Astronomy Principles and Practice Fourth Edition.pdf

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316 Astronomical optical measurements Figure 19.7. (a) The effect of atmospheric turbulence. (b) The dancing effect of a star image when viewed with a small telescope. of a single corrugation, then the energy collected does show marked fluctuations and scintillation is exhibited. For a telescope of the order of 1 m, the noise of intensity scintillation of a star may be a few per cent, with time-scales of a few milliseconds up to ∼1 s. Unlike photon shot noise, the scale of the
Disturbances caused by the atmosphere 317 fluctuations is directly proportional to the brightness of the source, the constant of proportionality, κ, depending on the quality of the site, on the telescope size and on the direction of the star (altitude and azimuth). Thus, for bright stars with the photometric noise dominated by intensity scintillation, a single brightness measurement would be recorded simply as B ± κ B. Without scintillation, with the noise dominated by photon-counting statistics, a measurement of the same star would be noted as B ± √ B. Clearly, there is a range of brightness values for which the accuracy of any photometry is dominated by scintillation and a range dominated by photon counting statistics. The demarcation occurs when κ B = √ B or κ = 1/ √ B. If, for example, κ ∼ 1%, over a measurement time of 1 s, the photometric noise is dominated by scintillation if the photon count rate is greater than 10 4 s −1 . It is well known that, to the naked eye, planets generally do not appear to twinkle. This is because they have a greater apparent angular size than the stars. Any small component within an extended object exhibits intensity scintillation but if the object has a sufficient angular size, then there are sufficient elements for the overall scintillation to smooth out. Experiments have shown that scintillation begins to be apparent when the object subtends an angle of 10 arc seconds or less and that the magnitude of the scintillation increases as the angular size of the object decreases, until it cannot be differentiated from stellar scintillation when the angle subtended is about 3 arc seconds. In effect, it can be said that the apparent angular size, α, of the corrugations in the wavefront is of the order of 3 arc seconds and their physical size, r 0 , obtained from experiments investigating the relationship between scintillation and telescope diameter, is of the order of 100 mm. Thus, the typical distance in the atmosphere where the deforming turbulence is taking place is given by r 0 α = 100 × 206 265 mm 3 ≈ 7 × 10 6 mm = 7km. By considering the theory associated with turbulent media, Fried characterized the fluctuations with a scale over which the parts of the corrugated wavefront can be considered as being essentially plain. This dimension is referred to as the Fried parameter, being synonymous with the r 0 given here. The visual behaviour of the ‘seeing’, as it affects the appearance of a star image, also depends on the value of r 0 in relation to the telescope diameter. For a small telescope of a few centimetres diameter, in addition to rapid fluctuations in apparent brightness, the expected diffraction pattern is likely to be seen but with the whole structure dancing around in constant agitation. When a telescope of a few tens of centimetres or larger is used, the image loses its sharpness and appears as an ill-defined blob without scintillation. This image is known as the seeing disc. When a starfield is recorded on a photograph or on a CCD frame, the images are recorded with a spread which is dominated by the seeing disc. By making an intensity scan through any stellar image, the profile of the seeing disc may be compared with that of the theoretical Airy diffraction pattern (see figure 19.8). The size of the disc is usually expressed in terms of arc seconds, one definition being the angular diameter between the positions at which the intensity has dropped by a factor of two relative to the peak intensity. The seeing disc size and shape gives an indication of the quality of the observing site—a good site will have many nights in the year when the seeing disc is 1 arc second or smaller. There are many observatories, however, where such good quality seeing is not usually available. Another important aspect to the description of the deteriorated stellar image is the way the flux is redistributed relative to that expected in the diffraction pattern. The more the image is concentrated into an area of a detector, the more easily a faint object might be detected; the more the concentration of the image, the more radiation might be accepted into the narrow slit of a spectrometer. This aspect is described by comparing the peak intensity of the seeing disc, I S , relative to that of the peak of the
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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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Page 262 and 263: 266 The optics of telescope collect
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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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370 Radio telescopes Figure 21.19.
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372 Radio telescopes Figure 21.22.
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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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