Astronomy Principles and Practice Fourth Edition.pdf

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Appendix: Astronomical and related constants A.1 Physical constants Velocity of light c = 2·997 925 × 10 8 ms −1 Constant of gravitation G = 6·668 × 10 −11 Nm 2 kg −2 Planck constant h = 6·625 × 10 −34 Js Boltzmann constant k = 1·380 × 10 −23 JK −1 Stefan–Boltzmann constant σ = 5·669 × 10 −8 Wm −2 K −4 Wien displacement law constant λ max T = 2·90 × 10 −3 mK Mass of electron m e = 9·108 × 10 −31 kg Electron charge e = 1·602 06 × 10 −19 C Solar parallax P ⊙ = 8·′′ 794 05 Constant of aberration = 20·′′ 49 Constant of nutation = 9·′′ 207 Obliquity of ecliptic at any epoch t: ε = 23 ◦ 26 ′ 21·′′ 45 − 46·′′ 815T where T = (t − 2000·0)/100 Constant of general precession = 50·′′ 290 966 per Julian year (at standard epoch 2000·0) Permittivity of free space ɛ 0 = 8·854 24 × 10 −12 Fm −1 A.2 Time Length of the second 1 dynamical second = 1/31 556 925·975 of length of tropical year at 1900·0 1 mean solar second (smoothed) = 1 dynamical second to about 1 part in 10 8 1 mean second = 1·002 737 909 3 mean sidereal seconds Length of the day 454 1 mean solar day = 1·002 737 909 3 sidereal days = 24 h 03 m 56·s5554 mean sidereal time = 86 636·5554 mean sidereal seconds 1 sidereal day = 0·997 269 566 4 mean sidereal days = 23 h 56 m 04·s0905 mean solar time seconds = 86 164·0905 mean solar seconds
Mathematical constants, systems of units and conversion factors 455 Length of the month Synodic 29·d530 59 29 d 12 h 44 m 03 s Sidereal 27·321 66 27 07 43 12 Anomalistic 27·554 55 27 13 18 33 Nodical 27·212 22 27 05 05 36 Tropical 27·321 58 27 07 43 05 Length of the year Tropical ( to ) 365·d242 20 365 d 05 h 48 m 46 s Sidereal (fixed star to fixed star) 365·256 36 365 06 09 10 Anomalistic (perigee to perigee) 365·259 64 365 06 13 53 Julian 365·25 365 06 00 00 A.3 Mathematical constants, systems of units and conversion factors 1radian= 57·◦295 78 = 3437·′747 = 206 264·′′ 8 Square degrees in a steradian = 3282·806 A sphere subtends 4π steradians at its centre π = 3·141 59 e = 2·718 28 log 10 e = 0·434 29 log e 10 = 2·302 58 1km= 0·621 37 miles = 0·539 96 nautical miles = 3280·8ft 1 mile = 1·6093 km 1 international nautical mile = 1·8250 km = 6076·11 ft 1 Å= 10 −7 mm 1AU= 149 600 000 km = 92 960 000 miles 1parsec= 206 264·8AU 1kms −1 = 2236·9 miles per hour 1 foot per second = 0·304 80 metres per second 1 AU per year = 2·9456 miles per second = 4·7404 km s −1 1 kilogram = 2·204 622 lb 1lb= 0·453 592 kg 1 electron volt (eV) = 1·602 06 × 10 −19 J Basic SI units Physical quantity Name of unit Symbol length metre m mass kilogram kg time second s electric current ampere A thermodynamic temperature degree Kelvin K
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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
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Newton’s law of gravitation 171 a
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The Principia of Isaac Newton 173 N
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The two-body problem 175 Figure 13.
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The two-body problem 179 13.6.5 The
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The astronomical unit 183 For an ex
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Chapter 14 Celestial mechanics: the
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14.3 General properties of the many
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Special perturbation theories 189 F
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Special perturbation theories 191 F
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14.6 Dynamics of artificial Earth s
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The geostationary satellite 195 in
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Interplanetary transfer orbits 197
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Then V B = V c2 − V A ,sinceV c2
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Problems—Chapter 14 205 (figure 1
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210 The radiation laws Figure 15.1.
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212 The radiation laws Table 15.1.
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216 The radiation laws In order to
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218 The radiation laws where σ is
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220 The radiation laws The brightne
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222 The radiation laws centrifugal
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226 The radiation laws is moving pa
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230 The radiation laws In most phys
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232 The radiation laws radiation ha
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234 The radiation laws radiation is
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236 The radiation laws Figure 15.14
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Chapter 16 The optics of telescope
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240 The optics of telescope collect
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Chapter 17 Visual use of telescopes
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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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Page 398 and 399: 404 Practical projects to give the
Page 400 and 401: 406 Practical projects Figure 24.2.
Page 402 and 403: 408 Practical projects measurement
Page 410 and 411: 416 Practical projects Summer Time
Page 412 and 413: 418 Practical projects Figure 24.12
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Page 422 and 423: 428 Practical projects 24.5 Solar d
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Page 426 and 427: 432 Practical projects 24.5.4 The e
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Page 434 and 435: 440 Practical projects Table 24.2.
Page 436 and 437: 442 Practical projects 24.7.2 The i
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Page 446 and 447: 452 Web sites • W 20.5—www.mrao
Page 450 and 451: 456 Appendix: Astronomical and rela
Page 452 and 453: Bibliography 1 Source books The Ast
Page 454 and 455: Answers to problems Chapter 7 1. 32
Page 456 and 457: 462 Answers to problems Figure A8.2
Page 458 and 459: 464 Answers to problems Figure A10.
Page 460 and 461: 466 Answers to problems Figure A13.
Page 462 and 463: 468 Answers to problems 5. 1·64 6.
Page 464 and 465: 470 Index black body radiation, 216
Page 466 and 467: 472 Index atom, 221 line, 353 illum
Page 468 and 469: 474 Index potential energy, 177 pow
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