The Flammarion engraving by an unknown artist, first documented in Camille Flammarion's 1888 book L'atmosphère: météorologie populaire.

Transcription

1 The Flammarion engraving by an unknown artist, first documented in Camille Flammarion's 1888 book L'atmosphère: météorologie populaire.

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4 Horizon Coordinates: Altitude (angular height above horizon) Azimuth (angular distance along horizon from N through E)

5 Summary horizon coordinates horizon zenith meridian (N-Z-S) altitude & azimuth circumpolar stars 5

6 Celestial Coordinates: Declination (degrees/arcmin/arcsec above/below the CE) Right ascension (hours/minutes/seconds along CE eastward from VE) where 360 o = 24 h Vernal equinox is the position of the Sun on the Celestial Equator (on Mar 21st)

7 Betelgeuse RA = 05 h 55 m 10.3 s DEC = Rigel RA = 05 h 14 m 32.2 s DEC =

8 Ecliptic

9 Moon s orbit is not circular (apogee = furthest / perigee = closest), and it is inclined to the celestial equator, thus eclipses are rare.

10 solar eclipse lunar eclipse

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12 YOU HAVE WON OBSERVING TIME AT THE UVIC OBSERVATORY TONIGHT WHAT WILL YOU OBSERVE? 1. Betelgeuse RA 05 h 55 m 10.3 s DEC M71 (globular cluster) RA 19 h 53 m 46.5 s DEC M31 (Andromeda galaxy) RA 00 h 42 m 44.0 s DEC Proxima Centauri RA 14 h 29 m 42.0 s DEC

13 Summary horizon coordinates horizon zenith meridian (N-Z-S) altitude & azimuth circumpolar stars (read Chapters ) celestial coordinates celestial sphere celestial equator celestial poles right ascension & declination vernal equinox ecliptic eclipse 13

14 heliocentric view geocentric view

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16 Distances to Stars from Stellar Parallax Apparent motion of a star relative to background stars. The angle of parallax is half the angular shift over a 6 month period

17 Stellar Parallax: [See pp. 38, 58] Using the small angle formula: (a = 1 AU) p (radians) = a / d where 1 AU = 1 Astronomical Unit i.e., the average distance Sun to Earth 2 π (radians) = 360 o radians are not the most useful unit, since most parallactic angles < 1 Define a new unit of distance, parsec: If p = 1 then d = 1 parsec (pc) d = 1 pc = 1 AU / [2 π / (360 x 3600)] rad/

18 Stellar Parallax: [See pp. 38, 58] Thus, if you know the parallactic angle, Then you can determine the distance. e.g., Proxima Centauri has p = 0.77 d = 1/p (if 1 AU, and p in ) d = 1.3 pc 1 AU = 1.5 x 10 8 km ** 1 pc = (360 x 3600 /2 π) = AU 1 pc = 3.1 x km d = 4 x km

19 Astronomical Unit : 1 AU = (a + b) / 2 a b

20 From Earth, - only ~50 stars with measurable p. Satellites do better: - longer baseline - higher resolution (no blurring from Earth's atmosphere) Hipparcos (High Precision Parallax Collecting Satellite) - ESA launch, : ~ 2.5 million stars, p < 1 milliarcsec!! Notice those distances > 1000 pc GAIA - ESA launch date December larger orbit, larger mirror ~ 1000 million stars, p < milliarcsec, or ~ 40 kpc measuring the diameter of a human hair at a distance of 1000 km.

21 NOTE: Apparent Motion (parallax) Space Motion 21

22 Proper Motion = µ in arcseconds/year (an angular velocity) distinct from parallax since it does not repeat itself yearly. ~350 stars have µ > 1 arcsec/year

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24 Radial Velocity, v r Recall that the wavelengths of spectral lines λ depends on the motion of the emitter relative to the observer. Measured by the Doppler shift of the star s spectral lines. λ / λ o = ( (c + v r ) / (c - v r ) ½ when v r = 0, λ = λ o

25 Radial Velocity, v r Expand this formula when v r << c such that, λ / λ o = ( (c + v r ) / (c - v r ) ) ½ λ / λ o = (1 + v r / c) ½ / (1 v r / c) ½ (1 + ½(v r / c) + ) (1 + (-½)(-v r / c) + ) 1 + v r / c rearrange this as, v r / c = (λ /λ o ) 1 = ( λ λ o ) / λ o = Δλ / λ o blue shift : λ < λ o red shift: λ > λ o

26 Transverse (tangental) velocity, v t [See pp ] Measure this using the proper motion: v t = µ d (small angle formula) Units on these parameters are odd: µ (arcsec/yr), d (pc) v t (AU/yr) Thus, convert AU/yr to km/s: v t = 4.74 µ d (km/s)

27 Space Velocity, v (with respect to the Sun) v 2 = v r 2 + v t 2 Space Direction, θ (v makes an angle θ with respect to the line of sight) tan θ = v t / v r

28 Moving Cluster Method for distance: (First Lab Exercise) - stars in a cluster have a common motion, or the cluster would disperse (ignoring small internal motions) - notice that proper motions vary (by angle) but space motions are the same. - errors in proper motions make the convergent point hard to locate precisely thus, works best on nearby, large clusters, e.g., the Hyades (in lab)

29 If all the stars in the cluster appear to be moving towards C, then v t is related to v r as: using v t = v r tan θ v t = 4.74 µ d then d = v r tan θ / 4.74 µ if C is found, then measuring v r, µ, and θ allows you to find d [pc], and these are all measurable.

30 Hyades cluster, distance: d = / pc (ESA, 19 Feb 1998) Hyades proper motions are from Hipparcos, (results using parallax with GAIA are still TBD) Hyades distance is one of the most fundamental measurements in astronomy, and sets the zero point of the cosmic distance scale, i.e., the distance scale used to find distances to galaxies, and ultimately the size of the Universe.

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32 Go out in the early morning and appreciate the Hyades in a new way Aldebaran

33 Summary of the astronomy language: horizon coordinates horizon zenith meridian (N-Z-S) altitude & azimuth circumpolar stars celestial coordinates celestial sphere celestial equator celestial poles right ascension & declination ecliptic vernal equinox Stellar parallax Parallactic Angle Parsec Astronomical Unit Space Motion Proper Motion Angular Velocity Doppler shift phases & eclipses apogee & perigee inferior & superior conjunction greatest elongation 33