Astronomy Principles and Practice Fourth Edition.pdf

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Nutation 145 Figure 11.10. The gravitational pull of the Sun on the non-spherical Earth. The effect of the Sun is complicated by the fact that not only is the Sun’s angular distance above the plane of the equator changing throughout the year but its orbit is elliptical so that its gravitational pull varies. The complete analytical description of the Sun’s precessional effect is, therefore, very complicated. The Moon’s effect is more complex still but, because its orbit is inclined at only a few degrees to the plane of the ecliptic, its main contribution to precession is similar to that of the Sun. The uniform motion of the north celestial pole along the small circle about the north pole of the ecliptic due to the combined effects of Sun and Moon is called luni-solar precession. As we have seen, this produces a continuous movement of along the ecliptic at a rate of 50·′′ 2 per annum (the modern value) and a corresponding movement of the celestial equator. 11.11 Nutation In attempting to measure stellar parallax, Bradley had been attempting to remove the last main objection to the heliocentric theory of the Solar System. He had failed to detect parallax but in discovering and interpreting correctly the phenomena of stellar aberration he had provided striking evidence that the Earth was in motion about the Sun. He now knew that any parallactic displacement of the star had to be less than two seconds of arc, so closely did observed shifts and calculated shifts due to aberration agree. But we find him writing in 1729: I have likewise met with some small varieties in the declinations of other stars...which do not seem to proceed from the same cause (of aberration). The small remaining differences between Bradley’s observations and calculations did lead him after 19 years of careful work to the discovery of nutation. The displacements were found to have a period of 18 2 3 years and were interpreted by Bradley as being due to a minute wobble of the Earth’s axis of rotation. He suggested also that the cause of this wobble was the Moon’s action on the Earth’s equatorial bulge. The plane containing the Moon’s orbit about the Earth is itself precessing, so that in aperiodof18 2 3 , the line of intersection of the Moon’s orbital plane with the plane of the ecliptic makes one complete revolution of the ecliptic.
146 The reduction of positional observations: II Figure 11.11. The conical movement of a spinning top compared with the precession of the Earth’s pole. In figure 11.12 we exhibit the result of nutation. Due to luni-solar precession, the north celestial pole arrives at some time at the point P 1 , while the vernal equinox arrives at 1 . But because of nutation, there is an additional effect so that the true positions of the pole and the vernal equinox are
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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
Page 94 and 95: The relationship between mean solar
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Page 98 and 99: The tropical year and the calendar
Page 100 and 101: The Earth’s geographical zones 10
Page 102 and 103: Hence, the period of the year durin
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Page 106 and 107: Twilight 107 For this to happen, ZB
Page 108 and 109: h m s Date Approximate ZT 16 30 0 J
Page 110 and 111: Problems—Chapter 9 111 Date (00 h
Page 112 and 113: Atmospheric refraction 113 Figure 1
Page 114 and 115: where ZOL = r. But ZOL = ζ .AlsoAB
Page 116 and 117: so that we have But Hence, Similarl
Page 118 and 119: Now But θ is a small angle so we m
Page 120 and 121: Geocentric parallax 121 Figure 10.6
Page 122 and 123: The semi-diameter of a celestial ob
Page 124 and 125: Measuring distance in the Solar Sys
Page 126 and 127: Stellar parallax 127 Figure 10.10.
Page 128 and 129: Stellar parallax 129 after. The val
Page 130 and 131: Problems—Chapter 10 131 Recent ob
Page 132 and 133: Chapter 11 The reduction of positio
Page 134 and 135: The velocity of light 135 Table 11.
Page 136 and 137: The constant of aberration 137 Figu
Page 138 and 139: Diurnal and planetary aberration 13
Page 140 and 141: Precession of the equinoxes 141 Fig
Page 142 and 143: Effect of precession on a star’s
Page 146 and 147: The tropical and sidereal years 147
Page 148 and 149: Chapter 12 Geocentric planetary phe
Page 150 and 151: The Copernican System 151 Figure 12
Page 152 and 153: Planetary configurations 153 (a) V
Page 154 and 155: The synodic period 155 Figure 12.5.
Page 156 and 157: Measurement of planetary distances
Page 158 and 159: Stationary points 159 Figure 12.8.
Page 160 and 161: Stationary points 161 Using equatio
Page 162 and 163: The phase of a planet 163 Figure 12
Page 164 and 165: Problems—Chapter 12 165 with an o
Page 166 and 167: Planetary orbits 167 Figure 13.1. M
Page 168 and 169: Planetary orbits 169 If P 1 SP 2 is
Page 170 and 171: Newton’s law of gravitation 171 a
Page 172 and 173: The Principia of Isaac Newton 173 N
Page 174 and 175: The two-body problem 175 Figure 13.
Page 178 and 179: The two-body problem 179 13.6.5 The
Page 182 and 183: The astronomical unit 183 For an ex
Page 184 and 185: Chapter 14 Celestial mechanics: the
Page 186 and 187: 14.3 General properties of the many
Page 188 and 189: Special perturbation theories 189 F
Page 190 and 191: Special perturbation theories 191 F
Page 192 and 193: 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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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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