3. Lunar Motions & Eclipses Lunar motions & lunar phases Lunar axial rotation & orbital revolution Eclipses & the line of nodes Lunar eclipses Solar eclipses Relative Earth–Moon–Sun distances

Lunar Motions Primary patterns Secondary patterns The Moon orbits the Earth The Moon moves West to East relative to the Sun The Moon moves West to East relative to the stars Secondary patterns The Moon’s angular diameter varies This is caused by changing distance from the Earth The Moon’s West to East speed varies The Moon is as much as 5° above & below the ecliptic The Moon’s orbit around Earth is tilted ~ 5° to the ecliptic Almost half of the Moon is never visible from Earth The Moon’s orbital period & axial rotation period are equal The Moon’s orbital velocity is constantly changing The Moon’s axial rotation is remarkably constant

Lunar Phases: Static & Dynamic Static phases Moon’s appearance right now New moon All of the Moon is invisible First-quarter moon Right half of the Moon is visible Full moon All of the Moon is visible Third-quarter moon Left half of the Moon is visible Dynamic phases Moon’s change right now Waxing Increasing in apparent size Crescent Right side is less than half visible Gibbous Right side is more than half visible Waning Decreasing in apparent size Gibbous Left side is more than half visible Crescent Left side is less than half visible

Static & Dynamic Lunar Phases

Earth & Moon: Both Show Phases! Galileo spacecraft, 1992

Lunar Rotation & Revolution Lunar phases Rapidly changing Lunar features Slowly changing Moon rotates once for every one revolution around Earth Same side of the Moon always faces toward Earth Moon’s orbit around the Earth is elliptical At perigee… Moon’s orbital location closest to the Earth At apogee… Moon’s orbital location farthest from the Earth Moon’s speed around the Earth is variable At perigee… Gravity is strongest & orbital speed is fastest At apogee… Gravity is weakest & orbital speed is slowest Moon’s speed around its axis is constant At perigee… Axial rotation lags behind orbital speed Right-hand edge of the Moon moves slightly into view At apogee… Axial rotation gets ahead of orbital speed Left-hand edge of the Moon moves slightly into view

The Moon’s “Near Side” Faces Earth

Two Different Months Sidereal month Synodic month The Moon orbits the Earth one time relative to the stars 360.0° of orbital revolution Sidereal month Important to astronomers on the Moon’s surface There are none of these right now! Synodic month The Moon orbits the Earth one time relative to the Sun ~ 372.2° of axial rotation Synodic month Important to all people on the Earth’s surface There are lots of these right now!

Sidereal & Synodic Months ~12.2°

Eclipses & the Line of Nodes Isolated orbital planes Earth orbits around the Sun Ecliptic Moon orbits around the Earth Tilted ~ 5.2° relative to the ecliptic Intersecting orbital planes Any two planar surfaces intersect in a straight line Each intersection of this line with an orbital path is a node The entirety of this line is the line of nodes Planes of the Earth’s & Moon’s orbits intersect Line of nodes Ascending node Moon is moving above the ecliptic Moon is moving North of the ecliptic Descending node Moon is moving below the ecliptic Moon is moving South of the ecliptic Points at which Moon & Sun appear to cross in the sky Only points in the sky where eclipses can occur

Orbital Inclination & the Line of Nodes ~ 5.2°

Lunar Eclipse Basics Lunar eclipses occur only at full moon The Earth moves between the Sun & Moon The Earth’s shadow falls on the Moon The Earth’s shadow is quite large ~ 3.8 times the Moon’s diameter An entire hemisphere of the Earth experiences a lunar eclipse Similar to many people in a building seeing that building’s shadow Lunar eclipses occur only during nighttime hours You are looking directly at the Moon, therefore… Lunar eclipses can be safely observed without filters Types of lunar eclipses Total Moon passes through the Earth’s umbra Partial Moon passes through the Earth’s penumbra

Geometry of a Lunar Eclipse

A Partial Lunar Eclipse (Time-Lapse)

The Line of Nodes & Eclipses

Solar Eclipse Basics Solar eclipses occur only at new moon The Moon moves between the Sun & Earth The Moon’s shadow falls on the Earth The Moon’s shadow is quite small ~ 1% of the Earth’s diameter Only a small part of the Earth experiences a solar eclipse Similar to a few people outdoors being in an airplane’s shadow Solar eclipses occur only during daytime hours You are looking directly at the Sun, therefore… Solar eclipses must be observed only with filters Types of solar eclipses Total Moon appears large enough to cover the Sun Moon is near perigee Moon appears rather large Annular Moon appears too small to cover the Sun Moon is near apogee Moon appears rather small Partial Moon is not directly in line with the Sun

Geometry of a Solar Eclipse

A Total Solar Eclipse (Snapshot)

A Total Solar Eclipse (Time-Lapse)

An Annular Solar Eclipse (Time Lapse) In Latin, “annulus” means “ring”

Total Solar Eclipse Paths on Earth

Earth’s Shape & Size Ancient people knew that the Earth is spherical Earth’s shadow on the Moon is always circular Only possible if the Earth is a sphere Observations by port residents on shore Departing ships appear smaller & hulls disappear first Observations by sailors approaching shore Mountains appear larger & tops appear first Ancient people calculated Earth’s diameter Eratosthenes ~ 200 B.C. Lived in Alexandria & often traveled due South to Syene Summer solstice Sun was ~ 7° away from vertical at Alexandria Summer solstice Sun was almost exactly vertical at Syene Knew the distance from Alexandria to Syene (7°) / (360°) is proportional to (A to S distance) / (Earth circumference) Accurate to ~ 2.5% ! ! !

Eratosthenes & the Earth’s Diameter

Relative Earth–Moon–Sun Distances Aristarchus’s exercise in applied geometry Earth–Moon–Sun distance ~ 280 B.C. Earth–Moon–Sun form a right triangle at first & third quarters Critical measurements Determine time of first & third quarter moons Measure Earth–Sun–Moon angle at first & third quarter moons Estimated angle of ~ 87° Estimated ratio of distances = ~ 20 : 1 Actual angle of ~ 89° Actual ratio of distances = ~ 390 : 1 Critical problem Almost impossible to do with available technology

Geometry of the Earth-to-Sun Distance

Important Concepts Static lunar phases Dynamic lunar phases New, first quarter, full & third quarter Dynamic lunar phases Waxing, waning, crescent & gibbous Moon–Earth distance Perigee & apogee Different months Sidereal & synodic months Eclipses & the line of nodes Ascending & descending nodes Lunar eclipses: Earth’s shadow Occur only at full moon Visible from half the Earth Partial [penumbral] & full [umbral] Solar eclipses Occur only at new moon Visible from within lunar shadow Partial, full & annular Earth’s shape & size Shape of Earth’s shadow on the Moon Eratosthenes: Alexandria & Syene Earth–Moon–Sun distances Estimate lunar phase times Measure Earth–Sun–Moon angle