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TheDraconides2011andcomets!
Writtenby:AndreasMsvraaGaardeGad&VibePrimdahlTnnes
HighSchool:AlssundgymnasietSnderborg,GrundtvigsAll86,DK-6400Snderborg,Denmark
Teacher:MichaelLentferJensen
Mail:[email protected]
Phone:+4540883618
Figure1:MeteorOctober8thduringthedraconidmeteorshower
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Draconides!lotsofshootingstarsoncoldandcleardanishnight.
WehaverecentlybeenwatchingthemeteorshowercalledDraconidesonOctober8th
2011.We
countedatotalof204shootingstarsinjust2hoursandfiveminutes!
Themaximumfrequencyofshootingstarsweobservedwas3.8perminute!Andtheaveragewas
1.6perminute.
Wedividedtheobservationtimeinintervalsof5minutesandnotedeverysinglemeteorwitha
pencilonapostitnote.Theoutcomeofourobservationsispresentedinfigure2.
Figure2:Numberofmeteorsobservedin5minutesintervals.
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ComparingourobservationswiththeobservationsofNasathereareclearlyagreements.Nasahas
predictedthemaximuminthedraconidmeteorshowerat21:11(CEST=UT+2h)Danishtime(DT)
and 21:40, and our maximum is approximately 22:05. This Is close
to the prediction. Nasa
predictedveryhighactivityuntilalmost22:53(DT)whichfitsourobservation.Afterthattime,the
amountofobservationsfelldrastically.
Under the observation we clearly felt the increase of meteor
shower observed during the
predictedmaximumtime.
Figure3:Timepredictionsforthedraconidmeteorshower,NASA.[1]i
The meteors show upsince the Earth ishit bydusty filaments from
the Comet21P/Giacobini-
Zinner.
Butwhatisactuallyholdingcometsintotheirorbitaroundthesun?
Letusstartwithalookonforcesofacircularmotion:
= !
Fcircle
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Thecircleforceiscausedbythegravityofthecentralobject.Thisgoesfortheplanetsaswell.
AsNewtondescribesthroughhisdifferentlawsofphysicstwoobjectswithamassesmandMand
theradiusr,drageachotherwithaninternalgravity.Seetheformulabelow:
=!
!
!
!!
= 6,6710!!! !!!!!!!
Thisisoneofthemostimportantformulasintheuniverse.Thislawexplainswhyallcomet
remainsandmeteoritesintheearlydayswereformedintoplanetslikeourownearth.
Conclusion:
Wehavenowintroducestheformulaforgravityandcircular
motion.
IsaacNewtonwasoneofthefirsttoconsiderthepossibilityfor
travelinspace.
OneofIsaacNewtonsideasdealtwithplacingacanonona
mountain.Ifyoushootofthecanonballitwouldland
somewhereontheearth(spotA).Ifyouincreasedthespeedof
thecanonballunderthefiring,theballwouldlandfurther
away(spotB).
Newtonsideawasthatifyouincreasedthespeedontheballenough,itwouldntland,but
continueorbitingtheplanet.
Inasituationlikethistheballwillremaininaperfectcircularorbitaroundtheplanet.Therefore
theforcesofgravityandtheforceofthecirclewillequaleachother:
!"#!$% = !"#$%&'
!
= !
!
=
!
Asshownbyreducingtheformulathesmallmass(satellite)canbereducesonbothsides,and
thereforeithasnoeffectontheforcesbetweenthetwoobjects.
Figure4-pictureofearth,canonand
canonball
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Byreducingfurtherwiththeradiuswegetthefollowingformula:
!=
Fromtheformulaaboveitisclearthatthespeedofthesatelliteisindependentofitsownmass.
Whenthesatelliteisorbitingaroundtheearthitisimpossibletodefinethemassofthesatellite.
Keplerslawsofcircularmotion:
Ifwelookattheformulafrombefore:
!=
Acirclehasacircumference:2
ThetimeittakesforourplanettorunthroughanorbitiscalledT
Thereforewecandescribethespeedofourplanetwiththedistanceintheorbitdividedwiththe
timeoftheorbit.
=
=
2
Assignment1:
Nowwecancombinethetwodifferentformulas.
=!!!
!and! =
!!
!
2
!
=
4 !
!
!=
4 !
!=
!
!
!=
4 !
4 !
=
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Thereforeformulacanbedescribedas:
!
!=
Thisclearlyshowsthattimeoftheorbitandtheradiusisdependentoneachother.
Anellipseisacircle$,andinmostaspectsoftheuniverseobjectsdoesntmoveincircularorbits
butinellipses.
Figure5-drawingofanellipse
Thedrawingaboveshowsanobjectmovingaroundourownsun.F.eks.acometorasmallplanet.
Thelonghorizontalradiusoftheellipseiscalleda(red),andtheshortverticalradiusoftheellipse
iscalledb(green).
Thesunisnotplacedinthecenteroftheellipse,butplacedinthefocalpointoftheellipse.The
distancebetween(0,0)thecenteroftheellipseandthesuniscalled
asshownonthefigure.
Comparingtotheearthandthesuntheeccentricity = !
!",andthesunisthereforealmostinthecenteroftheellipse.
Awaytofindbiswiththisformula:
= (1 !)
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Assignment2
Wewillfindbwhene=0,andexplainwhathappenstothelengthof
= 1 0!
=
Thisshowsus,thatwhene=0,thesunisinthecenteroftheellipse.Thisalsomeansthatthe
ellipseisnowaperfectcircle,becausethelengthofaandbarethesame.
Keplerslove
JohannesKepler1571-1630expressedaseriesoflawsrevolvingtheplanetsorbitingaroundthesun,basedontheobservationsoftheDanishastronomerTychoBrahe.
1.Law:
Allplanetsmoveinellipticorbitswiththesuninoneofthefocalpoints.(1609)
2.Law:
Radiusvector-thelinethatgoesfromthesunandouttotheplanetoverrunsthesameareapr
time.(1609)lookatfigure6below.
3.Law:
!!
!!= =
!!!
!!(1618)
Thesecondlawiseasiestdescribedbyadrawingliketheonebelow:
Figure6-theconstantareaoverrunpr.time
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Fromtime1until2:Theplanetisfarawayfromthesunandthereforethespeedislow.Youcan
seethisinkeplers3.Law:!!
!!=
.Whentheradius(a)islarge,theT(timefororbit)getslarger,and
thereforethespeedislower.
Fromtime3until4:theplanetisclosetothesun,andthereforethespeedishigh.InthesamewayasbeforeyoucanseethisfromKeplers3.Law.
Keplerobservedthattheareaofthetwogreyareasonfigure6wasthesame.
Wecanthereforeconcludethatwhentheplanetisclosetothesunitsspeedishigh,andopposite
whentheplanetisfarawayfromtheplanetthespeedislow.
LookingatKeplers3.Lawagain.
3.Law:
!!
!!= =
!!!
!!(1618)
Thelawwasshownearlierwithperfectcircles,butthelawalsoincludesellipses.
Assignment3.
Weknowthedistancefromtheearthtothesun1AU(AstronomicalUnit)=149,6million
kilometersinmeters149,6billionmeters.
Furthermorewenowthattheorbitaltimeisoneyear.Inseconds31557600s.
!
!=
(31557600s)2149,6 10
9m
3= 2,97449 10
19
AnofficialmeasurementonGiacobini-Zinnershowsthata(horizontalradius)is3,526AUforthe
comet.
NowwecancalculatetheperiodTforthiscometwithKeplers3.Law.
!
3,526 149,6 109m
!= 2,97449 10
19
2,97449 10!!" 3,526 149,6 10!m 3 = = 2,08943 10!
Inyears:
2,08943 10!
31557600s
year
= 6,62099
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Thismeansthatittakes6,3837
10!"ofTNTtoequaltheamountofkineticenergyinGiacobini-Zinner.
The6thofAugust1945,anatomicbombwasdroppedoverHiroshimainJapan.Thisbomb
unleashedenergyequalto12.000tonsofTNTandthisbombkilledabout80.000people.Togeta
feelingforhowmuchkineticenergyGiacobini-Zinnerhas,wewillnowshowhowmanybombslike
theoneinHiroshimathatis.
6,3837 10!"
12.000 = 5,31975
10!ThismeansthatifGiacobini-Zinnerhitstheearth,itwillbeequivalenttotheearthbeinghitby
morethan5,3millionatomicbombs!
Note:
IfGiacobini-ZinnerhitsanoceanontheEarth,itwouldtriggerenormoustsunamissomewhere
between300-1000metershigh,movingupto400
km/t.
Otherthanthat,itwouldcauseotherserious
environmentaldisasters:
Firstoff,dustwouldbehurledintheatmosphere,causingthesunlightwillnotbe
abletopenetratethedustmakingthe
temperaturedecreasetill40.
NitrogenandOxygenwill,withwater,createnitricacid,causingthesnowtobeliketheacid
inbatteries.
Lastly,whenthedusthassettledagain,theatmospherewillbefullofCO2becauseofallthefires.Thiswillmeanthatthegreenhouseeffectwillreachcrazydimensions.
i
[1]http://www.spaceweather.com/archive.php?view=1&day=07&month=10&year=2011
Figure8imagefromthemovie:thedayaftertomorrow.
