Coordinates, Time, MagnitudesAST443, Lecture 3Stanimir Metchev2Administrative• Keys to ESS 437A– see Owen Evans (ESS 255, 2-8061)– $25 refundable deposit• Homework 1:– Bradt, problems 3.22, 3.32, 4.22, 4.53• Reading for next week:– Bradt: 5, 6.3– Wall & Jenkins: 1–2– Howell: 1–33Outline• Celestial coordinates (cont.)• Astronomical time• Distance measurement• Brightness measurement4Coordinate Transformations• equatorial ↔ ecliptic• equatorial ↔ horizontal! cos"cos#= cos$cos%cos"sin#= cos$sin%cos&' sin$sin&sin"= cos$sin%sin&+ sin$cos&cos$sin%= cos"sin#cos&+ sin"sin&sin$= sin"cos&' cos"sin#sin&! cos asin A = "cos#sin HAcos acos A = sin#cos$" cos#cos HA sin$sin a = sin#sin$+ cos#cos HA cos$cos#sin HA = "cos asin Asin#= sin a sin$+ cos a cos A cos$φ ≡ observer’s latitude5Equatorial CoordinateSystems• FK4– precise positions and motions of 3522 stars– adopted in 1976– B1950.0• FK5– more accurate positions– fainter stars– J2000.0• ICRS (International Celestial Reference System)– extremely accurate (± 0.5 milli-arcsec)– 250 extragalactic radio sources• negligible proper motions– J2000.06Outline• Celestial coordinates (cont.)• Astronomical time• Distance measurement• Brightness measurement7Astronomical Time• sidereal time– determined w.r.t. stars– local sidereal time (LST)• R.A. of meridian• HA of vernal equinox– sidereal day: 23h 56m 4.1s• object’s hour angleHA = LST – α8Astronomical Time• sidereal time– determined w.r.t. stars– local sidereal time (LST)• R.A. of meridian• HA of vernal equinox– sidereal day: 23h 56m 4.1s• object’s hour angleHA = LST – α• solar time– solar day is 3 min 56 seclonger than sidereal day9Astronomical Time• universal time– UT0: determined from celestial objects• corrected to duration of mean solar day• HA of the mean Sun at Greenwich (a.k.a., GMT)– UT1: corrected from UT0 for Earth’s polar motion10PolarMotion11Astronomical Time• universal time– UT0: determined from celestial objects• corrected to duration of mean solar day• HA of the mean Sun at Greenwich (a.k.a., GMT)– UT1: corrected from UT0 for Earth’s polar motion• 1 day = 86400 s, but duration of 1 s is variable– UTC: atomic timescale that approximates UT1• kept within 0.9 sec of UT1 with leap seconds• international standard for civil time• set to agree with UT1 in 1958.012Precession and Nutation• The Earth precesses…– Sun’s and Moon’s tidal forces– precession cycle: 25,800 years– rate is 1º in 72 years (alongprecession circle) = 50.3″/year• … and nutates– Sun and Moon change relativelocations– largest component has period of18.6 years (19″ amplitude)eclipticcoordsNE13Astronomical Time• tropical year– measured between successive passages of the Sun through the vernalequinox– 1 yr = 365.2422 mean solar days• mean sidereal year– Earth: 50.3″/yr precession in direction opposite of solar motion– 365.2564 days• Julian calendar– leap days every 4th year; 1 yr = 365.25 days– Julius Caesar in 46 BCE– t0 = noon on Jan 1st, 4713 BC• Gregorian calendar– no leap day in century years not divisible by 400 (e.g., 1900)– 1 yr = 365.2425 days– Pope Gregory XIII in 1582• by 1582 tropical and Julian year differed by 12 days14Coordinate Epochs• Coordinates are given at B1950.0 or J2000.0 epochs– Besselian years (on Gregorian calendar; tropical years)– Julian years (Julian calendar)• Gregorian calendar is irregular– complex for precise measurements over long time periods• Julian epoch:– Julian date: JD = 0 at noon on Jan 1, 4713 BC– J = 2000.0 + (JD – 2451545.0) / 365.25– J2000.0 defined at• JD 2451545.0• January 1, 2000, noon15Outline• Celestial coordinates (cont.)• Astronomical time• Distance measurement• Brightness measurement16Trigonometric Parallax• distance to nearby star is 1 parsec (pc) when angle p = 1 arc second (1")• 1 pc = 3.26 light years (ly) = 2.06x105 AU = 3.09x1018 cm• Proxima Cen is at 1.3 pc ~ 4.3 ly17Stellar Proper Motion•µ ≡ annual propermotion•θ ≡ position angle(PA) of proper motionBarnard’s star, 1.8 pc, µ =10.3″/yrequatorial coordsNEθ18Stellar Proper Motion•µ ≡ annual propermotion•θ ≡ position angle(PA) of proper motionequatorial coordsNEθ! µ"=µcos#µ$cos"=µsin#19Outline• Celestial coordinates (cont.)• Astronomical time• Distance measurement• Brightness measurement20Magnitudes• Stefan-Boltzmann Law: F = σ T 4[erg s–1 cm–2]• apparent magnitude: m = –2.5 lg F/F0– m increases for fainter objects!– m = 0 for Vega; m ~ 6 mag for faintest naked-eye stars– faintest galaxies seen with Hubble: m ≈ 30 mag• 109.5 times fainter than faintest naked-eye stars– dependent on observing wavelength• mV, mB, mJ, or simply V (550 nm), B (445 nm), J (1220 nm), etc• bolometric magnitude (or luminosity): mbol (or Lbol)– normalized over all wavelengths21Absolute Magnitude andDistance Modulus• The apparent magnitude of a star at 10 pc– used to compare absolute brightnesses of different starsM = m + 2.5 lg F(r) / F(10 pc)• Distance modulus (DM)– a proxy for distancem – M = 5 lg (r / 10 pc)– DM = 0 mag for object at 10 pc– DM = –4.4 mag for Proxima Cen– DM = 14.5 mag to Galactic