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Topic 02

Part 1

Short version 9/30/2012

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

1. 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.

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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

x

61b.1 Surviving Babylonian “Cuneiform” Clay Tablets of astronomical positions of sun & planets

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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 Twins

180° Scorpion0° Great Bull

81c. Egyptians get it from Babylonians

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

92. The Ecliptic 2b.1 Ecliptic is the dashed line on your Starwheel10

Its NOT the same as the equator!

2b.2 Obliquity of the Ecliptic 11

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

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.

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2c.1 Ecliptic on Mercator MapSpring equinox when sun at ascending node

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0°

Asc

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un“F

irst P

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Arie

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Summer

Fall

Winter

2c.2 Ecliptic Longitude on Polar Map 14

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°

Eq

uin

oct

ial C

olu

re

Solstitial Colure

North Ecliptic Pole

2c.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)

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 17 3a.3 Precession of Equinoxescauses Ascending Node of Sunto 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.

19 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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B. Annual Motion

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

• 3. Seasons

21 1. Solar Calendars

(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 it slip, knowing that it will be back in phase with

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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)

232. 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

25 3a.1 Seasons vs Hemisphere

The seasons are opposite in the southern hemisphere.

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The Earth’s axis of rotation is tilted 23° with respectto the Earth’s orbital plane, but keeps pointed towards the North Star during the orbit

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

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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)

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3c.1 Seasons Not the Same Length !

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

330 BC: Callippus of Cyzicusdevelops 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.

3c.3 Earth’s Orbit is Elliptical 32

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?

C. Daily Motion of Sun

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

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

Fig 1-1, p.20

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C.1b Local Horizon System 35

Prime Meridian is line fromNorth to South through Zenith

C.2a Daily Path of Sun 36

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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 -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

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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.

• 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

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

• 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 43 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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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