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`Astronomy100 Homework#2Solutions 1,Problem327(2pts).AccordingtoKepler'sthirdlaw,(b)JupiterorbitstheSun morequicklythanSaturn.Becausethesemimajoraxisissmaller,theorbitalperiod P=a3/2willbesmaller. 2.Problem340(2pts).TherecentlydiscoveredobjectSednaorbitsoursun beyondPluto,atanaveragedistanceof509AU.Whatisitsorbitalperiod? a=509AU,P2=a3. P=a3/2=5093/2=11,480years 3.Problem341(3pts).TherecentlydiscoveredEris,whichisslightlylargerthan Pluto,orbitstheSunevery560years.Whatisitsaveragedistance(semimajoraxis) fromtheSun?HowdoesitsaveragedistancecomparetothatofPluto? a=P2/3=5602/3=67.9AU.ThisisfurtherfromtheSunthanPluto,whichhasa semimajoraxisof~40AU. 4.Problem428(2pts).Whenvisitinganotherplanet,(b)yourmasswouldbethe sameasonEarth,butyourweightwouldbedifferent.Weightdependsonthe strengthofgravity. 5.Problem434(2pts).IfEarthweretwiceasfarfromtheSun,theforceofgravity attractingEarthtothesunwouldbe(c)onequarterasstrong.Gravityfollowsan inversesquarelawinproportiontodistance. 6.Problem436(2pts).IftheMoonwereclosertotheEarth,hightideswouldbe (a)higherthantheyarenow.AstheMoongetscloser,thegravitationalforceof attractionincreases.Thedifferenceintheforceofattractionbetweendifferentparts ofEarthandtheMoonwillalsoincrease. 7.Problem444(3pts).Imagineanothersolarsystem,withastarofthesamemass astheSun.Supposethereisaplanetinthatsolarsystemwithamasstwicethatof Earthorbitingatadistanceof1AU,whatistheorbitalperiodofthisplanet?Explain. MakingtheapproximationMPlanet&lt;&lt;MStar,Newton'sversionofKepler's3rdLawtells usPPlanet2=aPlanet3/MStar(solarmasses).Sincethemassofthestarhasn'tchangedin thisproblem,M=1andP=a3/2=(1AU)3/2=1year. 8.Problem445(4pts).Supposeasolarsystemhasastarthatisfourtimesas massiveasourSun.IfthatsolarsystemhasaplanetthesamesizeasEarthorbiting atadistanceof1AU,whatistheorbitalperiodoftheplanet?Explain. Again,Newton'sversionofKepler's3rdLawisPEarth2=aEarth3/M(solarmasses). Here,M=4.SoP2=a3/4=(1AU)3/4=0.25.P=0.25=0.5years. ExtraCredit:Problem442(+2pts).UsethedatainTable4.1toanswereachofthe followingquestions. a)Comparetheenergyofa1megatonHbombtotheenergyreleasedbyamajor earthquake. Theenergyreleasedbyanearthquakeis2.5*1016J/4*1015J=6.25timeslarger b)IftheUnitedStatesobtainedallitsenergyfromoil,howmuchoilwouldbe neededeachyear? AnnualUSenergyconsumption/Energyreleasedbyburning1literofoil=1020J/ 1.2*107J=8.3*1012litersofoil. c)ComparetheSun'sannualenergyoutputtotheenergyreleasedbyasupernova. Theenergyreleasedbyasupernovais~1044J/1034J=1010timeslarger.`

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