coordinates, time, magnitudes13 astronomical time • tropical year –measured between successive...
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Coordinates, Time, Magnitudes
AST443, Lecture 3Stanimir Metchev
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Administrative
• Keys to ESS 437A– see Owen Evans (ESS 255, 2-8061)– $25 refundable deposit
• Homework 1:– Bradt, problems 3.22, 3.32, 4.22, 4.53
• Reading for next week:– Bradt: 5, 6.3– Wall & Jenkins: 1–2– Howell: 1–3
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Outline
• Celestial coordinates (cont.)
• Astronomical time
• Distance measurement
• Brightness measurement
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Coordinate Transformations• equatorial ↔ ecliptic
• equatorial ↔ horizontal!
cos"cos# = cos$ 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&
!
cosasinA = "cos# sinHA
cosacosA = sin#cos$ " cos#cosHAsin$
sina = sin# sin$ + cos#cosHAcos$
cos# sinHA = "cosasinA
sin# = sinasin$ + cosacosAcos$
φ ≡ observer’s latitude
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Equatorial 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– J2000.0
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Outline
• Celestial coordinates (cont.)
• Astronomical time
• Distance measurement
• Brightness measurement
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Astronomical 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 angle
HA = LST – α
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Astronomical 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 angle
HA = LST – α• solar time
– solar day is 3 min 56 seclonger than sidereal day
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Astronomical 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
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PolarMotion
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Astronomical 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 1958.0
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Precession and Nutation• The Earth precesses…
– Sun’s and Moon’s tidal forces– precession cycle: 25,800 years– rate is 1º in 72 years (along
precession circle) = 50.3″/year• … and nutates
– Sun and Moon change relativelocations
– largest component has period of18.6 years (19″ amplitude)
eclipticcoords
NE
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Astronomical 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 days
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Coordinate 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, noon
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Outline
• Celestial coordinates (cont.)
• Astronomical time
• Distance measurement
• Brightness measurement
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Trigonometric 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 ly
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Stellar Proper Motion
• µ ≡ annual propermotion
• θ ≡ position angle(PA) of proper motion
Barnard’s star, 1.8 pc, µ =10.3″/yr
equatorial coords
N
E
θ
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Stellar Proper Motion
• µ ≡ annual propermotion
• θ ≡ position angle(PA) of proper motion
equatorial coords
N
E
θ
!
µ" = µcos#
µ$ cos" = µsin#
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Outline
• Celestial coordinates (cont.)
• Astronomical time
• Distance measurement
• Brightness measurement
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Magnitudes• 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 wavelengths
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Absolute Magnitude andDistance Modulus
• The apparent magnitude of a star at 10 pc– used to compare absolute brightnesses of different stars
M = 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 center