PHYS 228 Astronomy.doc

PHYS228Astronomy&&theSolarSystemHeliocentricModelofCopernicusGeneralTerms:-orbitsclosertoSunthanEarth(-2)-orbitsfartherfromSunthanEarth(-2)sSynodicperiod-toreturntosamepositioninsky,relativetoSun,asseenbyEarthSiderealperiod-pleteoneorbitw/:LetS=,P=,E=siderealperiodofEarth==1/P-1/1/S=1/E-1/Defn:AstronomicalUnit:AverageorbitalradiusofEarthKepler’sweepsoutequalperiodsinequaltimesP2=a3GeometricalPropertiesofEllipticalOrbitsr+r’=2a=constant(1-1)bydefnofellipseb2=a2-a2e2=a2(1-e2)(1-2)fromPythagoreantheoremwhere a=semimajoraxisofellipseb=semiminoraxise=eccentricityr=a(1-e2)/(1+ecosq)(1-3)equationofellipseA=pab(1-5) areaofellipsee=(ra-rp)/(ra+rp) eccentricityofellipsera/rp=(1+e)/(1-e) ratioofapheliondistancetoperiheliondistancera+rp=2a relationbetweenaphelion/periheliondistancesandmajoraxis rp=a(1-e) relationsbetweenaphelion/periheliondistances,semimajor ra=a(1+e) axis,entricityLawofAreasandAngularMomentumdA/dt=rvt/2=r2(dq/dt)/2=H/2=A/P=pab/PKepler’s2ndlaw-ofareasv2=G(m1+m2)[2/r-1/a] visvivaequation(velocityatanypointrinorbit)vper=2pa/P[(1+e)/(1-e)]1/2 velocityatperihelionvaph=2pa/P[(1+e)/(1-e)]-1/2 velocityataphelionNewtonianMechanicsLawofinertiaF=maEqualbutoppositeforces(action&reaction)Newton’sLawofUniversalGravitationFcent=mv2/r(1-14)v=2pr/PFgrav=GMm/r2(1-15)whereG=-11m3/=(GMÅ/RÅ2)m=gm=mgW=mgWeightwhereg=’sFormofKepler’s3rdLawP2=4p2/G(m1+m2)a3PHYS228Astronomy&:ecliptic prograde(direct)WseenfromaboveEarth’sorbitalplanesynchronousrotation- e=(re-rp)/s-Mercury,Venus,Earth,Marsrelativelysmall,lowmasssimilarorsmallerthanEarth’position®s-Jupiter,Saturn,Uranus,Neptunelarge,highmass(15to318MÅ)liquid&p®-heavyelementssinktocenter,lightelementsrisetosurface ExplainsEarth’sNi-Fecore,butlightsilicaterocksincrust stohaverockycores,surroundedbylightH&HeAvera