3. Lunar Motions & Eclipses

1. 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

2. 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

3. 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

4. Static & Dynamic Lunar Phases

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

6. 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

7. Moon’s “Near Side” Faces Earth

8. 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

9. ~12.2° Sidereal & Synodic Months

10. 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

11. ~ 5.2° Orbital Inclination & the Line of Nodes

12. 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

13. Geometry of a Lunar Eclipse Lunar Eclipse Animation

14. Partial Lunar Eclipse (Time-Lapse)

15. The Line of Nodes & Eclipses

16. 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

17. Geometry of a Solar Eclipse Solar Eclipse Animation

18. A Total Solar Eclipse (Snapshot)

19. A Total Solar Eclipse (Time-Lapse)

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

21. Total Solar Eclipse Paths on Earth http://eclipse.gsfc.nasa.gov/SEatlas/SEatlas3/SE2001-25T-1.GIF

22. 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% ! ! !

23. Eratosthenes & Earth’s Diameter

24. 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

25. Geometry of Earth-Sun Distance

26. Partial Lunar Eclipse from Discovery

27. Solar Eclipse of 4 January 2011

28. Solar Eclipse 2011: Graz, Austria

29. Lunar Eclipse: 2008

30. 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