Solution Manual to An introduction to modern astrophysics

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1、CHAPTER1TheCelestialSphere1.1FromFig.1.7,EarthmakesS=P˚orbitsabouttheSunduringthetimerequiredforanotherplanettomakeS=Porbits.IfthatotherplanetisasuperiorplanetthenEarthmustmakeoneextratriparoundtheSuntoovertakeit,henceSSDC1:P˚PSimilarly,foraninferiorplanet,thatplane

2、tmustmaketheextratrip,orSSDC1:PP˚RearrangementgivesEq.(1.1).1.2Foraninferiorplanetatgreatestelongation,thepositionsofEarth(E),theplanet(P),andtheSun(S)formarighttriangle(∠EPSD90ı).Thuscos.∠PES/DEP=ES.FromFig.S1.1,thetimerequiredforasuperiorplanettogofromopposition(p

3、ointP1)toquadrature(P2)canbecombinedwithitssiderealperiod(fromEq.1.1)tofindtheangle∠P1SP2.InthesametimeintervalEarthwillhavemovedthroughtheangle∠E1SE2.SinceP1,E1,andSformastraightline,theangle∠P2SE2D∠E1SE2∠P1SP2.Now,usingtherighttriangleatquadrature,P2S=E2SD1=cos.∠P

4、2SE2/.E1SP1E2P2FigureS1.1:Therelationshipbetweensynodicandsiderealperiodsforsuperiorplanets,asdiscussedinProblem1.2.1.3(a)PVenusD224:7d,PMarsD687:0d(b)Pluto.Ittravelsthesmallestfractionofitsorbitbeforebeing“lapped”byEarth.1.4Vernalequinox:˛D0h,ıD0ıSummersolstice:˛D6

5、h,ıD23:5ıAutumnalequinox:˛D12h,ıD0ıWintersolstice:˛D18h,ıD23:5ı12Chapter1TheCelestialSphere1.5(a).90ı42ı/C23:5ıD71:5ı(b).90ı42ı/23:5ıD24:5ı1.6(a)90ıL<ı<90ı(b)L>66:5ı(c)Strictlyspeaking,onlyatLD˙90ı.TheSunwillmovealongthehorizonattheselatitudes.1.7(a)Boththeyear

6、2000andtheyear2004wereleapyears,soeachhad366days.Therefore,thenumberofdaysbetweenJanuary1,2000andJanuary1,2006is2192days.FromJanuary1,2006toJuly14,2006thereare194days.Finally,fromnoononJuly14,2006to16:15UTis4.25hours,or0.177days.Thus,July14,2006at16:15UTisJD2453931.

7、177.(b)MJD53930.677.1.8(a)˛D9m53:55sD2:4731ı,ıD2ı9016:200D2:1545ı.FromEq.(1.8),D2:435ı.(b)dDrD1:71015mD11,400AU.1.9(a)FromEqs.(1.2)and(1.3),˛D0:193628ıD0:774512mandıD0:044211ıD2:652660.Thisgivesthe2010.0precessedcoordinatesas˛D14h30m29:4s,ıD62ı43025:2600

8、.(b)FromEqs.(1.6)and(1.7),˛D5:46sandıD7:98400.(c)Precessionmakesthelargestcontribution.1.10InJanuarytheSunisatarightascensionofapproxim