Astronomy Principles and Practice Fourth Edition.pdf

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288 Detectors for optical telescopes astronomer’s task to decipher the strengths of the images in terms of the original energy which caused the production of the images. The process is carried out by measuring the strength of an image and relating it to an amount of incident energy by means of a calibration curve. The most convenient way of measuring the strength or blackening of a photographic image is to pass a beam of light through the processed plate and measure the intensity of the beam after its passage through the plate. The laboratory instrument designed especially to make such measurements is usually called a microphotometer and the transmitted beam’s strength is normally monitored photelectrically. If I 0 is the original intensity of the beam and I its intensity when it is passing through a particular area in the plate, then the transmittance, T , of the plate at the selected area is given by The opacity, O, of the plate is defined as T = I I 0 . O = I 0 = 1 I T . When relating the strengths of photographic images, it is usual practice to use the term density, D, which is defined as the logarithm of the opacity. Hence, D = log 10 O and, therefore, D =−log 10 T. The calibration curve relating the densities of areas on the plate to the original energies producing the blackening is normally represented by plotting D against the logarithm of some known exposures, where the exposure, E, is defined as the illumination of the image, Á, multiplied by the time, t, for which the energy falls on to the plate. This form of calibration curve is known as the characteristic curve of the emulsion. A typical characteristic curve is illustrated in figure 18.3. It can be seen from figure 18.3 that unless the exposure is above a threshold, any image cannot be seen against the fog-level. After the toe of the curve, the characteristic curve becomes linear, making it relatively easy to describe density values in terms of incident energy. The relationship can be expressed in the form D = A + γ log Át = A + γ log E. (18.1) The slope, γ , of the linear part of the characteristic curve is called the gamma of the emulsion and it is a measure of the way points within an extended image are contrasted. Beyond the linear part of the curve, the slope begins to decrease and the curve levels out. In this region, exposure to further amounts of energy gives rise only to small increases of blackening and the plate is said to be over-exposed. Between the limits of under- and over-exposure, the photographic plate has a useful dynamic range giving scope to cover illuminations differing by a factor of just over 100. What this means is that the magnitude range that can be covered on any single exposure is of the order of five to six. If, for example, an exposure is made such that 12th magnitude stars are just detectable, stars brighter than the sixth will be overexposed. Fainter magnitudes might be recorded by extending the exposure, but the zone of over-exposure will also move to fainter stars. Comparisons of characteristic curves allow the best emulsions to be chosen for particular observations. We can consider a simple example of their use by examining figure 18.4, where the toes of two characteristic curves, Y and Z, are illustrated. If it is required to use the least exposure to detect an object, then it is easy to see that emulsion Y would be chosen. If it is required that a density of one or over should be recorded using the least exposure, then it is obvious that emulsion Z would be chosen.
Photographic photometry 289 Figure 18.3. The characteristic curve of a typical emulsion, illustrating the regions of under exposure, correct exposure and over exposure. Figure 18.4. A comparison of the characteristic curves of two emulsions. When photographic photometry is being undertaken, it is important that the plates should have calibration exposures imposed on them so that they receive exactly the same treatment in the development process as the images of interest. Because of the faintness of most celestial objects, their measurement by photography requires long exposure times and, in contrast, the calibration exposures are normally made by using a relatively bright illumination and short exposure times. It is possible, with care, to arrange that the total energy collected in a certain part of an astronomical plate is matched exactly by that which is used to provide one of the calibration exposures. If the densities of these images are compared, however, it is very likely that they will not be the same. The photographic plate is said to suffer reciprocity failure—the degree of blackening depends not just on the total amount
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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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338 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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