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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

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.


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


https://pds-rings.seti.org/tools/ephem2_mar.html

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?


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


Fig.6

Fig.7

Celestialequator

Solarvs.SiderealTime

Theearthistitledwithrespecttoitsorbitalplane.Ifweimagineaplanethatpassesthroughtheequatorofearth,andextenditoutwardinalldirections,thiswillbethecelestialplane.

IftheEarthrotatesarounditsownaxisexactlyonce,thedistantstarswillappeartobeinthesameposition.However,thesunwillnot!Theearthneedstorotateabout1degreemoreinorderforthesuntobeinthesameplaceinthesky.Thuswehavetwo'days'.Thesolardayisthetimeittakesforthesuntocrossthemerdianagain(24hours)whilethesiderealdayisthetimeittakestorotateexactlyonce.(It'sabout4minutesless).


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


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)


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


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.
