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

– Moon orbits the Earth– Moon moves West to East relative to the Sun– Moon moves West to East relative to the stars

• Secondary patterns– Moon’s angular diameter varies

• Caused by changing distance from the Earth– Moon’s West to East speed varies

• Caused by changing distance from the Earth– Moon’s orbit around Earth tilted ~ 5° to the ecliptic

• Moon is as much as 5° above & below the ecliptic– Almost half of the Moon is never visible from Earth

• Moon’s orbital period & axial rotation period are equal

Lunar Phases: Static & Dynamic• Static phases Moon’s status right now

– New moon All of Moon isinvisible

– First -quarter moon Right half of Moon isvisible

– Full moon All of Moon isvisible

– Third-quarter moon Left half of Moon isvisible

• Dynamic phases Moon’s change over time– Waxing Increasing in apparent size

• Crescent moon Right side is less than half visible

• Gibbous moon Right side is more than half visible

– Waning Decreasing in apparent size• Gibbous moon Left side is more than half

visible• Crescent moon 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 orbit around Earth• Same side of the Moon always faces Earth

– Moon’s orbit around Earth is elliptical• At perigee… Moon is closest to Earth• At apogee… Moon is farthest from Earth

– Moon’s speed around Earth is variable• At perigee… Gravity strongest & orbital speed

fastest• At apogee… Gravity weakest & orbital speed

slowest– Moon’s speed around its axis is constant

• At perigee… Axial rotation lags behind orbital speed

• At apogee… Axial rotation gets ahead of orbital speed

Moon’s “Near Side” Faces Earth

Two Different Months• Sidereal month

– The Moon orbits the Earth once relative to the stars• 360.0° of orbitalrevolutionSidereal month• Important to astronomersliving on the Moon’s surface

• Synodic month– The Moon orbits the Earth once relative to the Sun

• ~372.2° of axial rotation Synodic month• Important to all peopleliving on the Earth’s surface

Sidereal & Synodic Months

~12.2°

Eclipses & the Line of Nodes• Isolated orbital planes

– Earth orbits around the SunEcliptic– 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 w/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 ofthe ecliptic– Descending node Moon is moving “below” the

eclipticMoon 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 sees a lunar eclipse– Similar to many people in a building seeing that building’s shadow

• Lunar eclipses occur only at night– You are looking directly at the Moon, therefore…– Lunar eclipses can be safely seen without filters

• Types of lunar eclipses– Total Moon passes through Earth’s

umbra– Partial Moon passes through Earth’s

penumbra

Geometry of a Lunar Eclipse

Lunar Eclipse Animation

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 ~ 1% Earth’s diameter• Only a small part of Earth sees 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 with filters• Types of solar eclipses

– Total Moon looks big enough to cover the Sun• Moon is near perigee Moon appears rather

large– Annular Moon looks 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

Solar Eclipse Animation

A Total Solar Eclipse (Snapshot)

A Total Solar Eclipse (Time-Lapse)

Annular Solar Eclipse (Time Lapse)

In Latin, “annulus” means “ring”

Total Solar Eclipse Paths on Earth

http://eclipse.gsfc.nasa.gov/SEatlas/SEatlas3/SE2001-25T-1.GIF

Earth’s Shape & Size• Ancient people knew that Earth is spherical

– Earth’s shadow on the Moon is always circular• Only possible if the Earth is a sphere

– Observations by port residents onshore• Departing ships grow smaller & hulls disappear first

– Observations by sailors approachingshore• Mountains grow 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° proportional to (A-to-S distance) / (Earth circumference)

Accurate to ~ 2.5% ! ! !

Eratosthenes & Earth’s Diameter

Relative Earth-Moon-Sun Distances• Aristarchus’ exercise in applied geometry

– Earth-Moon-Sun distance~ 280 B.C.

• Earth-Moon-Sun form right triangle at 1st & 3rd quarters• Critical measurements

– Determine time of first & third quarter moons– Measure Earth-Sun-Moon angle at 1st & 3rd

quarter moons» Estimated angle of ~ 87° Estimated distance ratio

~ 20 : 1» Actual angle of ~ 89° Actual

distance ratio ~ 390 : 1

• Critical problem– Determine time of 1st & 3rd quarter moons– Almost impossible to do with available technology

Geometry of Earth-Sun Distance

Partial Lunar Eclipse from Discovery

Solar Eclipse of 4 January 2011

Solar Eclipse 2011: Graz, Austria

Lunar Eclipse: 2008

• Static 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

Important Concepts