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Home , Blue moon, Eclipse season, Full moon, Lunar eclipse, Metonic cycle, New Moon

Northeastern Illinois University

Lunar Phases, , Ancient

Greg Anderson Department of Physics & Astronomy Northeastern Illinois University

Winter- 2020

c 2012-2020 G. Anderson : Past, Present & Future – slide 1 / 66 Northeastern Illinois Overview University

The Lunar Phases Eclipses The Ancient Roots of Science Review

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 2 / 66 Northeastern Illinois University

The Moon Quarter Moon and Moon Earth and Moon

Lunar Phases

Months

Eclipses The Ancient Roots of Science The Moon Review

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 3 / 66 Last Quarter Moon in the Lower Canons, c G. Anderson Earth and Moon (NASA’s Reconnaissance Orbiter) Earth and Moon from Change’s 5-T1 Northeastern Illinois University

The Moon

Lunar Phases Fig: Phases Phases Label the Eight Lunar Phases Question

Months

Eclipses The Ancient Lunar Phases Roots of Science

Review

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 7 / 66 Northeastern Illinois Fig: Moon Phases University

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 8 / 66 Northeastern Illinois Phases of the Moon University

The Moon always keeps the same face towards the Earth. Rotation and Revolution are synchronous. Moon Phase: Fraction of the side visible to us. • Waxing: increasing illumination – Waxing : just after – Waxing Gibbous: just before

• Waning: decreasing illumination – Waning Gibbous: just after Full Moon – Waning Crescent: just before New Moon

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 9 / 66 Northeastern Illinois Label the Eight Lunar Phases University

sunlight

Earth

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 10 / 66 Northeastern Illinois Label the Eight Lunar Phases University

First Quarter

Waxing Gibbous Waxing Crescent

noon sunlight midnight Full Moon New Moon

Waning Gibbous Waning Crescent

Last Quarter

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 10 / 66 Northeastern Illinois Q: What phase is it? University

At 6 A.M. you look up in the sky and see a moon with half its face bright and half dark near the Upper Meridian. What phase is it? A) first quarter B) waxing gibbous C) third quarter (last quarter) D) half moon

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 11 / 66 Northeastern Illinois Q: What phase is it? University

At 6 A.M. you look up in the sky and see a moon with half its face bright and half dark near the Upper Meridian. What phase is it? A) first quarter B) waxing gibbous C) third quarter (last quarter) D) half moon

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 11 / 66 Northeastern Illinois University

The Moon

Lunar Phases

Months Lunar Months Sidereal & Synodic Lunar Position Analogy Metonic Cycle Metonic Cycle II Months Earth and Moon Perigee & Apogee Peri & Apogee Precession Anomalistic Inclination Draconic Phases

Eclipses The Ancient Roots of Science

Review

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 12 / 66 Northeastern Illinois Lunar Months University

The Moon keeps the same face towards the Earth. Rotation and Revolution are synchronous. One “” on the moon = 29.5 Earth days. • Lunar Sidereal Period (Sidereal Month): From the Latin sidus for . The it takes the Moon to complete one with respect to to the .

Tsidereal = 27.3 days

• Lunar Synodic Period (Synodic Month): From the Greek synodos coming together. The time between successive New . Tsynodic = 29.5 days

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 13 / 66 Northeastern Illinois Sidereal & Synodic Months University

T = 29.5d = Synodic

T = 27.3d = Sidereal

New Moon

T =0d New Moon

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 14 / 66 Northeastern Illinois Lunar Movement on University

Relative to the stars, the Moon moves 360◦ in 27.3 days or 360◦/27.3=13.2◦/day, which is just over half a degree per hour (approximately equal to its apparent size).

Eastward on Celestial Sphere one day later 13.2◦

Not to scale

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 15 / 66 Northeastern Illinois Metonic Cycle Analogy University

Imagine two runners jogging around a track. Runner A circles the track once every 3 and runner B circles the track once every 4 minutes. How often does the scene repeat itself?

A) every 3 minutes b

b B) every 4 minutes C) every 12 minutes D) every 20 minutes

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 16 / 66 Northeastern Illinois Metonic Cycle Analogy University

Imagine two runners jogging around a track. Runner A circles the track once every 3 minutes and runner B circles the track once every 4 minutes. How often does the scene repeat itself?

A) every 3 minutes b

b B) every 4 minutes C) every 12 minutes D) every 20 minutes

4 × (3 minutes)=3 × (4 minutes) = 12 minutes

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 16 / 66 Northeastern Illinois The Metonic Cycle University

1 = 365.24 days While twelve synodic months are only:

12 × (29.53) = 354.36 days

• Difference: 365.24 − 354.36 = 10.87 days per year. • After 19 : 19 × 10.87 ≈ 206.5 days. • Coincidence: 206.5 days ≈ 7 synodic months. To keep a 12-month “lunar year” in sync with the solar year, add an intercalary 13th month on seven occasions during the nineteen-year period. 19 years ≈ 235 synodic months = (19 × 12)+7 ≈ 254 sidereal months

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 17 / 66 Northeastern Illinois The Metonic Cycle II University • Named for Greek astronomer Meton (Mǫτων) of Athens. In 432 BCE, Meton noted:

19 years ≈ 235 synodic months • Meton popularized this cycle, it was already known and used: – Babylonian 499 BCE – Ancient systems 484 BCE

The position and phase of the Moon tonight will repeat in 19 years from today.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 18 / 66 Northeastern Illinois Blue Moon University

• The phrase “Once in a blue moon” means very rarely. It has nothing to do with the color of the moon, instead it refers to an extra full Moon. • In current usage, a blue moon often refers to the full moon in a calendar month. Since the synodic month is 29.5 days long, “blue moons” are rare. • Historically a blue moon referred to the thirteenth full moon in a year which happens seven in the nineteen year Metonic cycle. An average of once every 2.7 years.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 19 / 66 Northeastern Illinois Earth and Moon University ǫ =0.0549 Moon

To relative scale

Earth orbit around

Earth

Earth-Moon distances To Sun: semi-major axis = 384,748 km 150 million km perigee = 362,600 km apogee = 405,400 km

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 20 / 66 Northeastern Illinois Perigee & Apogee University

Not to scale

Perigee Apogee 362,600 km 404,400 km

(closest) (farthest)

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 21 / 66 Northeastern Illinois Moon at Perigee & Apogee University

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 22 / 66 Northeastern Illinois Precession of the Moon’s Perigee University

Precession of perigee of Moon: Once in ≈ 9 years. Caused by Solar tidal forces

The closest point to the Earth in the Moon’s orbit is called perigee. The furthest point is called apogee.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 23 / 66 Northeastern Illinois Anomalistic month University

Because the elliptical precesses every nine years, the time the Moon spends between two successive perigees (or apogees) is slightly longer than a sidereal month.

Tsidereal = 27.32 days

Tanomalistic = 27.55 days

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 24 / 66 Northeastern Illinois Inclination of Moon Orbit University

The moons orbit is tilted by about 5◦ with respect to the .

ascending node ecliptic 5◦

descending node

The plane of the Moon’s orbit precesses over a full circle in about 18.6 years.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 25 / 66 Northeastern Illinois Draconic or Nodical Month University

Because the plane of the Moon’s orbit precesses westward once per 18.6 years, the time between two successive transits of the moon through its ascending node is slightly shorter than a sideral month.

Tsidereal = 27.32 days

Tdraconic = 27.21 days

ecliptic ascending node5◦

descending node

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 26 / 66 Northeastern Illinois Libration University

Simplified Picture • : One hemisphere of the Moon faces Earth. • Our first view of the resulted from lunar exploration in the 1960s. Over time, 59% of the Moon’s surface is seen from Earth due to libration: the slow rocking back and forth of the Moon as viewed from Earth. Libration is caused by: inclination of the Moon’s axis, eccentricity of the Moon’s orbit, and the Earth’s rotation. • Libration Video

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 27 / 66 Northeastern Illinois Moon Phases: NASA University

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 28 / 66 Northeastern Illinois University

The Moon

Lunar Phases

Months

Eclipses Eclipses Umbra, Penumbra & Antumbra Umbra of Earth Lunar Eclipses Descending Node Total Lunar Eclipse Saros 137 Solar Eclipses Fig 2-24 Conditions for Fig 2-23 Eclipse Intervals Predicting Eclipses Saros Cycle Saros Cycle Saros 136 The c 2012-2020 Ancient G. Anderson Universe: Past, Present & Future – slide 29 / 66 Roots of Science Northeastern Illinois Eclipses University

Lunar eclipse: Earth’s on Moon.

Solar eclipse: Moon’s shadow on Earth.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 30 / 66 Northeastern Illinois Umbra, Penumbra & Antumbra University antumbra

umbra penumbra

Looking towards the Sun from the... Umbra Penumbra Antumbra

Total Eclipse Partial Eclipse Annular Eclipse

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 31 / 66 Image Credit & Copyright: Wang, Letian Umbra of Earth Northeastern Illinois Lunar Eclipse University

Penumbra

Umbra

No eclipse

Sun

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 33 / 66 Northeastern Illinois Lunar Eclipse University

Penumbra

Umbra

Penumbral eclipse

Sun

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 33 / 66 Northeastern Illinois Lunar Eclipse University

Penumbra

Umbra

Partial eclipse

Sun

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 33 / 66 Northeastern Illinois Lunar Eclipse University

Penumbra

Umbra

Total eclipse

Sun

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 33 / 66 Northeastern Illinois Lunar Eclipse University

Penumbra

Umbra

Partial eclipse

Sun

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 33 / 66 Northeastern Illinois Lunar Eclipse University

Penumbra

Umbra

Penumbral eclipse

Sun

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 33 / 66 Northeastern Illinois Lunar Eclipse University

Penumbra

Umbra

No eclipse

Sun

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 33 / 66 Northeastern Illinois Lunar Eclipse University

Penumbra

Umbra

Sun

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 33 / 66

Northeastern Illinois Solar Eclipses University

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Northeastern Illinois Conditions for Syzygy University

Syzygy: the straight line configuration of three celestial bodies in a gravitational system. Solar and lunar eclipses occur when the Sun, Earth and Moon are close to syzygy.

Two conditions must be met to have an eclipse • It must be a full moon (lunar eclipse) or a new moon (solar eclipse) • The Moon must be at or near one of the two points where its orbit crosses the ecliptic plane.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 39 / 66 Northeastern Illinois Fig 2-23 University

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 40 / 66 Northeastern Illinois University

The only times in a year an eclipse can occur due to the five degree inclination of the Moon’s orbit. • Average eclipse season lasts ≈ 34.5 days • Time between eclipse : Just under six months (173.3 days). There are 2-3 eclipse seasons per year. Each year the eclipse season starts 18.6 days earlier.

• UNL Animation

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 41 / 66 Northeastern Illinois Solar Eclipse Intervals University

The interval between successive solar eclipses can be 1,5, or 6 synodic months.

Interval Between Successive Solar Eclipses in the last 5,000 years:

Synodic Months No. Percent 1 1,361 11.4% 5 2,743 23.1% 6 7,793 65.5%

Successive solar eclipses tend to be dissimiliar

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 42 / 66 Northeastern Illinois Predicting Eclipses University

Imagine three runners jogging around a track. Runner A circles the track once every 3 minutes, runner B circles the track once every 4 minutes, and runner C circles the track once every 5 minutes. How often does the scene repeat itself?

b A) every 4 minutes

b

b B) every 12 minutes

C) every 20 minutes

D) every 60 minutes

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 43 / 66 Northeastern Illinois Predicting Eclipses University

Imagine three runners jogging around a track. Runner A circles the track once every 3 minutes, runner B circles the track once every 4 minutes, and runner C circles the track once every 5 minutes. How often does the scene repeat itself?

b A) every 4 minutes

b

b B) every 12 minutes

C) every 20 minutes

D) every 60 minutes

Once every sixty minutes:

20 × (3 minutes)=15 × (4 minutes)=12 × (5 minutes) = 60 minutes

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 43 / 66 Northeastern Illinois Saros Cycle University

Three of the Moon’s orbital periods are important for eclipses:

Synodic Month (New Moon to New Moon) 29.53 days Anomalistic Month (perigee to perigee) 27.55 days DraconicMonth (nodetonode) 27.21days

An accidental harmony (One Saros):

223 synodic months ≈ 242 draconic months ≈ 239 anomalistic months

One saros after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry. Thus, a nearly identical eclipse will occur. 1 1saros = 223 synodic months = 18 years and 11 days 3

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 44 / 66

Northeastern Illinois University

The Moon

Lunar Phases

Months

Eclipses The Ancient Roots of Science Time 7 Days The Ancient Roots of Egyptian Obelisk Ancient Astronomy Predicting Rain Science Stonehenge Scientific Thinking The Greeks Star Trails Greek Geocentric Cosmology Geocentric Parallax Stellar Parallax Retrograde Motion of Mars Epicycles Further Study

Review c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 47 / 66 Northeastern Illinois Divisions of Time University

Our basic units of time are astronomical in origin: • Year: time for Earth to orbit the Sun. • Month: time for the Moon to orbit Earth. • : one day for each “ancient ” • Day: time for Earth to revolve on its axis • Hour: One twelfth of daylight.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 48 / 66 Northeastern Illinois Seven Days of the Week University

Object English Meaning French Spanish Sun Sunday Sun’s day Dimanche Domingo Moon Monday Moon’s day lundi lunes Mars Tuesday Tiu’s day mardi martes Wednesday Woden’s day mercredi mi´ercoles Jupiter Thursday Thor’s day jeudi jueves Friday Freya’s day vendredi viernes Saturday Saturn’s day samedi s´abado

Correlation between days and the seven Astronomical objects known to ancient peoples: Sun, Moon, Mars, Mercury, Jupiter, Venus, and Saturn. The seven-day week traces back at least three millennia ago when Babylonian astronomers assigned days of the week to “planets”.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 49 / 66 Northeastern Illinois Egyptian Obelisk University

The origins of our modern clocks can be traced back to ancient Egyptians who divided daylight into twelve equal parts over 4000 years ago. small NB 12 is divisible by 2,3,4,6.

Pictured: Relocated ancient Egyptian obelisk (sundial).

Latin: A.M. (ante meridiem), P.M. (post meridiem)

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 50 / 66 Northeastern Illinois Ancient Astronomy University

Astronomy was the backbone of many ancient social, political, and religious systems. Ancient astronomers noticed patterns and built structures to marking seasons, align with ,...

This helped some ancient civilizations keep track of seasons, navigate, predict eclipses,...

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 51 / 66 Northeastern Illinois Predicting Rain University

Rainfall in Nigeria: People from central Africa used the orientation of the waxing crescent moon to predict rainfall.

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Northeastern Illinois Scientific Thinking University

Scientific thinking is based on everyday notions of • Observation • Critical thinking • Trial and error experiments

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 54 / 66 Northeastern Illinois Greek Contributions University

Greek Contributions to Scientific Thinking • Valued critical thinking: debate and challenging ideas • Used mathematics to give precision to ideas • Created models of nature • Beginnings of reasoning from observations

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 55 / 66 Northeastern Illinois Eratosthenes University

Eratosthenes of Cyrene, 276 - 195 BCE, computed Earth’s circumference in 240 BC. (Carl Sagan video)

Determined angle between Alexandria and Aswan (Syene) from the Sun’s rays on the as θ ≈ 7◦12′ θ S S = Rθ R Known that S ≈ 5000 stadia

Earth circumference (comp. to 40,075 km):

S 360◦ C =2πR =2π = 5000 ≈ 250, 000 stadia ≈ 40, 000km θ  7.2◦ 

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 56 / 66 Northeastern Illinois Star Trails University

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 57 / 66 Northeastern Illinois Greek Geocentric Cosmology University

⋆ Stars Saturn Y X Jupiter Mars ♂ ☼ Sun Venus ♀ ' Mercury Moon $ ♁ Earth

Aristotle’s crystalline spheres

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 58 / 66 Northeastern Illinois Greek University

Plato and Aristotle’s Geocentric model: Earth is at the center of the universe: The sky appears to rotate from east to west around the earth each day. The Earth is stationary: No stellar parallax could be observed. Heavenly objects move in perfect circles: Stars appear to orbit the NCP at a constant rate. Prejudice for simplicity and elegance of geometry.

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 59 / 66 Northeastern Illinois Parallax University

The apparent shift in position of nearby objects in comparison to more distant objects resulting from the movement of the observer. c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 60 / 66 Northeastern Illinois Parallax University

The apparent shift in position of nearby objects in comparison to more distant objects resulting from the movement of the observer. c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 60 / 66 Northeastern Illinois Stellar Parallax University

b b

b b b b

b b b b

b b b b Jan sky Jun sky Animation p

d d(parsecs) = 1/p(arcseconds)

1 AU

June January

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 61 / 66

Northeastern Illinois Epicycles University Ancient Astronomers (Apollonius, , ...) modeled the cyclical motion of “planets” across the celestial sphere using epicycles and uniform circular motion. Roman-, Egyptian astronomer, Claudius Ptolemaeus published his epicycle model in the in the 2nd century AD. epicycle

♂

♁

deferent

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 63 / 66 Northeastern Illinois Further Study University

• How Does a Lunar Eclipse Work (NASA)? • NASA Eclipse Web Site • YouTube: Eclipses • Tezcatlipoca Next: Origins of Astronomy

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 64 / 66 Northeastern Illinois University

The Moon

Lunar Phases

Months

Eclipses The Ancient Roots of Science

Review Review Review

c 2012-2020 G. Anderson Universe: Past, Present & Future – slide 65 / 66 Northeastern Illinois Review University

• What is the ecliptic? • List a few reference points for defining a month. e.g. the distant stars (sidereal). • What is the Moon phase during a solar eclipse? During a lunar eclipse? • How could you modify the Moon’s orbit so that lunar eclipses happen once per month? Would you change the eccentricity? the inclination of the orbit? or something else? • If the Earth’s axis was tilted by more than 23.5 degrees would the difference between the seasons become more extreme (hotter & colder winters) or less extreme? • The seven days of the week are named after what objects? List them. • How did Eratosthenes estimate the size of Earth in 240 BCE?

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