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Home , Capricorn (astrology), Colure

Ecliptic and 2 Annual Motion II. and Annual Motion

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

Topic 02 B. Annual Motion, the Calendar

Part 1 C. Daily Path of Sun & Short version 9/30/2012 Archeoastronomy

A. The Ecliptic 3 A. The Ecliptic 4 1. The • 3000 BC Babylonians • 1. The Zodiac in Early Bronze Age • 2. Ecliptic Coordinates start with 4 constellations for 4 • 3. Precession seasons

• 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 5 1b.1 Surviving Babylonian “Cuneiform” Clay 6 visible in east rising just before sunrise Tablets of astronomical positions of sun & planets

Season Starts on Helical Rise of star Spring Aldebaran Summer Regulus Fall Antares Winter ? Ibex () x

1 1b.2 2000 BC Babylonians refined it to 12 7 1c. Egyptians get it from Babylonians 8 associated with constellations (each 30° wide)

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

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

120° Furrow (Woman holding wheat) 300° Fish Tails

150° Weighing Scales 330° Hired Farm Laborer ()

2. The Ecliptic 9 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 11 2b.3 Obliquity of the Ecliptic 12 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.

2 2c.1 Ecliptic on Mercator Map 13 2c.2 Ecliptic Longitude on Polar Map 14

Spring when sun at ascending node The sun moves about 1 degree east along the 0° ecliptic each day. Summer 0° Spring Equinox 90° Summer Ascending node of sun of node Ascending Aries” “First Point of 90° 180° Fall Equinox 270Solstitial° Colure 0° 270° Winter Solstice Fall Winter

North Ecliptic Pole 180° Equinoctial Colure Equinoctial

2c.3 Ecliptic Longitude by Date 15 3a.1 Precession of 16

Each Zodiac Sign was 30° wide in longitude (one ) Hipparchus 130 BC finds position of Around 2000 BC started with Aries ascending solar node moves 1 west in 78 years (more exact 50” per year)

3a.2 Precession of Equinoxes 17 3a.3 Precession of Equinoxes 18 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.

3 3b.1 Source of 19 3b.2 Precession Circle 20 Precession The North Star will change! Reason: Moon & Sun tug on equatorial bulge of earth, trying to make it sit up straight. Causes rotating earth In Egyptian times 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

B. Annual Motion 21 1. Solar Calendars 22

• 1. Solar Calendars • 2. Definition of the Year (a)Egyptian: Earliest based upon helical rise of Sirius • 3. Seasons 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 seasons in 1 “Sothic Cycle” of 1461 years.

23 24 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) Sidereal year: 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) Tropical year: 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)

4 c). Gregorian Calendar 25 3a.1 Seasons vs Hemisphere 26 The Earth’s axis of rotation is tilted 23 with respect • 365.25 is longer than 365.2422 to the Earth’s orbital plane, but keeps pointed towards the North Star during the orbit • 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

The seasons are opposite in the southern hemisphere.

3a.2 Summer Solstice June 22 27 3a.3 Winter Solstice Dec 22 28

•Above Arctic Circle have 24 hours of sunlight •Above Arctic Circle have 24 hours of night •At tropic of Cancer sun is directly overhead •At tropic of Capricorn sun is directly overhead •Below Antarctic Circle has 24 hours of night •Below Antarctic Circle has 24 hours of daylight

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

Summer in Northern Hemisphere Sunlight coming in at a low altitude angle will have its energy spread out over more area. The sun is also up longer Day is also shorter (less time to heat up earth) Winter in Southern Hemisphere (more time to heat up earth)

5 3c.1 Seasons Not the Same Length ! 31 3c.3 Earth’s Orbit is Elliptical 32 430 BC Meton & Euktemon of Athens 2000 years later Copernicus will realize the earth goes around the sun, and Kepler will show that the orbit is an measure the length of the seasons. ellipse with varying speed.

94.1 days Spring 330 BC: Callippus of • Aphelion (furthest) is around July 3, moves slower 92.3 days Summer Cyzicus develops a complicated theory • Perihelion (closest) is 88.6 days Fall of spheres within around Jan 3, moves faster 90.4 days Winter spheres to explain why the sun would • DANGER: common misconception is that this is speed up and slow the reason for the seasons. down. Why is this wrong?

C. Daily Motion of Sun 33 C.1a The Local Sky looks like a hemisphere 34

1. 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 C.2b The Equinoctial Sun 37 C.2b The Summer Sun 38 •Spring (and Fall) Equinox, the sun is on the equator •Sun is on Tropic of Cancer, highest declination 23.5° •Sunrise is due East •Sunrise is in North-East •Sunset is due West •Sunset is in the North-West •Transit is when sun crosses prime meridian •Transit is at 52+23=75 altitude angle (above horizon) •Sun Transits at “local noon”, at 52 above the horizon •Length of day is around 15 hours

Tropic of Cancer

C.2b The Winter Sun 39 40 •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

41 42 2c.2 Transit Times 2c.3 Sun is a poor timekeeper • Sun moves further in • Note Sun transits 12:08 pm on near average at Hayward, because we than at are 8 minutes west of the center of equinoxes, makes sun get the pacific time zone. behind clock after both solstices

• Equation of Time: • Also the day is longer Sun is as much as 20 minutes than 24 hours when we early/late due to elliptical orbit of are near the perihelion earth, and obliquity of ecliptic. (sun moves faster on ecliptic). This is why the lower loop of the figure 8 • Analemma: is the figure 8 plot of is bigger in the analemma declination of sun vs equation of time

7 3. Archeoastronomy 43 3a.1 Rising and Setting Points 44 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 Stonehenge (2800 – 1500 B.C.) winter

Fig 3-11, p.70

3b.1 Stonehenge 3100 BC 45 3b.2 “the avenue” points towards summer sunrise 46 • The stone circle was added 1000 years later!

3b.3 Heelstone in the Avenue 47 3b.4 Summer Solstice Sunrise 48

8 49 Background music: “Four Seasons” Vivaldi 50 CSUEB Science Bldg, Jan 7, 2014

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