Astronomy Principles and Practice Fourth Edition.pdf

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Chapter 17 Visual use of telescopes 17.1 Magnifying power In order to make a visual inspection of the images which the telescope collector provides, some kind of eyepiece must be used. The effect of the use of an eyepiece is illustrated in a simplified way in figure 17.1, where the virtual image is at a position on or beyond the near point of the eye. (The actual final image is formed on the retina of the eye.) Under this circumstance, it can be seen that the image produced by the collector lies inside the focus of the eyepiece. The figure illustrates that, with this simple eyepiece, the viewed image is inverted. The magnifying power, m, of the overall optical system is defined as the ratio of the angle subtended by the virtual image at the eye, α e , and the angle, α c , subtended by the object at the collector. Thus, m = α e α c . (17.1) For astronomical observations, it is usual practice to adjust the position of the eyepiece so that the virtual image appears to be at infinity. It is obvious that in this adjustment, the eye lens must be at the exact distance of its focal length from the image produced by the collector in its focal plane. This situation is represented in figure 17.2. The collector aperture acts as the entrance pupil and the image of the collector aperture formed by the eyepiece acts as the exit pupil. The distance from the eye lens (or the last lens of a compound eyepiece) to the exit pupil is known as the eye relief. As all the rays from all parts of the field which can be viewed by the telescope pass through the exit pupil, it is at this position that the eye should be placed. The ray passing through the centre of the collector is known as the chief ray. It is not deviated at the collector aperture and it can be seen from figure 17.2 that it passes through the centre of the exit pupil. From figure 17.2, it can be seen that tan α e = h v and tan α c = h u where h is the distance of the chief ray from the optic axis when it arrives at the eyepiece, u and v are, respectively, the object and image distances corresponding to the entrance and exit pupil distances from the eyepiece. As both α c and α e are small angles, α e ≈ h v (17.2) 272
Magnifying power 273 Figure 17.1. Visual use of a telescope. The collector is depicted as an objective; it could equally well be a reflecting system. Figure 17.2. A schematic diagram of the astronomical telescope, illustrating the positions of the entrance and exit pupils. and α c ≈ h u . (17.3) By applying the general lens formula to the eyepiece lens, 1 u + 1 v = 1 F e . Therefore, and, since u = F c + F e , 1 v = 1 v = u − F e uF e F c F e (F c + F e ) .
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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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214 The radiation laws Figure 15.2.
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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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322 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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