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Topic 02

Part 1

Updated Aug 27, 2009

Ecliptic andAnnual Motion

Dr. Bill Pezzaglia

II. Ecliptic and Annual Motion

A. The Ecliptic, (Path of the Sun)

B. Annual Motion, the Calendar

C. Daily Path of Sun & Archeoastronomy

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A. The Ecliptic

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

3 A. The Ecliptic

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.

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A1. The Zodiac

• 3000 BC Babylonians in Early Bronze Age start with4 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

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Ibex (Aquarius)?Winter

ScorpioAntaresFall

LeoRegulusSummer

TaurusAldebaranSpring

ConstellationStarts on Helical Rise of star

Season

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x

71b.1 Surviving Babylonian “Cuneiform” Clay Tablets of astronomical positions of sun & planets

1b.2 2000 BC Babylonians refined it to 12 months associated with constellations (each 30° wide)

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330° Hired Farm Laborer (Aries)150° Weighing Scales

300° Fish Tails120° Furrow (Woman holding wheat)

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

240° Goat Fish (Capricorn)60° Worker in River Bed (cancer)210° Soldier30° Great Twins180° Scorpion0° Great Bull

91b.3 Zodiac: “Circle of Animals” 101c.1 Egyptians got it from Babylon

Temple of Hathor at Dendera

111c.2 Dendera: Zodiac on Roof 121c.3 Dendera: Zodiac on Roof

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2. Ecliptic Coordinates 13

•At first, positions of sun, moon and planets were measured relative to the bright stars in the zodiac constellations.

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

• school of scribes defines sexagessimal numbers(base 60).

142a. Hammurabi [1810-1750 BC]

The Babylonians determined the exact pathof the sun through the zodiac constellations

152b. The Ecliptic 2b.1 Ecliptic is the dashed line on your Starwheel 16

Its NOT the same as the equator!

2b.2 Obliquity of the Ecliptic 17

The Ecliptic is tilted 23½° to the equator (“obliquity”)

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.

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Fig 1-6, p.24

2b.4 From Earth’s point of view 19

Yellow is equatorBlue is ecliptic

Plane of the Earth’s orbit

Around the sun

Red is equatorBlack is ecliptic

2b.5 Ecliptic on Mercator MapAscending Node of Sun (blue) is start of spring

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2c.1 Ecliptic Longitude 21

Ecliptic Longitude is measured eastward along the ecliptic, starting at 0 degrees at the First Point of Aries.

0°

90°

270°

180°

Equi

noct

ial C

olur

e

Equi

noct

ial C

olur

e

Sols

titia

lCol

ure

Sols

titia

lCol

ure

2c.2 Ecliptic Longitude on Polar Map 22

The sun moves about 1 degree east along the ecliptic each day.

0° Spring Equinox90° Summer Solstice180° Fall Equinox270° Winter Solstice

0°

90°270°

180°

Equi

noct

ial C

olur

e

Solstitial Colure

North Ecliptic Pole

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)

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This causes the First Point of Aries (the place where the sun crosses the equator) to move relative to the zodiac constellations.

3a.2 Precession of Equinoxes 25 3a.3 Precession of Equinoxescauses Ascending Node of Sun to slide through zodiac constellations

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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 CircleThe North Star will change!

In Egyptian times it was Thuban in Draco!

Center of circle is the Ecliptic Pole

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3b.3 Precession Circle 29

The zodiac sign associated with spring changes every 2000 years

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Rome!RamAries2000 BC

BabyloniansBullTaurus4000 BC

NoteSymbolSignYear

3c.1 Nodal Precession

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Astrologers start with Aries at spring even though its really should be Pisces! Your

birthsign is off by one constellation!

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ChristianityFishPisces0

Rome!RamAries2000 BC

BabyloniansBullTaurus4000 BC

NoteSymbolSignYear

3c.2 Nodal PrecessionToday we are at the “dawning of

the Age of Aquarius”

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“new age”Aquarius2000 AD

ChristianityFishPisces0

Rome!RamAries2000 BC

BabyloniansBullTaurus4000 BC

NoteSymbolSignYear

3c.3 Nodal Precession

At the dawn of history is the myth of Atlantis, ruled by Mercurial mentants

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“new age”Aquarius2000 AD

ChristianityFishPisces0

Rome!RamAries2000 BC

BabyloniansBullTaurus4000 BC

Atlantis?Gemini6000 BC

NoteSymbolSignYear

3c.4 Nodal Precession B. Annual Motion

• 1. Solar Calendars• 2. Definition of the Year• 3. Seasons

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1. Solar Calendars• Earliest Calendars (Babylonian) are based instead on phases moon (we’ll do later)

• 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.

35 -early calendars continued-

• 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.

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JULIAN CALENDAR

• 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 4th year a leap day will be added to the last day of the year

• February 29 (month of atonement)

37 2. Definitions of “Year”

a) Sidereal year: 365.25636 daysone orbit of earth about sun, relative to the stars

b) Tropical year: 365.2422 daysspring equinox to spring equinoxyou want to base calendar on this

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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 years365+1/4-3/400=365.2425

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Fig 3-4, p.64

The Earth’s axis of rotation is tilted 23° with respectto the Earth’s orbital plane.

The orientation of the tilted axis remains thesame as the Earth revolves around the Sun

3a. The Seasons, and what causes them 40

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

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3a.4 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

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Tropic of Capricorn---

Tropic of Cancer--

3b.1 Solar Altitude Angle and Heat

Summer in Northern Hemisphere

Winter in Southern Hemisphere

Sunlight coming in at a low altitude angle will have its energy spread out over more area.

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Lambert’s Law (1760)Intensity is reduced by cosine of angle of incidence

3b.2 Why is it hotter in summer

The sun is also up longer (more time to heat up earth)

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Day is also shorter (less time to heat up earth)

3c.1 Seasons Not the Same Length !

94.1 days Spring92.3 days Summer88.6 days Fall90.4 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.

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430 BC Meton & Euktemon of Athens measure the length of the seasons.

473c.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!).

3c.3 Earth’s Orbit is Elliptical 48

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?

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3c.4 Precession of Perihelion 49

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.

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

1. Local Sky2. Diurnal Path of the Sun3. Archeoastronomy

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Fig 1-1, p.20

C.1a The Local Sky looks like a hemisphere 52

C.1b Local Horizon

Fig 1-1, p.20

53 C.1c Local Horizon System 54

Prime Meridian is line fromNorth to South through Zenith

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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

Tropic of Cancer

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 Capricorn

2c.1 The Analemma

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.

• Analemma: is the figure 8 plot of declination of sun vs equation of time

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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

• 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

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Fig 3-11, p.70

Stonehenge (2800 – 1500 B.C.)

3. Archeoastronomy 62

3a.1 Rising and Setting PointsAncient 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

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Fig 3-12, p.70(1000 A.D.) Doors aligned to vernal equinox!

3a.2 El Caracol Observatory, Chichen Itza, Yucatan 64

3b.1 Stonehenge 3100 BC• The stone

circle was added 1000 years later!

65 3b.2 “the avenue” points towards summer sunrise 66

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3b.3 Heelstone in the Avenue 67 3b.4 Summer Solstice Sunrise 68

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

3c.1 Sillbury Hill, England 69

The large ditch and embankment is clearly visible. Many of the stones have been removed.

3c.2 Avebury Circle 70

3c.3 Avebury Circle 71 3c.4 Avebury Circle 72In the past

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3c.5 Today there is little left 73 3c.6 Except it’s a good tourist attraction 74

Ring of Brogar of the Orkney Islands

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Ring of Brogar of the Orkney Islands

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Ring of Brogar of the Orkney Islands

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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

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Things to do• Fix movies (slide 5, 23).• Added Lambert’s law Aug 2009

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