Astronomy Principles and Practice Fourth Edition.pdf

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224 The radiation laws Figure 15.7. The energy levels of the hydrogen atom. For a transition between the m and n levels, it is, therefore, expected that a spectral line would occur at the frequency ν, the line being in emission for a downward transition (i.e. from an excited state to a less excited state) and being in absorption for an upward transition. Accordingly, spectral lines should appear at frequencies given by ν = E m − E n h or, in terms of wavelength, at ch λ = . (15.22) E m − E n By substituting values for E m and E n (see equation (15.20)), we have that λ mn = 8ε2 0 ch3 e 4 m e 1 (1/n 2 − 1/m 2 ) m and by substituting for the constants this reduces to λ mn = 9·12 × 10−8 (1/n 2 − 1/m 2 ) m. or, 912 λ mn = (1/n 2 − 1/m 2 Å. (15.23) ) It will be seen from equation (15.23) that the spectral lines can conveniently be expressed in terms of series, the first corresponding to n = 1, m ≥ 2 (Lyman series), the second corresponding to n = 2, m ≥ 3 (Balmer series), n = 3, m ≥ 4 (Paschen series), n = 4, m ≥ 5 (Brackett series), n = 5, m ≥ 6 (Pfund series), etc. Figure 15.8 illustrates the series which are particularly important in astronomy and the wavelengths of the chief spectral lines, in close agreement with those predicted by the simple Bohr theory (see equation (15.23)), are collected in table 15.2. It will be seen from table 15.2 that the Lyman series is to be found in the ultraviolet. This series was discovered in 1906 just before Bohr’s theory. The Balmer series occurs through the visible region and is an important feature in stellar spectra. Three of the lines of this series, Hα, Hβ and Hγ , correspond respectively to the C, F and G lines designated by Fraunhofer.
Spectral lines 225 Figure 15.8. Energy transitions giving rise to the Lyman, Balmer and Paschen series in the hydrogen spectrum. Table 15.2. The wavelength positions of spectral lines in the hydrogen spectrum. n = 1 n = 2 n = 3 Lyman series Balmer series Paschen series λ (Å) λ (Å) λ (Å) m = 2 Lα 1215 m = 3 Hα (Fraunhofer C) 6562 m = 4 Pα 18 751 m = 3 Lβ 1025 m = 4 Hβ (Fraunhofer F) 4861 m = 5 Pβ 12 818 m = 4 Lγ 972 m = 5 Hγ (Fraunhofer G) 4340 m = 6 Pγ 10 938 m = 5 Lδ 949 · · · · · · · · · ∞ 912 ∞ 3646 ∞ 8 208 If a hydrogen atom is sufficiently excited to allow an energy level which is greater than the upper limit—a limit which does not exist in classical dynamics—the electron will leave the atom, which is then said to be ionized. A similar reverse procedure can also be imagined where an electron which
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Chapter 1 Naked eye observations 1.
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A month 5 seen to rise above the ea
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A year 7 between south and west. An
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Chapter 2 Ancient world models Firs
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Ancient world models 11 Figure 2.1.
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Chapter 3 Observations made by inst
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Instrumentation in astronomy 15 Fig
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The role of the observer 17 Earth a
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Electromagnetic radiation 19 meteor
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Electromagnetic radiation 21 If, fo
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Electromagnetic radiation 23 device
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Direction of arrival of the radiati
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Brightness 27 Figure 5.3. The windo
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Brightness 29 physical conditions w
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Time 31 to house radio transmitters
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Chapter 6 The night sky 6.1 Star ma
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Simple observations 35 Figure 6.1.
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Chapter 7 The geometry of the spher
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Position on the Earth’s surface 4
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Position on the Earth’s surface 4
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Spherical trigonometry 51 determine
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Spherical trigonometry 53 Figure 7.
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The small spherical triangle 55 7.4
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Problems—Chapter 7 57 Although th
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Chapter 8 The celestial sphere: coo
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The equatorial system 61 Figure 8.2
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Circumpolar stars 63 Figure 8.4. A
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Also Hence, we have or The measurem
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The geocentric celestial sphere 67
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Transformation of one coordinate sy
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Right ascension 71 or cos 47 ◦ 39
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The Sun’s geocentric behaviour 73
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Sunset and sunrise 75 Figure 8.15.
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Megalithic man and the Sun 77 Figur
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The ecliptic system of coordinates
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Galactic coordinates 81 Table 8.1.
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Galactic coordinates 83 Figure 8.22
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Galactic coordinates 85 Figure 8.25
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Problems—Chapter 8 87 where ε is
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Sidereal time 89 Figure 9.1. The ti
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Sidereal time 91 Figure 9.3. An equ
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Mean solar time 93 Figure 9.4. Posi
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The relationship between mean solar
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The civil day and timekeeping 97 It
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The tropical year and the calendar
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The Earth’s geographical zones 10
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Hence, the period of the year durin
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Twilight 105 Figure 9.10. The heati
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Twilight 107 For this to happen, ZB
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h m s Date Approximate ZT 16 30 0 J
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Problems—Chapter 9 111 Date (00 h
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Atmospheric refraction 113 Figure 1
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where ZOL = r. But ZOL = ζ .AlsoAB
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so that we have But Hence, Similarl
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Now But θ is a small angle so we m
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Geocentric parallax 121 Figure 10.6
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The semi-diameter of a celestial ob
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Measuring distance in the Solar Sys
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Stellar parallax 127 Figure 10.10.
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Stellar parallax 129 after. The val
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Problems—Chapter 10 131 Recent ob
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Chapter 11 The reduction of positio
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The velocity of light 135 Table 11.
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The constant of aberration 137 Figu
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Diurnal and planetary aberration 13
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Precession of the equinoxes 141 Fig
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Effect of precession on a star’s
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Nutation 145 Figure 11.10. The grav
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The tropical and sidereal years 147
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Chapter 12 Geocentric planetary phe
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The Copernican System 151 Figure 12
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Planetary configurations 153 (a) V
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The synodic period 155 Figure 12.5.
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Measurement of planetary distances
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Stationary points 159 Figure 12.8.
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Stationary points 161 Using equatio
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The phase of a planet 163 Figure 12
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Problems—Chapter 12 165 with an o
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Planetary orbits 167 Figure 13.1. M
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Planetary orbits 169 If P 1 SP 2 is
Page 170 and 171: Newton’s law of gravitation 171 a
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Page 186 and 187: 14.3 General properties of the many
Page 188 and 189: Special perturbation theories 189 F
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Page 206 and 207: 210 The radiation laws Figure 15.1.
Page 208 and 209: 212 The radiation laws Table 15.1.
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274 Visual use of telescopes By sub
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276 Visual use of telescopes 17.3 M
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278 Visual use of telescopes By let
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280 Visual use of telescopes Figure
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282 Visual use of telescopes For sm
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284 Detectors for optical telescope
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306 Astronomical optical measuremen
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Chapter 20 Modern telescopes and ot
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332 Modern telescopes and other opt
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Chapter 21 Radio telescopes 21.1 In
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354 Radio telescopes Figure 21.2. A
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358 Radio telescopes Figure 21.6. T
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362 Radio telescopes (a) Paraboloid
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364 Radio telescopes Figure 21.12.
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366 Radio telescopes The record fro
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368 Radio telescopes 2 N N Figure 2
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Chapter 22 Telescope mountings 22.1
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376 Telescope mountings arc and thi
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378 Telescope mountings Figure 22.4
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380 Telescope mountings The design
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382 High energy instruments and oth
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404 Practical projects to give the
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406 Practical projects Figure 24.2.
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408 Practical projects measurement
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416 Practical projects Summer Time
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418 Practical projects Figure 24.12
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422 Practical projects point was ch
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426 Practical projects N φ Earth 1
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428 Practical projects 24.5 Solar d
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430 Practical projects allows the S
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432 Practical projects 24.5.4 The e
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438 Practical projects Now in t hou
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440 Practical projects Table 24.2.
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442 Practical projects 24.7.2 The i
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448 Practical projects right ascens
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450 Practical projects amenable to
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452 Web sites • W 20.5—www.mrao
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Appendix: Astronomical and related
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456 Appendix: Astronomical and rela
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Bibliography 1 Source books The Ast
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Answers to problems Chapter 7 1. 32
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462 Answers to problems Figure A8.2
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464 Answers to problems Figure A10.
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466 Answers to problems Figure A13.
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468 Answers to problems 5. 1·64 6.
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470 Index black body radiation, 216
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472 Index atom, 221 line, 353 illum
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474 Index potential energy, 177 pow
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