3. Lunar Motions & Eclipses. Lunar Phases: Static & Dynamic. Static & Dynamic Lunar Phases. Earth & Moon: Both Show Phases!

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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 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 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 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

2 Moon s Near Side Faces Earth Two Different Months Sidereal month The Moon orbits the Earth once relative to the stars 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 rotation Synodic month Important to all people living on the Earth s surface 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 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 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

3 Geometry of a Lunar Eclipse Partial Lunar Eclipse (Time-Lapse) Lunar Eclipse Animation 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 A Total Solar Eclipse (Snapshot) Solar Eclipse Animation

4 A Total Solar Eclipse (Time-Lapse) Annular Solar Eclipse (Time Lapse) In Latin, annulus means ring Total Solar Eclipse Paths on Earth 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 1 st & 3 rd quarters Critical measurements Determine time of first & third quarter moons Measure Earth-Sun-Moon angle at 1 st & 3 rd 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 1 st & 3 rd quarter moons Almost impossible to do with available technology

5 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 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

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