The Celestial SphereThe Celestial Sphere

Karen Meech Karen Meech

Institute for AstronomyInstitute for Astronomy

TOPS 2003TOPS 2003

Latitude and LongitudeLatitude and Longitude

Latitude (Latitude () meas from ) meas from equatorequator

Longitude (Longitude () point of ) point of reference – Greenwich reference – Greenwich UKUK

Units of measure:Units of measure: Deg, arcmin, arcsecDeg, arcmin, arcsec OO ‘ “ ‘ “

The Horizon SystemThe Horizon System

Altitude (h) – angle Altitude (h) – angle measured from the measured from the horizon to Zenith (Z)horizon to Zenith (Z)

Azimuth – the angle Azimuth – the angle measured from Nmeasured from NE E along horizonalong horizon

Problem as a celestial Problem as a celestial system?system?

Celestial SphereCelestial Sphere

Imaginary sphere Imaginary sphere where stars residewhere stars reside

Extension of Earth’s Extension of Earth’s equator, polesequator, poles

Celestial EquatorCelestial Equator Celestial polesCelestial poles

Zenith & NadirZenith & Nadir

Great CirclesGreat Circles

Circles covering the Circles covering the largest diameter on spherelargest diameter on sphere

NCP altitude = NCP altitude = Celestial MeridianCelestial Meridian – CM – CM

great circle through Z and great circle through Z and NCPNCP

Hour AngleHour Angle – angular – angular distance / time from CMdistance / time from CM HA = 0 on CMHA = 0 on CM ““-” indicates rising-” indicates rising ““+” indicates setting+” indicates setting

Declination & Right AscensionDeclination & Right Ascension DeclinationDeclination = Latitude = Latitude

Celestial Equator Celestial Equator = 0 = 0 Latitude, NCP elevationLatitude, NCP elevation Units: deg, arcmin, ‘’Units: deg, arcmin, ‘’

The The CelestialCelestial MeridianMeridian Great circle going through Great circle going through

zenith & NCPzenith & NCP Right AscensionRight Ascension = =

LongitudeLongitude Units: hh:mm:ssUnits: hh:mm:ss 360360oo = 24 hr (1 hr = 15 = 24 hr (1 hr = 15oo)) Where to start RA?Where to start RA?

Circles of DeclinationCircles of Declination

The Ecliptic & The Ecliptic & SeasonsSeasons

ObliquityObliquity – tilt of Earth’s orbital axis (23.5 – tilt of Earth’s orbital axis (23.5oo))

EclipticEcliptic – path of the Earth around the sun – path of the Earth around the sun Apparent path of the sun & planets in the skyApparent path of the sun & planets in the sky Traces a great circle on the celestial sphereTraces a great circle on the celestial sphere Intersects at 2 points: Intersects at 2 points: and and ( (vernal & autumnal equinoxvernal & autumnal equinox))

is visible at midnight on CM in Septemberis visible at midnight on CM in September

The EclipticThe Ecliptic

Right Ascension Right Ascension

Starting PointStarting Point

Longitude system: Longitude system: Prime MeridianPrime Meridian

Two intersections Two intersections between CE & eclipticbetween CE & ecliptic Vernal EquinoxVernal Equinox Autumnal EquinoxAutumnal Equinox

Units of measure:Units of measure: Hours, min, secHours, min, sec Measure Eastward Measure Eastward

from from (RA = 0) (RA = 0) RA increases to ERA increases to E

Time ScalesTime Scales UT/Local – measured from noon to noon UT/Local – measured from noon to noon

(movement of sun)(movement of sun) Earth’s orbital motion Earth’s orbital motion must rotate >360 must rotate >360oo

= 360/365.25 = 0.986= 360/365.25 = 0.986oo

24 : (360+ 24 : (360+ ) = sidereal : 360 ) = sidereal : 360 Sidereal day = 23Sidereal day = 23hh 56 56mm 04 04ss

Start defined when Start defined when is on the celestial meridian is on the celestial meridian

Relation between ST and RARelation between ST and RA

HA = ST – RAHA = ST – RA ST at night = RA of ST at night = RA of

object on CMobject on CM is on the CM at is on the CM at

midnight at midnight at Observing tipObserving tip

RA = 0 on CM in SepRA = 0 on CM in Sep Advances 2 hr / moAdvances 2 hr / mo

Airmass – Coordinate Airmass – Coordinate RelationsRelations

Best observe @ HA = 0Best observe @ HA = 0 Airmass Airmass – amt of atm– amt of atm Extinction = absorption Extinction = absorption

& scattering& scattering = sec(ZD)= sec(ZD) Spherical Trig – law of Spherical Trig – law of

cosinescosines

cos(scos(s11) = cos(s) = cos(s22)cos(s)cos(s33) + sin(s) + sin(s22)sin(s)sin(s33)cos(A)cos(A11))

Effect of AirmassEffect of Airmass

= sec(z) = sin(= sec(z) = sin() sin () sin () + cos() + cos() cos() cos() cos(HA)) cos(HA)

Higher airmass = more extinctionHigher airmass = more extinction Higher airmass = more refractionHigher airmass = more refraction Higher airmass = poorer seeingHigher airmass = poorer seeing

SummarySummary

Coordinates: Coordinates: , , CM – passes thru Z CM – passes thru Z

and NCPand NCP increases to Eincreases to E Altitude of NCP = Altitude of NCP = HA = ST – HA = ST – is on CM at is on CM at Best obs at small HA Best obs at small HA

(small (small ))

The AstrolabeThe Astrolabe

2-D model of csphere2-D model of csphere Greek origins: astron Greek origins: astron

+ lambanien+ lambanien Ancient laptop!Ancient laptop!

Oldest about 900 BC Oldest about 900 BC (Hipparchus)(Hipparchus)

Middle AgesMiddle Ages Arabian astronomersArabian astronomers

Astrolabe FunctionsAstrolabe Functions

View of night skyView of night sky Position of starsPosition of stars Rise/set of sun, starsRise/set of sun, stars Altitude of objectAltitude of object Measure time of yearMeasure time of year Measure time of nightMeasure time of night

Transparent OverlayTransparent Overlay

RA / Dec GridRA / Dec Grid

Elevation GuideElevation Guide

Astrolabe ExercisesAstrolabe Exercises

The Sky TonightThe Sky Tonight When an object rises When an object rises

or setsor sets Sunset for 6/20/02Sunset for 6/20/02

RA = 05:58:31RA = 05:58:31 Dec = +23:26:18Dec = +23:26:18 04:56 UT04:56 UT

Determine the time of Determine the time of yearyear

The Astrolabe The Astrolabe timepiecetimepiece