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XX(XXXX(XXX(  _,X(XXX(   'NAME_________________________________    _ROEMER_,JUPITER,ANDTHESPEEDOFLIGHT  b   L :5h(#;L <3   <325h  1  .3  0 '   LaunchStarryNight,andintheToolBox,clickonLocation.IntheTimeZonefield,enterthe  d number0andclickonSetLocation.ThisinstructsStarryNighttodisplaytimeanddateinUniversaltime.<3 ݌ '(#'(# Ќ  0 ' Nowchooseanequatorialorientation,andturnoffthedaylight.IntheTimeTool,enterthedateJuly21,2002,andthetime12:00:00AM(=0:00:00UT).FindJupiter.Changethefieldofviewto5o,andnotethatJupiterisquiteclosetotheSun.Thisaspectiscalledconjunction, x  whentheSunisbetweentheEarthandJupiter,andJupiterisfarthestfromtheEarth. '(#'(# 0 '  2. ' Changehefieldofviewto3'.ThiswillallowustoseeJupiterasitappearsthroughatelescope ` nearthatdate.AdvancethetimebyhoursuntilJupitersmoonIoentersthefieldontheleft.Continueadvancingbyhours,thenbyminutestobringIototheeastlimb(edge)ofJupiter.ThetimeisknownasBX3~XX,X(ingress#,X(XXBX3~#.RecordthisingresstimeinUT(upperrightofthescreen)in  TableI. '(#'(# 0 ' Continueadvancingthetimebyhours,thenminutestofindthetimeofBX3~XX,X(egress#,X(XXBX3~#.Recordthistime t inUTinTableI. '(#'(# 3.0 ' Inapreviousexperiment,wedeterminedthatthesynodicperiodofJupiter(thetimebetween  \ successiveconjunctions)isabout400days.Inanotherexperimenttoinvestigate_Kepler_'slaws,wediscoveredthattheperiodofIo'sorbitaroundJupiterisabout1.77days.Soin400days,Iowillexecuteabout400/1.77 225orbits.Letuschoosetomoveforward224orbitsintime  (since224isanevennumberandwewillneedtodivideby2soon).Thatmeansweneedtoadd224'1.77 396.5daystoJuly21,2002togiveusthenextdatenearconjunction. '(#'(# swC?/+bz0$ `@EI#M"JJsswC?/+bz0$ `@Eb"M"JJs0 ' IntheTimeTool,changethetimestepto396daysandsteponce.NoticethepositionofIo, V"! comingaroundJupitertoagaintransititsface.Advancethetimebyhours,thenbyminutestobringIototheeastlimb(edge)ofJupiter.RecordthisingresstimeinUTinTableI. '(#'(# 0 ' Continueadvancingthetimebyhours,thenminutestofindthetimeofegress.RecordthistimeinUTinTableI. '(#'(# 0 '  4. ' Fromthedifferenceinthetimesofingressandegress,computethetwomidtransittimes.Enter )$) thesetimesinhoursandminutesinTableI. '(#'(# 0 ' Changethisdifferenceinhoursandminutestodecimalpartsofaday,addthisvalueto396,andentertheresultingelapsedtimeintoTableI. -n(-'(#'(# *./ ddd Xdd Xdd X(#(#, d ,etd ,td ,` t +  100" b 1TABLEI ;01,! Z"00 ;INGRESS ;01,! Z"01 ;EGRESS ?010,! Z"01 ?MIDTRANSIT S00D, Z"   010 SAugust21,2003TRANSIT 201# 00 2 201#  01 2 6010#  01 6 J10;#     010 qJJuly21,2002TRANSIT 211# f 10 2 ;11,! f "11 ; 6110# f11 6 P10-;# f  q 110 qP 811-# 10- 8 811-# 11- 8 6110# 11- 6,-jX,X(difference=,X(X,-jԀh󀀀m P10-;#   q 110 PP 811-#R 10- 8 811-#R 11- 8 6110#R 11- 6,-jX,X(difference=,,,-jdays,X(X, L100;#R   P 110 8L,-jX,X(Elapsedtime=396+differenceindays,X(X,-j 8110-#x 100 8 8110-#x 110- 8 61100#x 110- 6b!b!F",-jX,X(days,X(X,-jԈ3)'x  8   1100 35.0 ' WemaynowcomputeaveryprecisevaluefortheperiodofIo,bytakingtheelapsedtimefrom b  TableIaboveanddividingby224orbits.Recordtheresultbelow, andinclude7placesafter H thedecimalpoint ..~'(#'(# 0 ' 0@'7PeriodP=elapsedtime/224=____________________days. '(#'(# 6.0 ' NowletusmovethesimulationtoatimewhenJupiterandEarthareasclosetogetherasthey $ canbeanaspectwecallopposition.Thatwouldbe112IoorbitsfromtheJuly2002start, % sincewechose224IoorbitstobeacloseestimateofthesynodicperiodforJupiter.Calculatethetimenecessaryfor112Ioorbits. '(#'(# 0 ' 0@'7dayselapsedsinceJuly21,2002=112'P=___________________days. '(#'(# 7.0 ' TheexpecteddateoftheabovecalculationisFebruary4,2003.Theexpectedtimeiscomputed ,, bychangingthedecimalportionoftheelapsedtimeinpart6abovetohoursandminutes: '(#'(# $4hw$0  04(#(#_____h_____m"/4(#4(# 0  +04(#(#_____h_____m0h4(#4(#0@h7thenaddingtheabovehoursandminutestothemidtransit Z$1 timeoftheJuly2002transitfromTableIabove, h(#h(# 0   (#(# 0  =04(#(#_____h_____m0h4(#4(#=expectedmidtransittimeonFebruary4,2003. '\"4h(#h(# 0  04(#(#0h4(#4(#RecordinTableIIbelow h(#h(# *'h44*  (($6 0 ' SetthesimulationbyenteringFebruary4,2003,andtheexpectedmidtransittimeyoucomputedabove.Notice: '(#'(# -'4h'` -0 ' 0'(#'(#a)04(#(#Jupiterappearslargerinthisviewthaninthepreviousviews.Why?. ~4(#4(# 0 ' 0'(#'(#b)04(#(#0' h'440Ioisapproximatelywhereitshouldbe,transitingJupiter.However,Ioisnotdirectlyin ^  frontofJupiter!Actually,youcanseethatmidtransittimeoccurredearlier.ThisisduetothefactthattheEarthisnowclosertoJupiter,andthelightcomingfromJupiterhasarrivedearlier.Thisdifferencebetweentheexpectedandobservedmidtransittimesisrelatedtothespeedoflight. 4(#4(#  4(#4(# 0 '  '(#'(# 8.0 ' AdjustthetimebyhoursandminutestofindthetimeofIosingress,thenegress.Recordthese  timesintheTablebelow. '(#'(# 0 ' Calculatethedifferenceinminutesbetweentheobservedmidtransittimeandtheexpectedmidtransittime.ThisdifferenceisaresultofthenearnessofEarthtoJupiter:thelightarrivesatEarthearlierthanweexpected.Compute,as_Roemer_Ԁdidin1675,thevalueofthespeedoflight. '(#'(# *23 dd d etd etd ` t ` ./(#(#, d ,td ,td ,4t +  100"  1TABLEII ;01,!f"00 ;INGRESS ;01,!f"01 ;EGRESS ?010,!f "01 ?MIDTRANSIT S00D,f!"  010 S,-jX,X(Feb4,2003EXPECTEDTRANSIT,X(X,-j 801-# D"00 8 801-# D#01- 8 6010# D$01- 6 J10;# D%  010 qJ,-jX,X(Feb4,2003OBSERVEDTRANSIT,X(X,-j 211#b"&10 2 ;11,!b"'"11 ; 6110#b"(11 6 P10-;#b") q 110 qP 811-## *10- 8 811-## +11- 8 6110## ,11- 6,-jX,X(difference=,X(X,-jԀ򀀀min H1007## - q 110 HH,-jX,X(C=Speedoflight= >% . Ѐ300,000,000km/difference/60= 8110-#%N!/100 8 8110-#>% 0110- 8 61100#>% 1110- 6C=km/sec3)'%N!3 0 H  1100 3 <(#,,|,,-j204MarchJanuary_20012_