1Announcements• Homework 2 is now available onthe OWL• Due 10/01/08 before midnight• 1st midterm: 10/2/08• Midterms will be “pyramid”exams: 75% of grade from in-class exam, 25% from take-home exam (same exam)• If you don’t do the take-homepart, then 100% of the grade willbe based on the in-class examscoreAstronomy 101: 9/30/2008Exam study materials are posted on the course web page,and a practice exam is available in OWL.PRS is on - please join!After Copernicus and Kepler,philosophers still adhered to the Greekmodel for 3 reasons:1. Falling objects should be left behind if theEarth moves2. The heavens must be perfect andunchanging3. Stellar parallaxFinal key scientist in this story:Galileo Galilei2Galileo’s arguments against theGreek objections:1. Used experiments to show that objects in motion tend toremain in motionFor example, Galileo argued that objectsin motion tend to remain in motion. Thisexplains why falling objects are not leftbehind when the Earth moves — they arealready in motion with the Earth, andthey remain in motion with the Earth asthey fall.Galileo’s arguments against theGreek objections:1. Used experiments to show that objects in motion tend toremain in motion2. Many observations (with the new-fangled inventioncalled the telescope showed that the heavens are farfrom perfect (e.g., spots on the Sun, jagged mountainsand valleys on the Moon)3. The Milky Way indicated that stars are far morenumerous than thought, and probably much moredistant than appreciated3Galileo’s Observations• Galileo saw shadows cast bythe mountains on the Moon.• Observed craters.• The Moon had a landscape; itwas a “place”, not a perfectheavenly body.• The Sun has nasty little spotson it — not a perfect thing!Galileo’s Observations• Galileo discoveredthat Jupiter had fourmoons of its own.• Jupiter was thecenter of its ownsystem.• Heavenly bodiesexisted which didnot orbit the earth.4Galileo’s observation of the phases of Venus wasthe final evidence which buried the geocentricmodel.Geocentric HeliocentricNo gibbous or full phases! All phases are seen!Galileo observed all phases!Recent Observations (2004)of Phases of Venus5Why don’t we see solareclipses more often?The umbra sweeps across a relatively small area on the surface of the Earth, and it moves quickly -- the shadowmoves across the surface at roughly 1,700 km/hour.Opportunities to observe a total solar eclipse are rare! The diameter of the umbra is ~270 km; the diameter of the penumbra is ~7000 km.(not to scale!) Solar eclipse…6The umbra sweeps across a relatively small area on the surface of the Earth, and it moves quickly -- the shadowmoves across the surface at roughly 1,700 km/hour.Opportunities to observe a total solar eclipse are rare! The diameter of the umbra is ~270 km; the diameter of the penumbra is ~7000 km.(not to scale!) Solar eclipse…These diameters depend on the Earth-Moon distance.If the Moon happens to be farther away at the time ofthe eclipse, the umbra diameter will be smaller (or evenzero if the umbra is above the surface of the Earth).O.K., the Moon casts a small shadow on theEarth. But, the Earth casts a big shadow onthe Moon. Why don’t we see lunar eclipsesmore often?7Why don’t we see eclipsesmore often?• Shouldn’t somebody see an eclipse at every new moonand every full moon? Solar eclipses seem to be quiterare; why?• Answer: the Moon’s orbit is tilted by 5 ° with respectto the Earth’s orbit (the “ecliptic plane”)Above: edge-on view of the Moon’s orbit, drawn to proper scale.When full and new moons occur near nodes, eclipses canhappen.The plane of the Earth’s orbit around the Sunis the ecliptic plane, here represented by thesurface of a pond.• Moon’s orbit tilted 5° to ecliptic plane– Crosses ecliptic plane only at the two nodes– Eclipse possible only when full/new Moons occurnear nodes8Summary: EclipsesWhen the Moon’s orbit intersects theecliptic plane:at new moonsolar eclipseat full mooneveryone on the nighttime side of Earth can see itlunar eclipseyou must be in Moon’s shadow to see itwithin umbra: total solar eclipsewithin penumbra: partial solar eclipseShouldn’t eclipses occurevery 6 months?Additional complication: the Moon’s orbitprecesses, i.e., it wobbles like a child’s top.9When the rotation axis of an objectslows changes direction, this is calledprecession.The Earth’s axis of rotation precesses, like the motion of a top.The Moon’s orbit also precesses.Due to this precession, the nodes shift, and the eclipse “seasons” occur less than 6 months apart.The combination of the shifting eclipse seasons and theMoon’s 29.5 day cycle leads to a complicated cycle thatrepeats every 18 years and 11.5 days. The “saros cycle”10Remarkably, some ancient astronomers were able torecognize the saros cycle and predict eclipse dates. Today,we can predict eclipse times with tremendous precision.• Note thatwhile thesaros cyclepredicts thedate of aneclipse, theposition ofthe shadowon theEarth shiftsMeasuring relations in the skyWe often measure the sky in angles, not distances.• Full circle = 360º• 1º = 60 arcmin• 1 arcmin = 60 arcsec11Measuring Angles in the Sky:Some points of referenceFor an object with a fixed size (a fixedlinear diameter), its angular diameterdecreases when the object’s distance isincreased.Angle (in radians) = linear diameter/distanceFull circle = 360°Full circle = 2π radians(π = 3.141592654)360° = 2π radians12PRS Question — working with anglesJupiter is about 5 times farther from theSun than the Earth is. If the angulardiameter of the Sun is about 0.5 degrees asseen from the Earth, then how manydegrees wide is the Sun as seen fromJupiter?• Enter a numeric answer into yourPRS unit.Answer: if we move an object five times farther away, its angulardiameter will be five times smaller. So, 0.5/5 = 0.1 degrees. Viewed from Jupiter, the angular diameter of the Sun is 0.1 degrees.PRS calculation:How Big is the Moon?• The angular diameter of the Moon is 0.5degrees.• In radians, the angular diameter is 0.0087radians. Roughly, ang. diameter = 0.009• The distance to the Moon is 384,000 km.For this calculation, use distance = 400,000km• HOW BIG IS THE MOON?13PRS calculation:How Big is the Moon?• Roughly, ang. diameter = 0.009• Roughly, distance = 400,000 km• The linear diameter of the Moon is1. 300 km2. 3,600 km3. 10,000 km4. 36,000 km5. 100,000 kmAngle (in