Download ASTRONOMY 113 Modern Astronomy

http://exo.missouristate.edu/ast/113/
ASTRONOMY 113
Modern Astronomy
Lecture: Tuesday, Thursday 9:30am-10:45am – Temple 0002
Tuesday, Thursday 2-3:15pm – Strong 0002
Dr. Peter Plavchan
626-234-1628
[email protected]
@PlavchanPeter
Office Hours: Tues,Thurs: 11am-1:30pm
Materials: Sapling Learning +Tophat + OpenStax Astronomy
Introductions
http://exo.missouristate.edu
You
Pleasetakeoutapieceofpaper,orcomposeanemailtomeonyour
phone/computer,andanswer:
1. Name&StudentID#(alsoforattendance)
2. Howmanysemesters haveyoucompletedatMSU?
3. Whatdoyouknoworhaveyouheardaboutastronomy?
4. Whatisyourdreamcareer?
5. Whyareyoutakingthisclass?
6. Whatdoyoudreaddoing?Whatdoyoulovedoing?
7. Canyougivemetipsonhowyoulearnbest?
8. Whatwouldyouliketoknowaboutme?
9. Whatwouldyoulikemetoknowaboutyou?
10. WhatcanIteachyou?
11. Whatcanyouteachme?
Syllabus & Exams
http://exo.missouristate.edu/ast/113/
Theinternetwillbeusedextensivelyin
thisclass.
Lecturenoteswillbepostedafterclass.
Pleaseletmeknowifyouneedhelp
accessingtheweb,orifthewebpages
arenotworking.
OpenStax
–
Free!
https://openstax.org/details/books/astronomy
TopHat
WewillbeusingtheTopHat(www.tophat.com)classroom
responsesysteminclass.YouwillbeabletosubmitanswerstoinclassquestionsusingAppleorAndroidsmartphonesandtablets,
laptops,orthroughtextmessage.
YoucanvisittheTopHatOverview
(https://success.tophat.com/s/article/Student-Top-Hat-Overviewand-Getting-Started-Guide)withintheTopHatSuccessCenter
whichoutlineshowyouwillregisterforaTopHataccount,aswell
asprovidingabriefoverviewtogetyouupandrunningonthe
system.
Anemailinvitationwillbesenttoyoubyemail,butifdon’treceive
thisemail,youcanregisterbysimplyvisitingourcoursewebsite.
TopHat
WewillbeusingtheTopHat(www.tophat.com)classroom
responsesysteminclass.YouwillbeabletosubmitanswerstoinclassquestionsusingAppleorAndroidsmartphonesandtablets,
laptops,orthroughtextmessage.
YoucanvisittheTopHatOverview
(https://success.tophat.com/s/article/Student-Top-Hat-Overviewand-Getting-Started-Guide)withintheTopHatSuccessCenter
whichoutlineshowyouwillregisterforaTopHataccount,aswell
asprovidingabriefoverviewtogetyouupandrunningonthe
system.
Anemailinvitationwillbesenttoyoubyemail,butifdon’treceive
thisemail,youcanregisterbysimplyvisitingourcoursewebsite.
TopHat
MorningSection:
http://app.tophat.com/e/193942
Note:ourCourseJoinCodeis 193942
AfternoonSection:
http://app.tophat.com/e/386199
Note:ourCourseJoinCodeis 386199
TopHatwillrequireapaidsubscription,andafullbreakdownofallsubscription
optionsavailablecanbefoundhere: www.tophat.com/pricing.
$24forasemester;$36forayear;$72for5years
ShouldyourequireassistancewithTopHatatanytime,duetothefactthatthey
requirespecificuserinformationtotroubleshoottheseissues,pleasecontact
theirSupportTeamdirectlybywayofemail([email protected]),theinapp
supportbutton,orbycalling1-888-663-5491.
Homeworks - SaplingDemo- $40
http://saplinglearning.com/
2
3(maysay1)
ClassBlog
http://www.blogger.com
Youwillbeinvitedtobeanauthorat:
http://ast113.blogspot.com
Thisiswheregrouppresentationswillbeposted!
GroupPresentations
•
•
•
•
•
•
•
Sign upforagroup presentation.
Presentationsare5 minutes each.Youwillbeexpectedtoprepareapresentation
withPowerpoint, Prezi,Google Sheetsorsimilar, andaddanaudio narrativewith
freesoftwarelikeJing, Screencast,etc.,andpostthefinalcombined video tothe
blog asasingle videoonyoutube orwithothervideosoftware(likeiMovie).
Fromeachlecturestopic, pickasubjecttogointodetailon.Consultwiththe
professor onthetopicscoveredinclasswellbeforeyouprepareyour presentation.
Donotpresentabroadoverviewoftheweekslecturematerials.
ThelastpartofthepresentationMUSTincludealistofworksreferences
(websitesok).
Willcounttowards10%offinalgrade.
Students intheclasswillpostquestions ascommentsontheblog, andyouare
required torespond totheminthetwoweeksfollowing yourpresentation, which
willcounttowardsyourgroup projectgrade.
Theweekafteryourpresentation, youwillberequired toaskatleastonequestion
ontheblog (postedasacomment)forthenextweek’spresenters.Theywillhave
torespond toyourquestions.
Extra Credit Options
Extracreditisavailableandcancontributeup to5-10%.Thepurpose ofextracreditis
tofind abalancebetweenyourinterestsandthesubjectmaterialofastronomy.
Possibleextracreditoptions mustbeapproved bytheinstructor, butcanincludefor
example:
•
Visit Baker Observatory or one of the on campus public viewing nights (by the
PSU bear). Bring back proof - photographic - of your visit. To qualify for the extra credit,
please write a one page summary of your visit. The public Baker Observatory night is
TBD
•
Astronomy as art. Many of you are non-science majors, and excel in other areas of
specialization - art, writing, music, etc. There is a vast history of art inspired by astronomy.
For example, consider constructing a scale model of our galaxy or local group of galaxies.
In order to qualify for the extra credit, please create an original work of art, music or writing
inspired by astronomy and the material you have learned in class. You may team with up to two
other people.
ALL EXTRA CREDIT REPORTS ARE DUE BY THE FINAL EXAM,
DIRECTLY TO ME.
AttendanceEnticement!
Thereare31lectures.Ifyouhave2orfewer
unexcusedabsences,youwillbe:
• Excusedfromthefinal,butonlyifclass
attendancestaysabove90%forthesemester
• Allowedonesheetofnotesonthefinalexam,
butonlyifclassattendancestaysabove80%
forthesemester
Our Place in the Universe
Our Modern View of the
Universe
A Modern View of the Universe
Our goals for learning:
•
•
•
•
What is our place in the universe?
How did we come to be?
Can we know what the universe was like in the past?
Can we see the entire universe?
Astronomy
The branch of science dedicated to the study
of everything in the Universe that lies above
Earth’s atmosphere
ScaleofourUniverse
• Videos
Universe
80 yr ago
What is our place in the universe?
400 yr
2500 yr
Star
A large, glowing ball of mostly hydrogen gas
that generates heat and light through nuclear
fusion at its center
Our star – the Sun
Context: “gas” in
astronomy usually
means H, or H2, but
could include other
atoms and molecules in
the gas state.
Planet
Mars
Neptune
A moderately large object that orbits (goes around) a star;
it shines by reflected light. Planets may be rocky, icy,
or gaseous in composition.
Moon (or satellite)
An object that orbits
a planet.
Ganymede (orbits Jupiter)
Asteroid
A relatively
small and
rocky object
which orbits a
star.
Comet
A relatively
small and icy
object that
orbits a star.
Solar (Star) System
A star and all
the material
that orbits it,
including its
planets and
moons.
Note: planets and orbits
are not to scale;
planets are tiny
compared to their
orbits.
Nebula
An interstellar cloud
of hydrogen gas and/or tiny smoke-like particles
called “dust”
Galaxy
A great island of stars in space, all held together by
gravity and orbiting a common center
M31, The Great Galaxy in Andromeda
Universe
The sum total of all matter and energy;
that is, everything within and between
all galaxies
How can we know what the universe was
like in the past?
• The key: light travels at a finite speed
– 300,000 km/s, 186,000 miles/s, 670 million miles per hour
• You can circle Earth 8 times in 1 second
• More on the Speed of Light when we discuss Relativity
Destination
Light travel time
Moon
1 second
Sun
8 minutes
Sirius
8 years
Andromeda Galaxy 2.5 million years
Thus,weseeobjectsastheywereinthepast:
Thefartherawaywelookindistance,
thefurtherbackwelookintime.
Light-year
•
•
•
•
•
The distance light can travel in one year.
About 10 trillion km (6 trillion miles).
A light-year is NOT a unit of time!
Can also talk about light-seconds.
At great distances we see objects as they were
when the universe was much younger.
What have we learned?
• Whatisourphysicalplaceintheuniverse?
– EarthispartoftheSolarSystem,whichisintheMilkyWaygalaxy,whichisa
member oftheLocalGroup ofgalaxiesintheLocalSupercluster
• How can we know that the universe was like in the
past?
– When we look to great distances we are seeing events that
happened long ago because light travels at a finite speed
• Can we see the entire universe?
– No, the observable portion of the universe is about 13.7
billion light-years in radius because the universe is about
13.7 billion years old. (We may round this number to 14
billion for convenience but the best modern measurements
give 13.7 billion years since the time from the Big Bang.)
The Scale of the Universe
Our goals for learning:
•
•
•
•
•
How big is Earth compared to our solar system?
How far away are the stars?
How big is the Milky Way Galaxy?
How big is the universe?
How do our lifetimes compare to the age of the
universe?
It is very important to grasp the huge distances and
enormous time spans that we deal with in astronomy. The
way to do this is to create a SCALE MODEL.
The easy questions
• How far away are the Sun and
Moon?
• The Moon is 384 million m
from Earth (~250,000 miles).
11
• The Sun is 1.5x10 m from
Earth (150 billion m, or ~93
million miles). This distance is
called 1 astronomical unit (AU).
How big is Earth compared to our Solar System?
Let’s reduce the size of the solar system by a factor of
10 billion; the Sun is now the size of a large grapefruit
(14 cm diameter or about 5.6 inches; 2.54 cm = 1 inch).
How big is Earth on this scale?
A.
B.
C.
D.
an atom
a ball point
a marble
a golf ball
Radius of the Sun = 700,000 km
Diameter Sun = 1.4 x 1011 cm
Divide by 1010 to get 14 cm
Let’s reduce the size of the solar system by a factor of 10
billion; the Sun is now the size of a large grapefruit (14 cm
diameter).
How big is Earth on this scale?
A.
B.
C.
D.
an atom
a ball point
a marble
a golf ball
How far apart would our model Sun and Earth be on this scale?
The scale of the solar system
• On a 1-to-10 billion scale:
– Sun is size of a large grapefruit (14 cm)
– Earth is size of a ball point, 15 meters away
– 15 meters is about 107 grapefruits
– Which means in the real solar system you could
fit about107 Suns into the Earth –Sun distance
How far away are the stars?
On our 1-to-10 billion scale, it’s just a few minutes walk to
Pluto. How far would you have to walk to reach the nearest
star to the Sun - Alpha Centauri?
A.
B.
C.
D.
1 mile
10 miles
100 miles
the distance across the U.S. (2500 miles)
How far away are the stars?
On our 1-to-10 billion scale, it’s just a few minutes walk to
Pluto. How far would you have to walk to reach the nearest
star to the Sun - Alpha Centauri?
A.
B.
C.
D.
1 mile
10 miles
100 miles
the distance across the U.S. (2500 miles)
Answer: D,thedistanceacrosstheU.S.
Thought Question
Suppose you tried to count the more than 100 billion (1011)
stars in our galaxy, at a rate of one per second…
How long would it take you?
A.
B.
C.
D.
a few weeks
a few months
a few years
a few thousand years
Suppose you tried to count the more than 100 billion stars in
our galaxy, at a rate of one per second…
How long would it take you?
A.
B.
C.
D.
a few weeks
a few months
a few years
a few thousand years (100 billion seconds is nearly
3,200 years. Why? Because there are about 30 million
seconds in a year, so 1011/3x107 = 0.33x104 = 3.3 x 103)
How big is the (observable) Universe?
• The Milky Way is one of about 100 billion galaxies.
• (1011 stars/galaxy) x (1011 galaxies) = 1022 stars
As many stars as grains of (dry) sand on all Earth’s beaches…
How do human lifetimes compare to the
AGE of the Universe?
• The Cosmic Calendar: a scale on which we
compress the history of the universe into 1 year!
How do human lifetimes compare to the
AGE of the Universe?
• The Cosmic Calendar: a scale on which we compress the
history of the universe into 1 year. 1 day represents about
40 million years; 1 second represents about 440 years.
What have we learned?
• How big is Earth compared to our solar system?
– The distances between planets are huge compared to their
sizes—on a scale of 1-to-10 billion, Earth is the size of a
ball point and the Sun is 15 meters away
• How far away are the stars?
– On the same scale, the stars are thousands of km away
• How big is the Milky Way galaxy?
– It would take more than 3,000 years to count the stars in
the Milky Way Galaxy at a rate of one per second, and
they are spread across 100,000 light-years
What have we learned?
• How big is the universe?
– The observable universe is almost 14 billion
light-years in radius and contains over 100
billion galaxies with a total number of stars
comparable to the number of grains of sand
on all of Earth’s beaches
• How do our lifetimes compare to the age of
the universe?
– On a cosmic calendar that compresses the
history of the Universe into one year, human
civilization is just a few seconds old, and a
human lifetime is a fraction of a second
Spaceship Earth
Our goals for learning:
•
•
•
•
How is Earth moving in our solar system?
How is our solar system moving in the Galaxy?
How do galaxies move within the Universe?
Are we ever sitting still?
How is Earth moving in our solar system?
• Contrary to our perception, we are not “sitting still.”
• We are moving with the Earth in several ways, and at
surprisingly fast speeds…
The Earth rotates
around its axis once
every day.
The spin rate at the Equator is ~1000 mph,
twice as fast as a commercial airliner.
Earth orbits the Sun (revolves) once every year:
• at an average distance of 1 AU ≈ 150 million km
• with Earth’s axis tilted by 23.5º (pointing to Polaris)
• and rotating in the same direction it orbits, counterclockwise as viewed from above the North Pole.
Our Sun moves relative to the other stars in the local
Solar neighborhood…
• typical relative speeds of more than 70,000 km/hr
• but stars are so far away that we cannot easily notice their motion
… And orbits the center of the Milky Way galaxy
every 230 million years.
More detailed study of the Milky Way’s rotation reveals
one of the greatest mysteries in modern astronomy
Most of Milky Way’s
light comes from disk
and bulge …
…. but most of the
mass is in a huge
and DARK halo.
How do galaxies move within the universe?
The Universe is
expanding.
In the 1920s Edwin
Hubble discovered
that galaxies are
carried along with
the expansion of
the Universe.
But how did
Hubble figure out
that the universe is
expanding?
Hubble discovered that:
• All galaxies outside our Local Group are
moving away from us.
• The more distant the galaxy, the faster it is
racing away.
Conclusion: We live in an expanding universe.
What have we learned?
• How is Earth moving in our solar system?
– It rotates on its axis once a day and orbits the
Sun at a distance of 1 A.U. = 150 million km
• How is our solar system moving in the Milky
Way galaxy?
– Stars in the Local Neighborhood move
randomly relative to one another and orbit the
center of the Milky Way in about 230 million
years
What have we learned?
• How do galaxies move within the universe?
– All galaxies beyond the Local Group are
moving away from us with expansion of the
Universe: the more distant they are, the faster
they’re moving
• Are we ever sitting still?
– No!
OKAY, NOW WE HAVE A GOOD OVERALL PERSPECTIVE.
NEXT WE NEED SOME MORE DETAILS
DiscoveringtheUniversefor
Yourself
PatternsintheNightSky
Ourgoalsforlearning:
• WhatdoestheuniverselooklikefromEarth?
• Whydostarsriseandset?
• Whydotheconstellationsweseedependon
latitudeandtimeofyear?
TheCelestialSphere
Starsatdifferent
distancesallappear
tolieontheCelestial
Sphere.
EclipticisSun’s
apparentpath
throughthecelestial
sphere.
TheCelestialSphere
The88official
constellations
coverthecelestial
sphere.
Itisimportanttorealizethat
thesenamedpatternshaveno
relationtolifeonEarthand
thestarsinagiven
constellationareoftennot
connectedwitheachother
physically.
TheMilkyWay
FishEyelensview
Abandoffaintlight
makingacircle
aroundthecelestial
sphere.
Whatisit?
Ourviewintothe
“plane” ofour
spiralgalaxy.
TheLocalSky
Altitude (above horizon) Azimuth (along horizon) specifies location
Zenith: The point directly overhead
Horizon: All points 90° away from zenith
Meridian: Line passing through zenith from N to S points
Wemeasuretheskyusingangles
• Fullcircle=360º
• 1º=60¢
(arcminutes)
• 1¢ =60²
(arcseconds)
AngularSize
360 degrees
angular size = physical size ×
2π × distance
€
Anobject’sangular
sizeappearssmaller
ifitisfartheraway
Aside:Wecandefine anewunitofangular
measurecalledaradian suchthat
1radian=360/2π =57.3degrees
Whydostarsriseandset?
Earth rotates west to east, so
stars appear to circle from
east to west.
Theskyvarieswithlatitudebutnot longitude
Theskyvaries asEarthorbitstheSun
• AstheEarthorbitstheSun,theSunappearstomoveeastward
alongtheecliptic.
• Atmidnight,thestarsonourmeridianareoppositetheSunin
thesky.
TheReasonforSeasons
Ourgoalsforlearning:
• Whatcausestheseasons?
• Howdowemarktheprogressionofthe
seasons?
• HowdoestheorientationofEarth’saxis
changewithtime?
Whatcausestheseasons?
Seasonsdepend onhowEarth’saxisaffectsthedirectnessofsunlight
Axistiltchangesdirectnessofsunlight
duringtheyear
Sun’saltitudeintheskyalsochanges
withseasons
Sun’sposition atnoon insummer:
higher altitudemeansmoredirect
sunlight.
Sun’sposition atnoon inwinter:
loweraltitudemeanslessdirect
sunlight.
Howdowemarktheprogressionoftheseasons?
• Wedefinefour specialpoints:
summer solstice
wintersolstice
spring (vernal) equinox
fall(autumnal) equinox
Wecanrecognizesolsticesandequinoxesby
Sun’spathacrosssky
Summersolstice: Highestpath,
riseandsetatmostextreme
north ofdueeast.
Wintersolstice: Lowestpath,rise
andsetatmostextremesouth of
dueeast.
Equinoxes: Sunrisesprecisely
dueeastandsetspreciselydue
west.
HowdoestheorientationofEarth’saxis
changewithtime?
•Althoughtheaxisseemsfixedonhumantime
scales,itactuallyprecesses overabout26,000years.
Þ Polariswon’talwaysbetheNorthStar.
Þ Positionsofequinoxesshiftaroundorbit;e.g.,
springequinox,onceinAries,isnowinPisces!
Earth’saxis
precesseslikethe
axisof aspinning
top
TheMoon,
OurConstantCompanion
Ourgoalsforlearning:
• WhydoweseephasesoftheMoon?
• Whatcauseseclipses?
PhasesofMoon
• HalfofMoonis
illuminatedbySun
andhalfisdark.
• NOTcausedby
Earth’sshadow!
• Weseeachanging
combinationof
thebrightand
darkfacesas
Moonorbits
WeseeonlyonesideofMoon
Synchronousrotation:
theMoonrotates
exactlyoncewitheach
orbitof~28days
Thatiswhyonlyone
sideisvisiblefromEarth
Whatcauseseclipses?
• TheEarthandMooncastshadows.
• Wheneitherpassesthroughtheother’sshadow,
wehaveaneclipse.
Whencaneclipsesoccur?
• Lunareclipses
canoccuronly
atfullmoon.
• Lunareclipses
canbe
penumbral,
partial,ortotal.
• August21st,
2017
Whencaneclipsesoccur?
• Solareclipses can
occuronlyatnew
moon.
• Solareclipsescan
bepartial,total,
or annular.
Whydon’twehaveaneclipseateverynewandfullmoon?
– TheMoon’sorbitistilted5° toeclipticplane…
– Sowehaveabouttwoeclipseseasons eachyear,withalunar
eclipseatnewmoonandsolareclipseatfullmoon.
LengthofaDay
• Siderealday:
Earthrotatesonce
onitsaxisrelative
tothedistantstars
in23hrs,56min,
and4.07sec.
LengthofaDay
• Solarday:TheSun
makesonecircuit
aroundtheskyin
24hours(by
definition)
Whyarethetwodifferent?
• Solardayislongerthanasiderealdaybyabout1/360
becauseEarthmoves about1° inorbiteachday
LengthofaMonth
• Siderealmonth:Moon
orbitsEarthin27.3days.
• Earth&Moontravel30°
aroundSunduringthat
time(30°/360° =1/12)
• Synodicmonth:Acycle
oflunarphases;
thereforetakesabout
29.5days,1/12longer
thanasiderealmonth
• Synodicmeans“meeting”
LengthofaYear
• Siderealyear:Timefor
Earthtocompleteone
orbitofSun
• Tropicalyear:Timefor
Earthtocompleteone
cycleofseasons
• Tropicalyearisabout20
minutes(1/26,000)
shorterthanasidereal
yearbecauseofEarth’s
precession.
Howdowetellthetimeofday?
• Apparentsolartime
dependsonthe
positionoftheSunin
thelocalsky
• Asundialgives
apparentsolartime
UniversalTime
• Universaltime(UT) isdefinedtobethemean
solartimeat0° longitude.
• ItisalsoknownasGreenwichMeanTime(GMT)
because0° longitudeisdefinedtopassthrough
Greenwich,England
• Itisthestandardtimeusedforastronomyand
navigationaroundtheworld
StandardTime&TimeZones
• Rapidtraintravelrequiredtimetobestandardized
intotimezones(timenolongerlocal)
Whenandwhydowehaveleap
years?
• Thelengthofatropicalyearisabout365.25days.
• Inordertokeepthecalendaryearsynchronized
withtheseasons,wemustaddonedayeveryfour
years(February29).
• Forprecisesynchronization,yearsdivisibleby100
(e.g.,1900)arenotleapyearsunlesstheyare
divisibleby400(e.g.,2000).
CelestialCoordinates
• Rightascension:Likelongitudeoncelestialsphere
(measuredinhourswithrespecttospringequinox).
• Declination:Likelatitudeoncelestialsphere(measured
indegreesabovecelestialequator)
TimebytheStars
• Siderealtime isequaltorightascensionthatis
passingthroughthemeridian
• Thus,thelocalsiderialtimeis0h0m whenthe
springequinoxpassesthroughthemeridian
• Astar’shourangle isthetimesinceitlast
passedthroughthemeridian
LocalSiderealTime=RA+HourAngle
Howcanyoudetermineyourlatitude?
•
•
Latitudeequalsaltitudeofcelestialpole
Altitudeanddeclinationofstarcrossing
meridianalsogiveslatitude.
• YoucandetermineSun’sdeclination
fromthedayoftheyear
• MeasuringtheSun’saltitudewhenit
crossesmeridiancantellyoulatitude
Howcanyoudetermineyour
longitude?
• Inordertodetermineyourlongitude
fromthesky,youneedtoknowtimeof
daybecauseofEarth’srotation
• Youalsoneedtoknowdayofyear
becauseofEarth’sorbit
• Accuratemeasurementoflongitude
requiresanaccurateclock.
GPSNavigation
• TheGlobalPositioningSystem(GPS)usesasetof
satellitesinEarthorbitasartificialstars
• GPSdevicesuseradiosignalstodetermineyour
positionrelativetothosesatellites
• GPSsatellitescorrectforGeneralRelativity!
• Ok,ontotheterrestrialplanets!
PlanetsKnowninAncientTimes
• Mercury
– difficulttosee;alwaysclose
toSuninsky
• Venus
– very brightwhenvisible;
morningorevening“star”
• Mars
– noticeablyred
• Jupiter
– verybright
• Saturn
– moderatelybright
Whatwasoncesomysterious
aboutplanetarymotioninoursky?
• Planetsusuallymoveslightlyeastward fromnightto
nightrelativetothestars.
• Butsometimestheygowestward relativetothestars
forafewweeks:apparentretrogrademotion
Weseeapparentretrogrademotionwhen
wepassbyaplanetinitsorbit.
ExplainingApparentRetrograde
Motion
• Easyforus toexplain:occurswhenwe“lap”
anotherplanet(orwhenMercuryorVenus
lapsus)
• Butverydifficulttoexplainifyouthinkthat
Earthisthecenteroftheuniverse!
• Infact,ancientsconsideredbutrejectedthe
correctexplanation
WhydidtheancientGreeksrejectthereal
explanationforplanetarymotion?
Theirinabilitytoobservestellarparallax wasamajor factor.
p
tanp=1AU/d(AU)
Forsmallangles:
d
p =1/d
Iftheanglep=1second
ofarcthendisdefinedas
1parsec(=206265 AU).
1AU
Nottoscale
TheGreeksknewthatthelackofobservable
parallaxcouldmeanoneoftwothings:
1. Starsaresofarawaythatstellarparallaxis
toosmalltonoticewiththenakedeye
2. EarthdoesnotorbittheSun;theEarthisthe
centeroftheuniverse
WithrareexceptionssuchasAristarchus,theGreeks
rejectedthecorrectexplanation(1)becausethey
didnotthinkthestarscouldbethat faraway
Thussettingthestageforthelong,historicalshowdown between
Earth-centered andSun-centered systems.