Professor Emeritus in Astronomy, Honorary Lecturer and Senior Research Fellow, University of Glasgow

Astronomy: Principles and Practice Fourth Edition A E Roy, PhD, FRAS, FRSE, FBIS Professor Emeritus in Astronomy, Honorary Lecturer and Senior Research Fellow, University of Glasgow D Clarke, PhD, MInstP, FRAS Honorary Research Fellow in Physics and Astronomy, University of Glasgow lop Institute of Physics Publishing Bristol and Philadelphia

Contents Foreword to fourth edition Foreword to third edition Foreword to second edition Foreword to first edition Acknowledgments xvii xix xx xxi xxiii PART 1 Introduction Chapters 1-6 1 Naked 1.1 1.2 1.3 1.4 1.5 eye observations Introduction Instantaneous phenomena 1.2.1 Day 1.2.2 Night A few hours 1.3.1 Day 1.3.2 Night A month A year 2 Ancient world models 3 Observations made by instruments 13 3.1 The subjectivity of simple measurements 13 3.2 Instrumentation in astronomy 14 3.3 The role of the observer 16 4 The nature of the observables 18 4.1 Introduction, 18 4.2 Macroscopic bodies 18 4.3 Atomic particles 19 4.4 Electromagnetic radiation 19 4.4.1 The wave nature of radiation 19 4.4.2 The photon nature of radiation 21 4.4.3 Polarization 22 3 3 4 4 4 4 4 5 5 6

viii - - Contents 5 The astronomer's measurements 24 5.1 5.2 5.3 5.4 5.5 Introduction Direction of arrival of the radiation Brightness 5.3.1 Factors affecting brightness 5.3.2 The magnitude system Polarization Time The night sky 33 6.1 Star maps and catalogues 33 6.2 Simple observations 35 24 24 27-27 29 30 31 PART 2 The Celestial Sphere and Elementary Celestial Mechanics Chapters 7-14 43 7 The geometry of the sphere 45 7.1 Introduction 45 7.2 Spherical geometry 45 7.3 Position on the Earth's surface 47 7.3.1 GPS satellites 50 7.4 Spherical trigonometry 51 7.4.1 The formulas 51 7.4.2 Proof of cosine formula 52 7.4.3 Proof of sine formula.. 54 7.4.4 Proof of the analogue to the cosine formula 54 7.4.5 Proof of the four-parts formula 55 7.5 Other formulas of spherical trigonometry 55 7.6 The small spherical triangle 55 Problems Chapter 7 57 8 The celestial sphere: coordinate systems 59 8.1 Introduction 59 8.2 The horizontal (alt-azimuth) system 59 8.3 The equatorial system 61 8.4 Southern hemisphere celestial spheres 62 8.5 Circumpolar stars 63 8.6 The measurement of latitude and declination 65 8.7 The geocentric celestial sphere 67 8.8 Transformation of one coordinate system into another 68 8.9 Right ascension 71 8.10 The Sun's geocentric behaviour 72 8.11 Sunset and sunrise 74 8.12 Megalithic man and the Sun 76 8.13 Sidereal time 78 8.14 The ecliptic system of coordinates 79 8.15 Galactic coordinates 80 Problems Chapter 8 86

Contents ix 9 The celestial sphere: timekeeping systems 88 9.1 Introduction 88 9.2 Sidereal time 88 9.3 Mean solar time 92 9.4 The relationship between mean solar time and sidereal time 95 9.5 The civil day and timekeeping 96 9.6 The Greenwich date and zone time (with date) 98 9.7 The tropical year and the calendar 99 9.8 The Julian date 99 9.9 Dynamical time 100 9.10 The Earth's geographical zones 101 9.11 The seasons 103 9.12 Twilight 105 Problems Chapter 9 110 10 The reduction of positional observations: I 112 10.1 Introduction 112 10.2 Atmospheric refraction 112 10.2.1 The laws of refraction 112 10.2.2 Astronomical refraction 114 10.2.3 Measurement of the constant of refraction 116 10.2.4 Horizontal refraction 117 10.3 Correction for the observer's altitude 118 10.4 Geocentric parallax 120 10.5 The semi-diameter of a celestial object 122 10.6 Measuring distance in the Solar System 124 10.6.1 The Moon 124 10.6.2 The planets 125 10.7 Stellar parallax. 126 10.7.1 Stellar parallactic movements 126 10.7.2 The parallactic ellipse 127 10.7.3 The measurement of stellar parallax 128 10.7.4 Theparsec 130 10.7.5 Extrasolar planets 130 Problems Chapter 10 131 11 The reduction of positional observations: II 133 11.1 Introduction.. 133 11.2 Stellar aberration 133 11.3 The velocity of light 135 11.4 The angle of aberration 136 11.5 The constant of aberration 137 11.6 Diurnal and planetary aberration 138 11.7 Precession of the equinoxes 140 11.8 Measuring the positions of T and the celestial equator 142 11.9 Effect of precession on a star's equatorial coordinates 143 11.10 The cause of precession 144 11.11 Nutation 145 11.12 The tropical and sidereal years 147 Problems Chapter 11 147

x Contents 12 Geocentric planetary phenomena 149 12.1 Introduction 149 12.2 The Ptolemaic System 150 12.3 The Copernican System 151 12.4 The astronomical discoveries of Galileo 152 12.5 Planetary configurations 153 12.6 The synodic period 154 12.7 Measurement of planetary distances 156 12.8 Geocentric motion of a planet 158 12.9 Stationary points 159 12.10 The phase of a planet 162 12.11 Improvement of accuracy 164 Problems Chapter 12 164 13 Celestial mechanics: the two-body problem 166 13.1 Introduction 166 13.2 Planetary orbits 166 13.2.1 Kepler's laws 166 13.2.2 Kepler's first law 167 13.2.3 Kepler's second law 168 13.2.4 Kepler's third law 169 13.3 Newton's laws of motion 170 13.4 Newton's law of gravitation 170 13.5 The Principia of Isaac Newton 173 13.6 The two-body problem 174 13.6.1 Equations of motion 174 13.6.2 The solution of the two-body problem ' 176 13.6.3 The energy integral 176 13.6.4 The velocity of a planet in its orbit 177 13.6.5 The period of revolution of a planet in its orbit, 179 13.6.6 Newton's form of Kepler's third law 179 13.6.7 Measuring the mass of a planet. 180 13.6.8 Co-periodic orbits 181 13.7 Solar radiation pressure 182 13.8 The astronomical unit 183 Problems Chapter 13,184 14 Celestial mechanics: the many-body problem 185 14.1 Introduction 185 14.2 The elements of an orbit 185 14.3 General properties of the many-body problem 187 14.4 General perturbation theories 187 14.5 Special perturbation theories 189 14.5.1 General principles 189 14.5.2 Chaos and unpredictability 190 14.6 Dynamics of artificial Earth satellites 193 14.6.1 Forces acting on artificial satellites 193 14.6.2 Effect of the Earth's shape on a satellite orbit 193 14.6.3 Effect of the Earth's atmosphere on a satellite orbit 194 14.7 The geostationary satellite 195 14.8 Interplanetary transfer orbits 195

Contents xi 14.8.1 Introduction 195 14.8.2 Transfer between circular, coplanar orbits about the Sun 196 14.8.3 Transfer between particles moving in circular, coplanar orbits 199 14.8.4 Transfer between planets 203 14.8.5 Interplanetary billiards 204 Problems Chapter 14 205 PART 3 Observational Techniques Chapters 15-23 207 15 The radiation laws 209 15.1 Introduction 209 15.2 The velocity of light 210 15.3 Kirchhoff 's law 211 15.4 Solid angle 214 15.5 Black body radiation 215 15.5.1 The basic behaviour 215 15.5.2 Stefan's law 217 15.5.3 Wien's displacement law 218 15.6 Magnitude measurements 218 15.6.1 The stellar output 218 15.6.2 Stellar magnitudes 218 15.7 Spectral lines 220 15.7.1 Introduction 220 15.7.2 The Bohr hydrogen atom 221 15.7.3 The hydrogen spectrum 223 15.7.4 Molecular spectra 226 15.8 Basic spectrometry ' 227 15.8.1 Simple considerations 227 15.8.2 The Doppler shift \ 227 15.8.3 Natural line width 229 15.8.4 Thermal line broadening 230 15.8.5 Collisional line broadening 230 15.8.6 Line broadening by rotation 230 15.9 Polarization phenomena 231 15.10 The Zeeman effect 234 Problems Chapter 15 236 16 The optics of telescope collectors 238 16.1 Introduction 238 16.2 The telescope collector 239 16.3 The telescope and the collected energy 241 16.3.1 Stellar brightness 241 16.3.2 Brightness of an extended object 242 16.3.3 Illumination 244 16.4 Telescope resolving power 245 16.5 Refractors 249 16.5.1 Objectives 249 16.5.2 Chromatic aberration 250 16.5.3 Spherical aberration 253

xii.. Contents 16.5.4 Coma 254 16.5.5 Astigmatism 255 16.5.6 Curvature of field 256 16.5.7 Distortion of field 257 16.6 Transmission efficiency of the refractor 257 16.7 Reflectors 258 16.7.1 Principles 258 16.7.2 Newtonian reflectors 259 16.7.3 Cassegrain reflectors 259 16.8 Transmission efficiency of the reflector 261 16.9 Comparison of refractors and reflectors 263 Problems Chapter 16 271 17 Visual use of telescopes 272 17.1 Magnifying power 272 17.2 Visual resolving power 274 17.3 Magnification limits 276 17.4 Limiting magnitude 277 17.5 Eyepieces 278 17.6 Micrometer eyepieces 280 17.7 Solar eyepieces 281 Problems Chapter 17 282 18 Detectors for optical telescopes 283 18.1 The optical spectrum 283 18.2 Spectral sensitivity 283 18.3 Quantum efficiency 283 18.4 The eye as a detector 284 18.5 The photographic plate 285 18.5.1 Introduction 285 18.5.2 Spatial resolution \ 286 18.5.3 Speed 286 18.5.4 Spectral sensitivity 287 18.6 Photographic photometry 287 18.7 Photographic efficiency 291 18.8 Limiting magnitude 291 18.9 Unsharp masking '293 18.10 Photoelectric devices 293 18.10.1 Introduction 293 18.10.2 Spectral sensitivity 293 18.10.3 Quantum efficiency 293 18.11 The photomultiplier 294 18.11.1 Its principle 294 18.11.2 DC amplification 296 18.11.3 Photon-counting photometry 297 18.11.4 Dark background 298 18.12 Limiting magnitude 298 18.13 Image converters 299 18.14 TV systems and other detectors 300 18.15 Charge coupled devices 300 Problems Chapter 18 304

Contents xiii 19 Astronomical optical measurements 19.1 Introduction 19.2 Positional measurements 19.3 Broadband spectral photometry 19.4 Standard magnitude systems 19.5 Colour indices 19.6 Bolometric magnitudes 19.7 Disturbances caused by the atmosphere 19.7.1 Introduction 19.7.2 Extinction 19.7.3 Atmospheric turbulence 19.8 Image photometry 19.8.1 Photographic photometry 19.8.2 Photoelectric photometry 19.8.3 CCD photometry 19.8.4 Polarimetry 19.9 Spectrometry Problems Chapter 19 20 Modern telescopes and other optical systems 20.1 The new technologies 20.1.1 Active optics 20.2 Adaptive optics 20.3 Measurements at high angular resolution 20.3.1 Michelson's stellar interferometer 20.3.2 Aperture synthesis 20.3.3 The intensity interferometer 20.3.4 Lunar occultation method 20.3.5 Speckle interferometry 20.4 The Schmidt telescope 20.5 The transit telescope 20.6 Zenith tubes 20.7 Portable positional instruments 20.7.1 The theodolite 20.7.2 The sextant 20.8 The coelostat 20.9 The coronagraph 21 Radio telescopes 21.1 Introduction 21.2 Antennas 21.3 Antenna design 21.3.1 The basic dipole 21.3.2 The half-wave dipole 21.3.3 The Yagi antenna 21.3.4 Antenna arrays 21.4 Parabolic dishes 21.5 Horn collectors 21.6 Interferometry 21.6.1 A basic interferometer 21.6.2 A phase-switched interferometer

xiv - - Contents 21.6.3 Very long baseline interferometry 366 21.7 Aperture synthesis 366 21.7.1 Lunar occultations 368 21.8 Polarization 371 21.9 Radar observations 372 Problems Chapter 21 373 22 Telescope mountings 374 22.1 Optical telescopes 374 22.2 Equatorial mountings 376 22.2.1 The German mounting 376 22.2.2 The fork mounting 376 22.2.3 The English mounting 376 22.2.4 The coude system 377 22.3 Telescope domes 378 22.4 Radio telescopes 380 23 High energy instruments and other detectors 381 23.1 Introduction 381 23.2 X-ray astronomy 381 23.2.1 X-ray energies 381 23.2.2 X-ray telescopes 382 23.2.3 X-ray spectrometry 385 23.2.4 X-ray detectors 386 23.3 y-ray astronomy 388 23.3.1 Detectors and satellites 388 23.3.2 y-ray spectral lines 389 23.3.3 Cerenkov radiation and detection 390 23.4 23.5 23.6 23.7 23.8 23.9 Ultraviolet astronomy Infrared astronomy Millimetre astronomy Neutrino astronomy 23.7.1 Introduction 23.7.2 Neutrino telescopes Gravitational radiation The missing mass problem 391 391 \ 393 ' 396 396 396 397 399 PART 4 Experimental Work Chapter 24 24 Practical projects 24.1 24.2 Introduction The Sun as a timekeeper 24.2.1 A horizontal sundial 24.2.2 A vertical sundial 24.2.3 A noon-marker 24.3 The Sun as a position finder 24.3.1 Simple determination of latitude 24.3.2 Theodolite observations 24.3.3 Sextant observations 24.4 Observational radio astronomy 401 403 403 403 404 405 406 407 408 409 412 423

Contents xv 24.4.1 Observing the Sun 425 24.4.2 Observing geostationary satellites 425 24.5 Solar disc phenomena: practical exercises 428 24.5.1 Visual observations - 428 24.5.2 Recording sunspots by drawing 428 24.5.3 Determination of the solar rotation period 429 24.5.4 The eccentricity of the Earth's orbit 432 24.5.5 Use of a pinhole camera 432 24.5.6 Atmospheric extinction 432 24.6 The Moon's orbit: practical projects 434 24.6.1 Measuring the Moon's distance 437 24.7 Planetary orbits 440 24.7.1 The outer planets 440 24.7.2 The inner planets 442 24.7.3 Kepler's second law 442 24.8 The telescope 443 24.8.1 Resolving power 444 24.8.2 Magnifying power 444 24.9 Photography of star fields 445 24.10 Spectra 445 24.11 Michelson's stellar interferometer 448 24.12 Digital photography. 449 Web sites 451 Appendix: Astronomical and related constants 454 A.I Physical constants 454 A.2 Time. 454 A.3 Mathematical constants, systems of units and conversion factors 455 A.4 Basic formulas ; 456 Bibliography 458 1 Source books 458 2 Practical projects 458 3 Books on specific topics 459 Answers to problems 460 Index 469