Fundamental Astronomy

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$P 0.1 Stabilişti natura şsi suma seriilor: a) Σ 1 n\ ; b) Σ arctan 1 n# + n ...$

470 Answers to Exercises Chapter 17 17.1 µ = 0.0055 ′′ a−1 . 17.2 a) 5.7 kpc. b) 11 kpc. Possible reasons for the discrepancy include: 1) The distance is so large that the approximations used for deriving Oort’s formulae are not very good. 2) Taking into account the interstellar extinction will reduce the distance in b). 3) The peculiar velocity of the star was neglected. 17.3 a) 3 (and the Sun). b) The number is of the order of 100,000. This is a typical selection effect: bright stars are rare but they are visible overt long distances. 17.4 a) If the thickness of the disk is H, the light has to to travel a distance s = min{r,(H/2)sec b} in the interstellar medium. Thus the magnitude will be m = M + 5lg(r/10 pc) + as. b)s = 200 pc, m = 10.2. Chapter 18 18.1 a) 26, b) 25. 18.2 The diameter must be of the order one one lightweek ≈ 1200 AU. M =−23.5. If this is the bolometric magnitude, the luminosity is L ≈ 2 × 10 11 L⊙, corresponding to 210 L⊙AU −3 . Chapter 19 19.1 r = v/H = 93 Mpc (if H = 75), diameter is 35 kpc, M =−20.4. Potential sources of error include: 1) inaccuracy of the Hubble constant, 2) peculiar velocity of the galaxy, 3) intergalactic extinction, 4) only 2-dimensional projection is observed, and the edge depends on the limiting magnitude used. 19.2 If H = 50 km s −1 Mpc −1 , r = 51 Mpc, or 74 times the distance of M31. If H is doubled, the distance is reduced to half of that, but is still higher than the value obtained in Exercise 18.1. A possible explanation is the peculiar velocity of the galaxy. 19.3 mν = 1.5 × 10 −35 kg, or 0.00002 times the mass of the electron. Chapter 20 20.1 If the greenhouse effect is neglected, the distances corresponding to temperatures 373 K and 273 K are 0.47 AU and 0.87 AU, respectively. The effective temperature of the young Sun was T = 4√ 0.7 × 5785 K = 5291 K. The corresponding limits then were 0.39 AU and 0.73 AU. Thus the continuously habitable zone would extend from 0.47 to 0.73 AU. 20.2 If there are n stars in a volume V, the distance between the nearest neighbours is of the order 3√ V/n. If binary and triple stars in Table C.17 are counted as single objects, there are 47 stars in a volume of 520 cubic parsecs. a) If a fraction 0.01 of them is habited, the average distance between neighbouring civilizations is 10 parsecs; b) 100 parsecs.
Further Reading The following list of references is not intended as a complete bibliography. It gives a number of intermediate level or more advanced works, which can serve as starting points for those who wish to learn about some specific topic in more detail or depth. General Reference Works Cox: Allen’s Astrophysical Quantities, Springer 2000. Harwit: Astrophysical Concepts, 4th ed., Springer 2006. Kutner: Astronomy: A Physical Perspective, 2nd ed., Cambridge University Press 2003. Lang: Astrophysical Formulae, 3rd ed., Springer 1999. Maran (ed.): The Astronomy and Astrophysics Encyclopedia, Van Nostrand – Cambridge University Press 1992. Meeus: Astronomical Algorithms, Willman-Bell 1991. Schaifers, Voigt (eds.): Landolt-Börnstein Astronomy and Astrophysics, Springer 1981–82. Shu: The Physical Universe, University Science Books 1982. Unsöld, Baschek: The New Cosmos, 5th ed., Springer 2002. Chapter 2. Spherical Astronomy Green: Spherical Astronomy, Cambridge University Press 1985. Seidelmann (ed.): Explanatory Supplement to the Astronomical Almanac, University Science Books 1992. Smart: Spherical Astronomy, Cambridge University Press 1931. Chapter 3. Observations and Instruments Evans: Observation in Modern Astronomy, English Universities Press 1968. Hecht, Zajac (1974): Optics, Addison-Wesley 1974. Howell (ed.): Astronomical CCD Observing and Reduction Techniques, ASP Conference Series 23, 1992. King: The History of the Telescope, Charles Griffin & Co. 1955, Dover 1979. Kitchin: Astrophysical Techniques, Hilger 1984; 4th ed., Institute of Physics Publishing 2003. Léna: Observational Astrophysics, Springer 1998. Roth (ed.): Compendium of Practical Astronomy 1–3, Springer 1994. Rutten, van Venrooij: Telescope Optics, Willman-Bell 1988. Chapters 4 and 5. Photometry and Radiation Mechanisms Chandrasekhar: Radiative Transfer, Dover 1960. Emerson: Interpreting Astronomical Spectra, Wiley 1996; reprinted 1997. Rybicki, Lightman: Radiative Processes in Astrophysics, Wiley 1979. Chapter 6. Celestial Mechanics Brouwer, Clemence: Methods of Celestial Mechanics, Academic Press 1960. Danby: Fundamentals of Celestial Mechanics, MacMillan 1962; 2nd ed. Willman-Bell, 3rd revised and enlarged printing 1992. Goldstein: Classical Mechanics, Addison-Wesley 1950. Roy: Orbital Motion, John Wiley & Sons 1978; 3rd ed. Institute of Physics Publishing 1988, reprinted 1991, 1994. Valtonen and Karttunen: The Three-Body Problem, Cambridge University Press 2006. Chapter 7. The Solar System Atreya, Pollack, Matthews (eds.): Origin and Evolution of Planetary and Satellite Atmospheres, 1989; Bergstrahl, Miner, Matthews (eds.): Uranus, 1991; Binzel, Gehrels, Matthews (eds.): Asteroids II, 1989; Burns, Matthews (ed.): Satellites, 1986; Cruikshank: Neptune and Triton, 1996; Gehrels (ed.): Jupiter, 1976; Gehrels (ed.): Asteroids, 1979; Gehrels (ed.): Saturn, 1984; Gehrels (ed.): Hazards due to Comets and Asteroids, 1994; Greenberg, Brahic (eds.): Planetary Rings, 1984; Hunten, Colin, Donahue, Moroz (eds.): Venus, 1983; Kieffer, Jakosky, Snyder, Matthews (eds.): Mars, 1992; Lewis, Matthews, Guerreri (eds.): Resources of Near- Earth Space, 1993; 471
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Fundamental Astronomy
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Dr. Hannu Karttunen University of T
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VI Preface to the First Edition The
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VIII Contents 5.6 Continuous Spectr
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X Contents 16. Star Clusters and As
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1. Introduction 1.1 TheRoleofAstron
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1.2 Astronomical Objects of Researc
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theory of relativity must be used t
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of the gas may be 10 −21 kg m −
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12 2. Spherical Astronomy angles co
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14 or 2. Spherical Astronomy sin B
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16 2. Spherical Astronomy defined t
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18 2. Spherical Astronomy the verna
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20 2. Spherical Astronomy pole. The
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22 2. Spherical Astronomy Fig. 2.16
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26 2. Spherical Astronomy
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30 2. Spherical Astronomy numbers,
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32 2. Spherical Astronomy In the 19
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34 2. Spherical Astronomy mid-Septe
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36 2. Spherical Astronomy correspon
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38 2. Spherical Astronomy second of
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2. Spherical Astronomy 40 Since ∆
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42 2. Spherical Astronomy For the s
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44 2. Spherical Astronomy red. What
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3. Observations and Instruments Up
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the long, oblique path through the
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Fig. 3.6a-e. Diffraction and resolv
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3.2 Optical Telescopes Fig. 3.10. T
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3.2 Optical Telescopes Fig. 3.13. T
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so thin that it absorbs very little
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3.2 Optical Telescopes 59
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3.2 Optical Telescopes 61
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3.2 Optical Telescopes ◭ Fig. 3.1
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and CCD-cameras have largely replac
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Fig. 3.22a-e. The principle of read
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than a prism. The dispersion can be
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3.4 Radio Telescopes Fig. 3.25. The
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Fig. 3.27. The Atacama Large Millim
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Fig. 3.30. The VLA at Socorro, New
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Fig. 3.31. (a) X-rays are not refle
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Fig. 3.33. Refractors are not suita
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tored by laser interferometers. If
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4. Photometric Concepts and Magnitu
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If we are outside the source, where
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magnitudes can be equal, the flux d
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flux L will now decrease with incre
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this line is extrapolated to X = 0,
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since due to extinction, radiation
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96 5. Radiation Mechanisms Fig. 5.1
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98 5. Radiation Mechanisms From (5.
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100 5. Radiation Mechanisms Fig. 5.
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104 5. Radiation Mechanisms We now
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5. Radiation Mechanisms 106 Again F
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110 5. Radiation Mechanisms We can
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112 5. Radiation Mechanisms differe
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114 6. Celestial Mechanics The solu
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116 6. Celestial Mechanics prove (6
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118 6. Celestial Mechanics in the d
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120 6. Celestial Mechanics But cons
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122 6. Celestial Mechanics by the e
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124 6. Celestial Mechanics Substitu
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126 6. Celestial Mechanics a cloud
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128 6. Celestial Mechanics Since th
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130 6. Celestial Mechanics Exercise
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132 7. The Solar System Fig. 7.1. (
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134 7. The Solar System for each ob
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136 7. The Solar System Fig. 7.5. L
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138 7. The Solar System Inserting t
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140 7. The Solar System Therefore o
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142 7. The Solar System Fig. 7.10.
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144 7. The Solar System behaves mor
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146 7. The Solar System Table 7.1.
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150 7. The Solar System of the plan
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152 7. The Solar System If we denot
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154 7. The Solar System where F⊥
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158 7. The Solar System larized fea
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162 7. The Solar System The outer c
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168 7. The Solar System weak and co
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170 7. The Solar System amount of w
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176 7. The Solar System ter the rin
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178 7. The Solar System face, most
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180 7. The Solar System The F ring,
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182 7. The Solar System Herschel hi
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188 7. The Solar System liding, sin
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196 7. The Solar System of this mat
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202 7. The Solar System Near the po
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204 7. The Solar System be solved f
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8. Stellar Spectra All our informat
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which appears as irregular fluctuat
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8.2 The Harvard Spectral Classifica
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ate of ionization is essentially de
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lines of titanium, scandium and van
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efore τ = 1, i. e. the radiation i
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yielding Iν(0,θ)= Sν(τ ∗ ) +
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222 9. Binary Stars and Stellar Mas
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10. Stellar Structure The stars are
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where a = 4σ/c = 7.564 × 10−16
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where me is the electron mass and N
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is produced by the proton-proton (p
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oxygen, which in turn reacts to for
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According to (4.7), (4.4) and (5.16
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Example 10.6 The Radiation Pressure
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11. Stellar Evolution In the preced
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increases. The stellar surface temp
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Since stars are most likely to be f
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Fig. 11.4a-c. Energy transport in t
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Fig. 11.5. The structure of a massi
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tract to planetlike brown dwarfs. S
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Fig. 11.10a-f. Evolution of a low-m
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Fig. 11.12. The Wolf-Rayet star WR
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In a neutron capture, a nucleus wit
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This is several orders of magnitude
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264 12.TheSun Fig. 12.2. (a) The ro
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266 12.TheSun according to the heli
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268 12.TheSun shines into view for
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270 12.TheSun was established that
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272 12.TheSun Fig. 12.11. In pairs
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274 12.TheSun Fig. 12.15. (a) Quies
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276 12.TheSun Fig. 12.17. An X-ray
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13. Variable Stars Stars with chang
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Fig. 13.3. The variation of brightn
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Fig. 13.5. The lightcurve of a long
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duced when the carbon condenses int
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13.3 Eruptive Variables Fig. 13.12.
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Fig. 13.15. Supernova 1987A in the
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14. Compact Stars In astrophysics t
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about 1.4 M⊙, which is thus the u
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1968. In the following year it was
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ditions required for hypernova expl
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This is greater than the speed of l
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Fig. 14.12. Scale drawings of 16 bl
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are (or, in the radio case, have on
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14.6 Exercises Exercise 14.1 The ma
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308 15. The Interstellar Medium Fig
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310 15. The Interstellar Medium R d
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312 15. The Interstellar Medium pol
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318 15. The Interstellar Medium Tab
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322 15. The Interstellar Medium met
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324 15. The Interstellar Medium
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326 15. The Interstellar Medium He
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330 15. The Interstellar Medium up
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332 15. The Interstellar Medium hav
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334 15. The Interstellar Medium len
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336 15. The Interstellar Medium dro
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338 15. The Interstellar Medium the
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340 16. Star Clusters and Associati
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17. The Milky Way On clear, moonles
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Fig. 17.3. The directions to the ga
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classes of stars are main sequence
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Fig. 17.9. The size of the volume e
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lar material similarly moves in the
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Fig. 17.14. In order to derive Oort
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Fig. 17.17. The radial velocity as
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a suitable mass distribution, such
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esting because it may be a small-sc
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material constituting the galaxy. I
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18. Galaxies The galaxies are the f
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Fig. 18.3. The classification of no
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18.1 The Classification of Galaxies
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Fig. 18.7. Compound luminosity func
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In order to measure the mass at eve
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length r0 = 1-5 kpc. In Sc galaxies
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18.4 Dynamics of Galaxies We have s
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gas. Some normal spirals may have b
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the Large and Small Magellanic Clou
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stars are forming and evolving into
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panion galaxy. The tail is interpre
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een made at these wavelengths with
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galaxies in our present neighbourho
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394 19. Cosmology tographs form an
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396 19. Cosmology Fig. 19.3. Hubble
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398 19. Cosmology element after hyd
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400 19. Cosmology 19.3 Homogeneous
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402 19. Cosmology The potential ene
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404 19. Cosmology In an expanding c
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406 19. Cosmology about 40,000 degr
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408 19. Cosmology rather slowly. In
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410 19. Cosmology Fig. 19.15. Corre
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412 19. Cosmology where Ω0 = ρ0/
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414 19. Cosmology Example 19.2 Find
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416 20. Astrobiology According to t
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Page 424 and 425: 424 20. Astrobiology Now panspermia
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Page 428 and 429: 428 20. Astrobiology cles that we s
Page 430 and 431: Appendices 431
Page 432 and 433: Ellipse. Equation in rectangular co
Page 434 and 435: A and B can be determined graphical
Page 436 and 437: When using matrix formalism it is c
Page 438 and 439: Similarly, a volume integral I = f
Page 440 and 441: B. Theory of Relativity Albert Eins
Page 442 and 443: time interval between the events is
Page 444 and 445: C. Tables Table C.1. SI basic units
Page 446 and 447: Table C.6. The Sun Property Symbol
Page 448 and 449: Table C.11. Osculating elements of
Page 450 and 451: Discoverer Year of a Psid e i r M
Page 452 and 453: Table C.16. Periodic comets with se
Page 454 and 455: Table C.17 (continued) C. Tables Na
Page 456 and 457: C. Tables Table C.19. Some double s
Page 458 and 459: Table C.22. Optically brightest gal
Page 460 and 461: Table C.23 (continued) Abbreviation
Page 462 and 463: C. Tables Table C.26. Millimetre an
Page 464 and 465: Table C.27 (continued) Satellite La
Page 466 and 467: 468 Answers to Exercises 6.2 a = 1.
Page 470 and 471: 472 Further Reading Morrison (ed.):
Page 472 and 473: 474 Further Reading Maps and Catalo
Page 474 and 475: Name and Subject Index A aberration
Page 476 and 477: coherent radiation 95 Cold Dark Mat
Page 478 and 479: forbidden transition 101, 332 four-
Page 480 and 481: Kellman, Edith 212 Kepler’s equat
Page 482 and 483: nautical mile 15 nautical triangle
Page 484 and 485: Reber, Grote 69 recombination 95, 9
Page 486 and 487: synchronous rotation 135 synchrotro
Page 488 and 489: Colour Supplement 491
Page 490 and 491: Plate 14. The first view from the s
Page 492 and 493: Plate 1 Plate 2 Colour Supplement 4
Page 494 and 495: Plate 6 Plate 5 Colour Supplement 4
Page 496 and 497: Plate 9 Colour Supplement Plate 10
Page 502 and 503: Plate 23 Plate 24 Colour Supplement
Page 504 and 505: Colour Supplement Plate 29 507
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