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