EquatorialTelescopeMoun2ng
What’s wrong with this picture?
OneSimpleConnec2on/Defini2on •  ThecurrentSiderealTimeequalstheHourAngleoftheVernalEquinox
http://www.polaris.iastate.edu/NorthStar/Unit4/unit4_sub2.htm
Celestial Sphere Review
AngularPerspec2ve
•  Equatorial and Local coordinates are all about measuring angles, whether it be
relative to the horizon or between two objects on the sky.
•  Angles can be estimated crudely with anatomy.
•  A fist at arm’s length subtends about ten degrees.
•  Your little finger at arm’s length subtends about a degree
•  Try it out on the Moon (which subtends ½ degree).
•  Orion from top to bottom (Betelgeuse to Rigel) subtends about 15 degrees.
TransformingfromR.A.,Dec,andHourAngleto
Al2tudeandAzimuth
GeometryonaSphere
•  Great circles on a sphere intersect
at (spherical) angles.
•  The intersection of three great
circles defines a spherical triangle
(with a sum of interior angles greater
than 180 degrees)
•  The sides lengths (a,b,c
which are actually angles
seen from the center of the
sphere) and the intersection
angles (A,B,C) are related by
the formulae at right.
Transforming between Hour
Angle, Dec and Altitude/
Azimuth is just a matter of
identifying the “sides”
From Chromey Chapter 3
EquatorialtoAlt/AzConversion
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Thequan22esweknow:Hourangle(viaR.A.andsidereal2me),Declina2on,and
La2tude–2sidesandoneinteriorangle.That’senoughtocalculatetheother
quan22es.
The Meridian
H is hour angle
a is altitude
A is azimuth
P is the equatorial pole
Z is the zenith
φ is the latitude
δ is the declination
Third side determined by 2 sides
and their interior angle
WhichWayistheEarthTurned:ApparentSolarTime
•  The direction on the celestial sphere toward which the Earth is turned at your
location has everything to do with what is up in the sky.
•  The Sun is also an important factor as it obscures the stars when it is up.
•  Apparent Solar Time is literally that. Measure the position to be exact the Hour
Angle and add 12) of the Sun in the sky to determine Earth's rotation angle relative
to the Sun.
Note: The Earth rotates and revolves around
the Sun “counterclockwise” when viewed from
the North Pole.
Apparent/LocalSolarTimevs.MeanSolarTime
•  LocalSolarTimeissundial2me.
–  Noon=the2mewhentheSuncrossestheMeridian
–  BecauseoftheEarth’sellip2calorbit(moreexactlybecauseofthevarying
angularspeedastheEarthmovesarounditsellip2calorbit–Kepler’s2ndLaw
inac2on)the2meofSolarNoondriYsthroughouttheyear.
•  TheobliquityoftheEarthisalsoafactorinthisdriY.
•  MeanSolarTimeaveragesthedaylengththroughouttheyear.
–  Therearefourdatesduringtheyearwheremean=apparentsolar2me
The Equation of Time – The offset between mean and apparent solar time
MeanSolarTimeandTimeZones
•  ForeachdegreeoflongitudeyougowestontheEarththeMeanSolar
Timeis4minutesearlier.
•  EverycityhasaslightlydifferentMeanSolarTimewhichledto
modestchaosintheearlyrailroadera(60milesisaboutonedegree)
From Popular Science, 1884
TimeZonesLocallyStandardizedTime
…attheexpenseofoffseangsolarnoon
…attheexpenseofoffseangsolarnoon
ModernTimeKeeping
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Defineasecond:9,192,631,770cyclesofthehyperfinecesium-133
transi2on.
BeatthatsecondwithoutfailandwithoutregardforwhichwaytheEarth
isturned–Interna2onalAtomicTime(TAI)=physics2me
Trackthevaria2onsinEarthrota2on–par2cularlythe2dalslowingdueto
theMoon'storqueontheEarth.Keepa2methattracksEarthrota2on
(UT1).
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ImplementbykeepingtrackofaTAI-UT1offset(orstretchthesecond).
WhereasTAItracksactualsecondsasneededforphysics,theUT1isnotuniform.
Putinastepcorrec2onwhenneededtoapproximateUT1towithina
second-CoordinatedUniversalTime(UTC)–ourstandardof2me(for
bejerorforworse)
UT1/UTCdetermineshowtheEarthisturnedrela2vetotheSun.As
astronomerswecareabouthowtheEarthisturnedrela2vetothestars.
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Sidereal2meisa2me-of-yeardependentoffsetfromUT1(althoughUTCisgood
enoughandthebasisofmostcomputerandradiocontrolledclocks).
However,tobepreciseyoumustalsoaccountforyourlongitudeoffsetfromthe
2mezonemeridian(75degreesforEasternTime,forexample)orfromGreenwich
ifusingUTC.
TransitTelescopes–MeasuringEarthRota2on/LST
TransitTelescopes–MeasuringEarthRota2on/LST
LST is the R.A. of the star currently crossing The Meridian
Varia2oninEarthRota2on
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Therota2onrateoftheEarthchangesduetosolar/lunar2des,
internalmo2ons,andshiYingofwaterandiceonthesurface.
TheseconditselfispreciselyfixedthusUT1driYsrela2vetoTAI.
Theseeffectsintegratetofullsecondsover1-2years.
Varia2oninEarthRota2on
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Therota2onrateoftheEarthchangesdueto2des,internalmo2ons,
andshiYingofwaterandiceonthesurface.
TheseconditselfispreciselyfixedthusUT1driYsrela2vetoTAI.
Theseeffectsintegratetofullsecondsover1-2years.
TidesandtheSlowingofEarth'sRota2on
•
SincetheEarthspinsfasterthantheMoonorbitstheEarthtriesto
dragits2dalbulgesoutoflinewiththeMoon
–
-theMoon,inturn,triestopullthembackintoalignment.
-TheconsequenceisthatEarthrota2onisslowingandtheMoonisgeang
fartherfromtheEarth.
LeapSeconds
•  Sincethesecondisoffixeddura2onandtheEarth’srota2onrateis
slowingUT1driYssteadilywithrespecttoTAI
•  ThisdriYismuchworsethannecessarybecausethe1956defini2on
ofthesecondwasbasedonastronomicalmeasurementsfromthe
mid1800’s(backwhentheEarthwasrota2ngfaster).
–  TheaverageslowingofEarth’srota2onperiodis1.4milliseconds/century
–  Westartedwithas“stale”second!
LeapSeconds
•  AleapsecondisaddedwhenUT1andUTCgettobe>0.9soutof
stepandonlyonJune30orDecember31.Ifneededonthatdaya
61stsecondgetsaddedtothelastminuteoftheUTday.
Es2mateLSTatthecurrent2me
•  Sidereal2meatNOONontheSpringEquinoxis0hours.
•  Rightnowitis40minutesshortoflocalnoon
•  Thesiderealclockhasrun3m56secondsfastsincethespring
equinox.
•  Actuallyforbejerprecisionnotethatthesidereal2meatnoonon
theFallequinoxis12hours.
–  October21(30days),November21(31days),December21(30days),
January21(31days)+14daystothepresentdate=136days.
–  Atnoonitwillbeabout12hours+136*3.93LST=20.908hours
•  Charlojesvilleisatlongitude78.5degrees–3.5degrees*4
minuteswestofthemeridian
Calcula2ngAirmass
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Airmass,thenumberofatmosphericthicknesseslighttraversesonthewayfromthe
startotheobserver,dependsonlyontheal2tudeofthetarget,a.
The Meridian
H is hour angle
a is altitude
A is azimuth
P is the equatorial pole
Z is the zenith
φ is the latitude
δ is the declination
ZenithAngleandAirmass
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Thecomplementoftheal2tudeangle,the“zenithangle”,measures
theangularsepara2onofastarfromthepointoverhead.
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Astarthatisjustrisingorseanghasazenithangleofz=90.
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Astaroverheadhasazenithangleofzero.
The“airmass”ofastarmeasuresthenumberofatmospheric
thicknessesastar'slightispassingthroughonitswaytotheobserver
andequalsthesecantofthezenithangle.
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Sincetheatmosphereajenuatesstarlight,knowingtheairmassiscri2cal
toprecisionstellarphotometry.
*
horizon
z
altitude
airmass = sec(z) = 1 / cos(z)
one
atmosphere
AirmassFactsandFigures
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Astaratthezenithhasairmass=1
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Astar45degreesfromthezenithhasairmass=1.41=1/cos(45)
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Astar30abovethehorizon,60degreesfromzenith,hasairmass=2=1/cos(60)
Ingeneralastronomerstrytoconductobserva2onsasclosetothezenithas
possibleandatworstatairmass~2.
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Starsareattheirsmallestairmasswhentheytransitthemeridian.Thisvaluedepends
onlyonthestar’sdeclina2onandtheobserversla2tude.
Astarwithdeclina2onequaltoyourla2tudepassesoverhead(minimumairmass=1)
*
horizon
z
altitude
airmass = sec(z) = 1 / cos(z)
one
atmosphere
PlaneParallelApproximatestheSphericalAtmosphere
Verymuchnottoscale
Angle c is the altitude
Angle b is the zenith angle, z
However,PlaneParallelisPlentyGoodEnough
AirmassCurves
Onemore2metopic-JulianDate
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Astronomersneedto2metagobserva2onsinaconvenientway
sinceMonth/Day/Yeariscumbersome
JulianDateisthenumberofdays(anddecimalfrac2onthereof)
sincenoonJan1,4713B.C.
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TheJuliandatefor2016February411:00:00.0ESTisJD2457423.167
Nohh:mm:ss.s!
Thisnumberisabitcumbersomeandearly(Sputnikera)
computa2onsdidnotwanttowastestorageontheunnecessary
leadingdigits.
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ModifiedJulianDateisJD–2400000.5
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The2meaboveisMJD57422.667
Thesubtrac2onof0.5daysshiYsthestartofanMJDtomidnightrather
thantheJuliandaystartatnoon
SunriseSunset
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Factorsinfluencingsunrise/sunset2me
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youtellme....What2medoestheSunsetontheSpringEquinox?it'snot
6:00p.m....
Recall Celestial Motion at Different Declinations
Celestial equator
(circumpolar)
When the Sun lies on the celestial equator days are 12 hours long
The Sun can get as far as +/- 23.5 degrees from the celestial equator in declination.
A graphical view of
Sunset throughout the
year.
Sunrise/Sunset
•  The equation of time skews
the symmetry of sunrise and
sunset.
•  In the northern hemisphere the
earliest sunset is around
December 5 (not 21!) and the
sun rapidly returns to the
evening sky.
•  The latest sunrise happens
around January 4.
Twilight(s)
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TwilightistheeffectoftheSunshiningontheatmospherewhile
thediskoftheSunisbelowthehorizon.
AstheSunsinkslowerbelowthehorizonsuccessivelyhigher/
thinnerlayersoftheatmosphereareilluminated.