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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

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3 lunar motions eclipses
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
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
Lunar Phases: Static & Dynamic
  • Static phases Moon’s status right now
    • New moon All of Moon is invisible
    • First-quarter moon Right half of Moon is visible
    • Full moon All of Moon is visible
    • Third-quarter moon Left half of Moon is visible
  • Dynamic phases Moon’s change over time
    • Waxing Increasing in apparent size
      • Crescent moon Right side is less than half visible
      • Gibbousmoon Right side is more than half visible
    • Waning Decreasing in apparent size
      • Gibbousmoon Left side is more than half visible
      • Crescent moon Left side is less than half visible
lunar rotation revolution
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
two different months
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 rotationSynodic month
      • Important to all people living on the Earth’s surface
eclipses the line of nodes
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 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 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
lunar eclipse basics
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
Geometry of a Lunar Eclipse

Lunar Eclipse Animation

solar eclipse basics
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
Geometry of a Solar Eclipse

Solar Eclipse Animation

total solar eclipse paths on earth
Total Solar Eclipse Paths on Earth

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

earth s shape size
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 verticalat Syene
      • Knew the distance from Alexandria to Syene
        • 7° / 360° proportional to (A-to-S distance) / (Earth circumference)

Accurate to ~ 2.5% ! ! !

relative earth moon sun distances
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
important concepts
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