Fundamental Astronomy

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

Table C.27 (continued) Satellite Launch date Target Smart-1 ESA Sep 28, 2003 Moon Rosetta ESA Mar 2, 2004 Churyumov-Gerasimenko Gravity Probe B USA Apr 20, 2004 relativity Messenger USA Aug 3, 2004 Mercury Swift USA Nov 20, 2004 gamma ray bursts Deep Impact USA Jan 12, 2005 Tempel 1 Mars Recon Orbiter USA Aug 12, 2005 Mars Venus Express ESA Nov 9, 2005 Venus New Horizons USA Jan 19, 2006 Pluto Akari Japan Feb 22, 2006 infrared C. Tables 465
Answers to Exercises Chapter 2 2.1 The distance is ≈ 7640 km, the northernmost point is 79◦N, 45◦W, in North Greenland, 1250 km from the North Pole. 2.2 The star can culminate south or north of zenith. In the former case we get δ = 65 ◦ , φ = 70 ◦ , and in the latter δ = 70 ◦ , φ = 65 ◦ . 2.3 a) φ>58 ◦ 7 ′ . If refraction is taken into account, the limit is 57 ◦ 24 ′ . b) φ = δ = 7 ◦ 24 ′ . c) −59 ◦ 10 ′ ≤ φ ≤−0 ◦ 50 ′ . 2.4 Pretty bad. 2.5 λ⊙ = 70 ◦ 22 ′ , β⊙ = 0 ◦ 0 ′ , λ⊕ = 250 ◦ 22 ′ , β⊕ = 0 ◦ 0 ′ . 2.6 c) Θ0 = 18 h. 2.8 α = 6h45min9s,δ =−16 ◦ 43 ′ . 2.9 vt = 16.7kms −1 , v = 18.5kms −1 , after ≈ 61,000 years. µ = 1.62 ′′ per year, parallax 0.42 ′′ . Chapter 3 3.1 a) The flux density in the focal plane as well as the exposure time are proportional to (D/ f ) 2 . Thus the required exposure is 3.2s.b)1.35 cm and 1.80 cm. c) 60 and 80. 3.2 a) 0.001 ′′ (note that the aperture is a line rather than circular; therefore the coefficient 1.22 should not be used). b) 140 m. Chapter 4 4.1 0.9. 4.2 The absolute magnitude will be −17.5 andapparent 6.7. 4.3 N(m + 1)/N(m) = 10 3/5 = 3.98. 4.4 r = 2.1 kpc, E B−V = 0.7, and (B − V )0 = 0.9. 4.5 a) ∆m = 1.06 mag, m = 2.42. b) τ = − ln 0.85 6 ≈ 0.98. Chapter 5 5.2 n = 166, which corresponds to λ = 21.04 cm. Such transitions would keep the population of the state n = 166 very high, resulting in downward transitions also from this state. Such transitions have not been detected. Hence, the line is produced by some other process. 5.3 If we express the intensity as something per unit wavelength, we get λmax = 1.1 mm. If the intensity is given per unit frequency, we have λmax = 1.9 mm. The total intensity is 2.6 × 10 13 Wm −2 sterad −1 . At 550 nm the intensity is practically zero. 5.4 a) L = 1.35 × 10 29 W. The flux in the given interval can be found by integrating Planck’s law numerically. Using the Wien approximation a rather complicated expression can be derived. Both methods give the result that 3.3% of the radiation is in the visual range, thus L V = 4.45 × 10 27 W. b) At a distance of 10 pc the observed flux density is 3.7 × 10 −9 Wm −2 . b) 10.3km. 5.5 Mbol = 0.87, whence R = 2.0 R⊙. 5.6 T = 1380 K. There are several strong absorption lines in this spectral region, reducing the brightness temperature. 5.8 vrms ≈ 6700 km s −1 . Chapter 6 6.1 va/vp = (1 − e)/(1 + e). For the Earth this is 0.97. 467
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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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Page 416 and 417: 416 20. Astrobiology According to t
Page 418 and 419: 418 20. Astrobiology of spiral gala
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Page 424 and 425: 424 20. Astrobiology Now panspermia
Page 426 and 427: 426 20. Astrobiology 20.9 Detecting
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 466 and 467: 468 Answers to Exercises 6.2 a = 1.
Page 468 and 469: 470 Answers to Exercises Chapter 17
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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