Lunar Phases, Eclipses, Ancient Astronomy

Orin Harris and Greg Anderson Department of Physics & Astronomy Northeastern Illinois University

Spring 2021

c 2012-2021 G. Anderson., O. Harris Universe: Past, Present & Future – slide 1 / 65 Overview

The Moon Lunar Phases Months Eclipses The Ancient Roots of Science Review

c 2012-2021 G. Anderson., O. Harris Universe: Past, Present & Future – slide 2 / 65 The Moon Earth and Moon Earth and Moon Earth and Moon

Lunar Phases

Months

Eclipses The Ancient Roots of Science The Moon Review

c 2012-2021 G. Anderson., O. Harris Universe: Past, Present & Future – slide 3 / 65 Earth and Moon (NASA’s Mars Reconnaissance Orbiter) Earth and Moon from Change’s 5-T1 Earth & Moon to scale

c 2012-2021 G. Anderson., O. Harris Universe: Past, Present & Future – slide 6 / 65 The Moon

Lunar Phases Phases Label the Eight Lunar Phases Question

Months

Eclipses The Ancient Roots of Science Lunar Phases Review

c 2012-2021 G. Anderson., O. Harris Universe: Past, Present & Future – slide 7 / 65 Phases of the Moon

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

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

c 2012-2021 G. Anderson., O. Harris Universe: Past, Present & Future – slide 8 / 65 Label the Eight Lunar Phases

sunlight

Earth

c 2012-2021 G. Anderson., O. Harris Universe: Past, Present & Future – slide 9 / 65 Label the Eight Lunar Phases

First Quarter

Waxing Gibbous Waxing Crescent

sunset noon sunlight midnight Full Moon sunrise New Moon

Waning Gibbous Waning Crescent

Last Quarter

c 2012-2021 G. Anderson., O. Harris Universe: Past, Present & Future – slide 9 / 65 Q: What phase is it?

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 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 10 / 65 The Moon

Lunar Phases

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

Eclipses The Ancient Roots of Science

Review

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 11 / 65 Lunar Months

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

Tsidereal = 27.3 days

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

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 12 / 65 Sidereal & Synodic Months

T = 29.5d = Synodic

T = 27.3d = Sidereal

New Moon

T =0d New Moon

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 13 / 65 Lunar Movement on Celestial Sphere

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). Note: in sky, moon moves 360◦/24h = 15◦/h

Eastward on Celestial Sphere one day later 13.2◦

Not to scale

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 14 / 65 Metonic Cycle Analogy

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

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 15 / 65 Metonic Cycle Analogy

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 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 15 / 65 The Metonic Cycle

1 year = 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 years: 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 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 16 / 65 The Metonic Cycle II

• 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 calendar 499 BCE – Ancient Chinese calendar systems 484 BCE

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

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 17 / 65 Blue Moon

• 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 second full moon in a calendar month. Since the synodic month is 29.5 days long, “blue moons” are rare, and cannot occur in February. • Historically a blue moon referred to the thirteenth full moon in a year which happens seven times in the nineteen year Metonic cycle. An average of once every 2.7 years.

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 18 / 65 Perigee & Apogee

Not to scale

Perigee Apogee 362,600 km 404,400 km

(closest) (farthest)

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 19 / 65 Earth and Moon

ǫ =0.0549 Moon

To relative scale

Earth orbit around Sun

Earth

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

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 20 / 65 Moon at Perigee & Apogee

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 21 / 65 Precession of the Moon’s Perigee

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 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 22 / 65 Anomalistic month

Because the elliptical orbit of the Moon 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 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 23 / 65 Inclination of Moon Orbit

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

ascending node ecliptic 5◦

descending node

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

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 24 / 65 Draconic or Nodical Month

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 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 25 / 65 Libration

Simpliﬁed Picture • Tidal locking: One hemisphere of the Moon faces Earth. • Our ﬁrst view of the far side of the Moon 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 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 26 / 65 Moon Phases: NASA

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 27 / 65 The Moon

Lunar Phases

Months

Eclipses Eclipses Umbra, Penumbra & Antumbra Umbra of Earth Lunar Eclipse Eclipses Descending Node Lunar Eclipse Total Lunar Eclipse Saros 137 Solar Eclipses Fig 2-24 Conditions for Syzygy Fig 2-23 Eclipse Season Solar Eclipse Intervals Predicting Eclipses Saros Cycle Saros Cycle Saros 136 The c 2012-2021G.Anderson.,O.Harris Ancient Universe:Past,Present&Future – slide 28 / 65 Roots of Science Eclipses

Lunar eclipse: Earth’s shadow on Moon.

Solar eclipse: Moon’s shadow on Earth.

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 29 / 65 Umbra, Penumbra & Antumbra

antumbra

umbra penumbra

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

Total Eclipse Partial Eclipse Annular Eclipse

c 2012-2021G.Anderson.,O.Harris Universe:Past,Present&Future – slide 30 / 65 Image Credit & Copyright: Wang, Letian Umbra of Earth Lunar Eclipse

Penumbra

Umbra

No eclipse

Sun