The Soft X-ray Background and its Origins - Astrophysics - University
The Origins Of Astronomy and...
10
The Origins Of Astronomy and Astrophysics 1. Ancient Astronomy 2. A Spherical Earth 3. The Ptolemaic System 4. Retrograde Motion 1. Ptolemaic System 5. Heliocentric 6. Geocentric vs. Heliocentric 7. Positions of Celestial Objects 1. The Altitude-Azimuth Coordinate System 2. The Equitorial Coordinate System 3. Basics of the earth's orbit 4. Celestial equator 8. Solar vs. Sidereal Time 1. Special Times of the year 2. Analemma 9. Equatorial System 10. Time 1. Julian Date 11. Summary Ancient Astronomy Fig. 1 A selection of ancient cosmologies. (unsourced) People made up all kinds of stuff - some of it very imaginative. Usually there would be some god or animals involved that were responsible for holding various parts up. Humans and their civilizations were invariably located at the center. Generally there was some sorting to do - put the heavy stuff down there, the light stuff up there. Some notable ancient philosophers: Lucretius, discussed the infinite universe. Celestial Sphere Sim. The early western views of the universe held that the earth was fixed in place and motionless at the center of the universe. The stars were all located on a sphere much bigger than the earth that rotated daily around the earth. The sun was on another sphere that rotated, as was the moon and the planets such as Mars and Venus. This framework was used to build the system of the world known as the Ptolemaic system. PHY 454 - origins-astro - J. Hedberg - 2017 Page 1
Transcript of The Origins Of Astronomy and...
TheOriginsOfAstronomyandAstrophysics
1.AncientAstronomy2.ASphericalEarth3.ThePtolemaicSystem4.RetrogradeMotion
1.PtolemaicSystem5.Heliocentric6.Geocentricvs.Heliocentric7.PositionsofCelestialObjects
1.TheAltitude-AzimuthCoordinateSystem2.TheEquitorialCoordinateSystem3.Basicsoftheearth'sorbit4.Celestialequator
8.Solarvs.SiderealTime1.SpecialTimesoftheyear2.Analemma
9.EquatorialSystem10.Time
1.JulianDate11.Summary
AncientAstronomy
Fig.1Aselectionofancientcosmologies.(unsourced)
Peoplemadeupallkindsofstuff-someofitveryimaginative.Usuallytherewouldbesomegodoranimalsinvolvedthatwereresponsibleforholdingvariouspartsup.Humansandtheircivilizationswereinvariablylocatedatthecenter.
Generallytherewassomesortingtodo-puttheheavystuffdownthere,thelightstuffupthere.
Somenotableancientphilosophers:Lucretius,discussedtheinfiniteuniverse.
CelestialSphereSim.
Theearlywesternviewsoftheuniverseheldthattheearthwasfixedinplaceandmotionlessatthecenteroftheuniverse.Thestarswerealllocatedonaspheremuchbiggerthantheearththatrotateddailyaroundtheearth.Thesunwasonanotherspherethatrotated,aswasthemoonandtheplanetssuchasMarsandVenus.ThisframeworkwasusedtobuildthesystemoftheworldknownasthePtolemaicsystem.
PHY 454 - origins-astro - J. Hedberg - 2017
Page 1
zenithto the sun
SyeneAlexandria D
α
β
Fig.2ThemethodofEratosthenesforestimatingthecircumferenceofthesphericalearth.
Fig.3ThePtolemaicsystemTitle:PioneersofSciencehttps://www.gutenberg.org/files/28613/28613-h/28613-h.htm
ASphericalEarth
ThePtolemaicSystem
Manyclassicalphilosophersbelievedinasphericalearth.Thatwasn'treallyinquestionbyanyadvancedwesterncivilizations.
Muchhasbeenwrittenaboutthehistoryofourunderstandingoftheuniverse,inparticularregardingthepositionoftheearthwithrespecttotheotherparts.Inshort,itwasmostlyduetopoorassumptionscreatedbyreligiousthinkinginadditiontothefactthatitishardtoseetheeffectsoftheearth'srotationinotherwaysbesideslookingatthestars.ThankstoAristotle,westernsciencewasforcedtoworkwiththefollowingconstraints:a)theearthwasatthecenteroftheuniverseandwasmotionless.b)everythingmovesaroundtheearth.c)celestialbodiesaredivineandmustmoveinperfectcircles.Theseviewswereadoptedbywesternreligionsandanydeviationsfromthemwereconsideredtobeagainstthereligiousorder:i.e.bad,andpunishable.
PHY 454 - origins-astro - J. Hedberg - 2017
Page 2
14151617
-25
-20
-15
-10
Right Ascension (hours)
Dec
linat
ion
(deg
)Mars Retrograde 2016
1/15/2016
9/15/2016
RetrogradeMotion
PtolemaicSystem
1.Wecan'tfeelthemotionoftheearth.2.Humansarethebest,andthereforeshouldbeatthecenter.3.Nostellarparallaxwasobserved.
Itdidn'ttaketoolongforthecarefulobserversofthenightskytorealizethatsometimes,theplanetswouldappeartomovebackwardsintheirtracksalongthestars.IfyoutooknoteofthenoteofpositionofMarsatthesametimeeverynight,overthecourseof9months,youwouldobserveitspathtobesomethinglikethisgraph.
Datafromhttps://pds-rings.seti.org/tools/ephem2_mar.html.
EpicyclesSim
Regardingpoint1:Attheequator,thesurfaceoftheearthismovingatabout460meterspersecond.Surely,weshouldbeabletofeelthis,right?Considertheaccelerationduetogravity:roughly9.8m/s2.Therotationoftheearthwouldleadtoanaccelertiontowardsitscentergivenby: ,where istheradiusoftheearth:about
6371kilometers.Thegiveacentripetalaccelerationofapproximately0.033m/s2.Whichisabout1/3ofapercenttheaccelerationduetogravity.Ifyouremembermeasuringlittleginthefirstyearlabs,youshouldrecallitwasdifficulttogetaveryprecisemeasurement,evenusingmoderntechnology.Thus,itwouldbeveryhardtomeasuresuchachangeseveralthousandyearsago.
RegardingPoint2:Theuniversedoesn'toweusanyfavors.Justifyingphysicallawsbasedonoursupposedgreatnessisneveragoodidea.(weknowthatnow)
RegardingPoint3:Parallaxwashardtomeasureanditeventookacenturyortwoafterthetelescopewasinventedtomeasureitaccurately,soit'shardtoblamethembackthen!
=acv2
RERE
PHY 454 - origins-astro - J. Hedberg - 2017
Page 3
sun
earth (June)
earth (December)
near star
far stars
Fig.4Therelativepositionofnearandfarstarswouldappeartochangeiftheearthwasinmotionduetoparallax
Fig.5FromDerevolutionibusorbiumcoelestium(OntheRevolutionsoftheHeavenlySpheres),1543.Thecopernicanworldviewgetsanillustration
Parallax
Heliocentric
Geocentricvs.Heliocentric
PositionsofCelestialObjects
Nosuchparallaxwasobservedbytheancients.ThisgavemoresupporttothePtolemaicsystem.
Whilenotthefirsttosuggestit,NicolausCopernicuswasthefirsttoprovideacompellingargumentfortheheliocentricmodelofthesolarsystem.Hewashesitanttoreleasehismanuscripthowever,anditdidnotgetprinteduntilhewasonhisdeathbed.
Nowweknowthatneitheroftheseistrue.Ourcurrentunderstandingoftheuniversesuggests(requires)thatthereisnocenter.
Howcanwedescribewherethingsare?
PHY 454 - origins-astro - J. Hedberg - 2017
Page 4
North
East
z
hA
star
zenith
SCP
NCP
α
δ
vernalequinox
celestialequator
TheAltitude-AzimuthCoordinateSystem
TheEquitorialCoordinateSystem
Basicsoftheearth'sorbit
Sun
Earth (Dec. 21)Earth (Jun. 21)
ecliptic plane
to NCP
Themostbasicmethodofdescribingthepositionofacelestialbodyistousethealtitude-azimuthcoordinatesystem.Allthatisrequiredistwomeasurements:thealtitude( )whichisdefinedastheanglemeasuredfromthehorizontotheobjectalongagreatcircle,andtheazimuth,( )whichistheanglemeasuredeastwardalongthehorizonfromthenorthpoletothegreatcircleusedforthealtitudemeasurement.Onecanalsousethezenithdistance( )toindicatetheanglemeasuredfromthezenithtotheobject.Notethat .
Thismethodisalsocalledthehorizoncoordinatesystemsinceitisbasedontheobserver'shorizon.Thisimpliesthatthemeasurementswillbedifferentfordifferentobservers,whichisamajorlimitationofthiscoordinatesystem.
hA
z z + h = 90∘
Theequitorialcoordinatesystemisabletoovercomethelimitationsofthealtitude-azimuthsystembydefiningpositionswithrespecttofeaturesintheskyandisthereforenotdependentontheobserversposition.
Thetwovariableswewillusearethedeclination:( )andtherightascension( ).Tounderstandwhatthesetwoanglesaremeasuredwithrespectto,weneedtounderstandtheearth'sorbitinmoredetail.
δ α
earth-simple-orbitsim
PHY 454 - origins-astro - J. Hedberg - 2017
Page 5
Fig.6
Fig.7
Celestialequator
Solarvs.SiderealTime
Theearthistitledwithrespecttoitsorbitalplane.Ifweimagineaplanethatpassesthroughtheequatorofearth,andextenditoutwardinalldirections,thiswillbethecelestialplane.
IftheEarthrotatesarounditsownaxisexactlyonce,thedistantstarswillappeartobeinthesameposition.However,thesunwillnot!Theearthneedstorotateabout1degreemoreinorderforthesuntobeinthesameplaceinthesky.Thuswehavetwo'days'.Thesolardayisthetimeittakesforthesuntocrossthemerdianagain(24hours)whilethesiderealdayisthetimeittakestorotateexactlyonce.(It'sabout4minutesless).
PHY 454 - origins-astro - J. Hedberg - 2017
Page 6
Calculatethedifferencebetweensolarandsiderealdays.
Example Problem #1:
Let'scalltheangularvelocityoftheEarthinit'sorbit,withreferencetothestars: .TherotationoftheEartharoundit'sownaxis(relativetothestars)willbe .Ifweaskedthesunhowquicklytheearthwasrotating(i.e.inthesolarreferenceframe)wewouldfindthethe wouldbeequaltothedifferencebetween and
,whichleadstothefollowing:
Sincethevectorsareapproximatelyparallel(the'renot,butwecanignorethe23.5°),thewecanwriteascalarequation:
Since ( istheperiod)wecanwrite:
Ourdefinitionofthesolarperiodis1day,then dayswhichismuchgreaterthan andwecanmakethefollowingapproximation:
Solvingforthedifferencethe and :
whichwhenconvertedtominutesgiveabout3.95minutesdifferencebetweenasolardayandasiderealday.
ω⃗Eω⃗sid
ω⃗sol ω⃗sidω⃗E
= +ω⃗sid ω⃗sol ω⃗E (1)
= +ωsid ωsol ωE (2)
omega = 2π
PP
= +1
Psid
1Psol
1PE
(3)
≈ 365PE Psol
= = ≈ (1 − )Psid ( + )1Psol
1PE
−1
Psol(1 + )Psol
PE
−1
PsolPsol
PE
(4)
Psol Psid
− = =Psol Psid(Psol)2
PE
1365
(5)
sun-eclipticsim
PHY 454 - origins-astro - J. Hedberg - 2017
Page 7
0 50 100 150 200 250 300 350
-20
-10
0
10
20
Days of the Year
Dec 21 Dec 21Sep 23 Jun 21 Mar 20
Dec
linat
ion
Autumnalequinox
Vernalequinox
SummerSolstice
WinterSolstice
061218 18
Right Ascension (hr)
Fig.8TheEcliptic
Fig.9AnAnalemmaPlot:
SpecialTimesoftheyear
Analemma
Thepositionofthesunintheskyvariesthroughouttheyear.Thepositionofthesunatthetimeoftheveranalequanoxisoneofourmainreferencepointsfordeterminingthepositionoftheobject.We'llsaythatthatlocationhasarightascensionof0.Adeclinationof0willbegivenbypositionalignedwiththecelestialequator.
Theplothereshowsthepositionofthesunat12pmoverthecourseofonefullyear.Thedaywhenthesunisthehighestintheskyiscalledthesummersolstice.Whenitisatthelowestpointiscalledthe wintersolstice.Thetwodaysrightinthemiddleofthesolsticesarecalledtheequinox:autumnalandvernal.(orfallandspring)
PHY 454 - origins-astro - J. Hedberg - 2017
Page 8
SCP
NCP
α
δ
vernalequinox
celestialequator
Fig.10
EquatorialSystem
HereissomeoutputfromJPLHorizonsdatabase.
Date__(UT)__HR:MN R.A._(ICRF/J2000.0)_DEC APmag ****************************************************** 2017-Aug-31 16:00 * 10 39 23.08 +08 29 39.1 -26.72 ******************************************************
Whatisthelowestlatitudefromwhichallthestarsofthebigdipperarevisible?Belowwhichlatitudeisthebigdippernevervisibleatall?
Example Problem #2:
Fig.11
PHY 454 - origins-astro - J. Hedberg - 2017
Page 9
Time
JulianDate
Summary
Ptolemaicvs.CopernicanPositionofCelestialObjectsBasicsofEarth'sorbitSolarvs.SiderealModernTimekeeping
Timekeepingandastronomyarelinked.Thedayisdefinedbythechangeinpositionofthesun.
WarrenField,AberdeenshireScotland,8thMillenniumBC.Usedtotracklunar
Youcan'tdomathwithdateformats,soweneedtohaveadifferentsystem.Wesetthe0daytobeJanuary14713BC,atnoon.Everydayafterthatjustadds1.January1stof2017willhavebeen2457755dayssincethensowecansaytheJDis2457755(atnoon).Timesothernoonjustgetfractionaldescriptions.TheModifiedJulianDate isverysimilar,exceptthatitstartsatmidnight,sonoononJanuary1stwouldbe2457755.5MJD.
PHY 454 - origins-astro - J. Hedberg - 2017
Page 10
