

Reason: Moon & Sun tug on equatorial bulge of earth, In Egyptian times trying to make it sit up straight. Causes rotating earth to “precesses” like a top, making one complete cycle it was Thuban in every “Chaldean Period” of 25,800 years. Draco!

Center of circle is the Ecliptic Pole

3b.3 Precession Circle 29 3c.1 Nodal Precession 30 The zodiac sign associated with spring changes every 2000 years Year Sign Symbol Note

4000 BC Taurus Bull Babylonians

2000 BC Aries Ram Rome!

5 3c.2 Nodal Precession 31 3c.3 Nodal Precession 32 Astrologers start with Aries at spring even Today we are at the “dawning of though its really should be ! Your birthsign is off by one constellation! the ” Year Sign Symbol Note Year Sign Symbol Note

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 33 34 B. Annual Motion At the dawn of history is the myth of Atlantis, ruled by Mercurial mentants

Year Sign Symbol Note • 1. Solar Calendars 6000 BC Atlantis? • 2. Definition of the Year 4000 BC Taurus Bull Babylonians • 3. Seasons

2000 BC Aries Ram Rome! 0 Pisces Fish Christianity 2000 AD Aquarius “new age”

35 -early calendars 36 1. Solar Calendars continued- • Earliest Calendars (Babylonian) are based instead on phases moon (we’ll do later)

• 4000 BC Egyptian starts with helical rise of Sirius, as floods come 25 days later. Has 3 seasons (Flood, Plant, Harvest) of 4 lunar months (30 • 2600 BC Egyptians have two calendars. One days) long (e.g. 360 days). Every few years, if Sirius is has 7 day weeks, 4 weeks to the , “late” a leap month has to be added to keep in phase but the “civil” calendar has 10 day weeks, 30 with floods. 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 37 38 JULIAN CALENDAR 2. Definitions of “Year” • 700 BC Roman calendar has 12 months, but wrong length. • 46 BC Julius Caesar has to decree the a) : 365.25636 days year will have 445 days to reset calendar. one orbit of earth about sun, • Thereafter, it starts on March 1 at the relative to the stars spring equinox (corresponding to Aries) b) : 365.2422 days • Every 4th year a leap day will be added spring equinox to spring equinox to the last day of the year you want to base calendar on this • February 29 (month of atonement)

c). 39 3a. The Seasons, and what causes them 40

• 365.25 is longer than 365.2422 The Earth’s axis of rotation is tilted 23° with respect • 1582 Pope Gregory drops 11 to the Earth’s orbital plane. 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 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 41 3a.3 Summer Solstice 22 42

•Above Arctic Circle have 24 hours of sunlight •At tropic of Cancer sun is directly overhead The seasons are opposite in the southern hemisphere. •Below Antarctic Circle has 24 hours of night

7 3a.4 Winter Solstice Dec 22 43 3b.1 Solar Altitude Angle and Heat 44

•Above Arctic Circle have 24 hours of night Lambert’s Law (1760) •At tropic of Capricorn sun is directly overhead Intensity is reduced by •Below Antarctic Circle has 24 hours of daylight cosine of angle of incidence

Summer in Northern Hemisphere Sunlight coming in Tropic of Cancer-- at a low altitude angle will have its Tropic of Capricorn--- energy spread out over more area.

Winter in Southern Hemisphere

3b.2 Why is it hotter in summer 45 3c.1 Seasons Not the Same Length ! 46 430 BC Meton & Euktemon of Athens measure the length of the seasons.

94.1 days Spring 330 BC: of 92.3 days Summer Cyzicus develops a complicated theory 88.6 days Fall of spheres within 90.4 days Winter spheres to explain why the sun would speed up and slow down. The sun is also up longer Day is also shorter (more time to heat up earth) (less time to heat up earth)

3c.2: Hipparchus (130 BC): The sun is assumed to travel on a 47 48 perfect circle at constant speed. The earth is eccentric (off-center). 3c.3 Earth’s Orbit is Elliptical From the earth’s point of view, the seasons divide the 2000 years later Copernicus will realize the earth goes sky into four 90 degree around the sun, and Kepler will show that the orbit is an segments. However, because ellipse with varying speed. of the eccentric, the path of the sun in each segment is a • Aphelion (furthest) is different length, hence seasons around July 3, moves slower have different length of time. • Perihelion (closest) is around Jan 3, moves faster Surprisingly, the did not verify this theory by trying • DANGER: common to measure a change in misconception is that this is apparent diameter of the sun the reason for the seasons. (due to distance to sun not Why is this wrong? being constant!).

8 3c.4 Precession of Perihelion 49 3c.5 Milutin Milankovitch (1879-1958) 50 Elliptical shape does influence climate, and the Position of the He proposed that these cyclic changes in the orbit of the earth might cyclical variations Perihelion changes slowly. in long term climate, i.e. explain periodic ice ages and global warming. •Today, winter and summer in northern hemisphere are milder 1. Precession of Perihelion (last slide) than in the southern hemisphere 2. Obliquity of Earth (tilt of earth) changes by a few degrees over 41000 years. •In 10,500 years the opposite will When its tilted more, the seasons will be occur, we’ll be at perihelion during more severe summer, northern hemisphere 3. : changes with cycle seasons will be severe, southern of 100,000 years. When orbit is more mild. 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 C.2b The Winter Sun 58 •Sun is on Tropic of Cancer, highest 23.5° •Sun is on Tropic of Capricorn, lowest declination -23.5° •Sunrise is in North-East •Sunrise is in South-East •Sunset is in the North-West •Sunset is in South-West •Transit is at 52+23=75° altitude angle (above horizon) •Transit is at 52-23=29° altitude angle (above horizon) •Length of day is around 15 hours •Length of day is about 9 hours

Tropic of Cancer

Tropic of Capricorn

59 60 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.

• : 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 2c.1 The Analemma

10 2c.3 Sun is a poor timekeeper 61 3. Archeoastronomy 62 • Sun moves further in near than at equinoxes, makes sun get behind 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 63 3a.2 El Caracol Observatory, Chichen Itza, Yucatan 64 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

(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 The large ditch and embankment is clearly visible. Many of pyramids). It is just outside of Avebury 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 78 References

• 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). • Added Lambert’s law Aug 2009

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