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
– First -quarter moon
– Full
moon
– Third-quarter moon
All
Right half
All
Left half
of Moon is
of Moon is
of Moon is
of Moon is
invisible
visible
visible
visible
• Dynamic phases Moon’s change over time
– Waxing
• Crescent moon
• Gibbous moon
– Waning
• Gibbous moon
• Crescent moon
Increasing in apparent size
Right side is less than half visible
Right side is more than half visible
Decreasing in apparent size
Left side is more than half visible
Left side is less than half visible
Static & Dynamic Lunar Phases
Earth & Moon: Both Show Phases!
Galileo spacecraft, 1992
Lunar Rotation & Revolution
• Lunar phases
• Lunar features
Rapidly changing
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 orbital revolution
Sidereal month
• Important to astronomers living on the Moon’s surface
• Synodic month
– The Moon orbits the Earth once relative to the Sun
• ~372.2° of axial
• Important to
rotation
all people
Synodic month
living on the Earth’s surface
Sidereal & Synodic Months
~12.2°
Eclipses & the Line of Nodes
• Isolated
orbital planes
– Earth orbits around the Sun
– Moon orbits around the Earth
Ecliptic
• 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
– Descending node
Moon is moving “above” the ecliptic
Moon is moving North of the ecliptic
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 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
– Partial
Moon passes through Earth’s umbra
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
– Annular Moon looks
• Moon is near apogee
– Partial
Moon appears rather large
too small to cover the Sun
Moon appears rather small
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
on
shore
• Departing ships grow smaller & hulls disappear first
– Observations by
sailors
approaching
shore
• 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°
» Actual
• Critical
Estimated distance ratio ~ 20 : 1
angle of ~ 89° Actual
distance ratio ~ 390 : 1
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
Important Concepts
•
Static lunar phases
•
– New, first quarter, full, third quarter
•
•
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]
•
– Shape of Earth’s shadow on the Moon
– Eratosthenes: Alexandria & Syene
Dynamic lunar phases
– Waxing, waning, crescent & gibbous
Solar eclipses
– Occur only at new moon
– Visible from within lunar shadow
– Partial, full & annular
Earth’s shape & size
•
Earth–Moon–Sun distances
– Estimate lunar phase times
– Measure Earth–Sun–Moon angle