Appendix A: Atmospheric Extinction Tables The following tables were initially published by Dan Green in the July 1992 issue of the International Comet Quarterly. The original paper may be found at http://www.icq.eps.har- vard.edu./ICQExtinct.html. Table A.1 “Average” atmospheric extinction in magnitudes for various elevations above sea level (h, in km) z h = 0 h = 0.5 h = 1 h = 2 h = 3 1 0.28 0.24 0.21 0.16 0.13 10 0.29 0.24 0.21 0.16 0.13 20 0.30 0.25 0.22 0.17 0.14 30 0.32 0.28 0.24 0.19 0.15 40 0.37 0.31 0.27 0.21 0.17 45 0.40 0.34 0.29 0.23 0.19 50 0.44 0.37 0.32 0.25 0.21 55 0.49 0.42 0.36 0.28 0.23 60 0.56 0.48 0.41 0.32 0.26 62 0.60 0.51 0.44 0.34 0.28 64 0.64 0.54 0.47 0.37 0.30 66 0.69 0.59 0.51 0.39 0.32 68 0.75 0.64 0.55 0.43 0.35 © Springer International Publishing Switzerland 2017 241 D.A.J. Seargent, Visually Observing Comets, Astronomer’s Pocket Field Guide, DOI 10.1007/978-3-319-45435-1 242 Appendix A: Atmospheric Extinction Tables z h = 0 h = 0.5 h = 1 h = 2 h = 3 70 0.82 0.70 0.60 0.47 0.39 71 0.86 0.73 0.63 0.49 0.40 72 0.91 0.77 0.66 0.52 0.43 73 0.96 0.81 0.70 0.55 0.45 74 1.02 0.86 0.74 0.58 0.48 75 1.08 0.92 0.79 0.62 0.51 76 1.15 0.98 0.84 0.66 0.54 77 1.24 1.05 0.91 0.71 0.58 78 1.34 1.13 0.98 0.76 0.63 79 1.45 1.23 1.06 0.83 0.68 80 1.59 1.34 1.16 0.91 0.74 81 1.75 1.48 1.28 1.00 0.82 82 1.94 1.65 1.42 1.11 0.91 83 2.19 1.86 1.60 1.25 1.03 84 2.50 2.12 1.83 1.43 1.17 85 2.91 2.46 2.13 1.66 1.36 86 3.45 2.93 2.53 1.97 1.62 87 4.23 3.59 3.10 2.42 1.99 88 5.41 4.59 3.96 3.09 2.54 89 7.38 6.26 5.40 4.22 3.46 90 11.24 9.53 8.23 6.42 5.28 Table A.2 “Winter” atmospheric extinction in magnitudes for vari- ous elevations above sea level (h, in km) z h = 0 h = 0.5 h = 1 h = 2 h = 3 1 0.25 0.21 0.19 0.15 0.13 10 0.25 0.22 0.19 0.15 0.13 20 0.26 0.23 0.20 0.16 0.14 Appendix A: Atmospheric Extinction Tables 243 z h = 0 h = 0.5 h = 1 h = 2 h = 3 30 0.28 0.25 0.22 0.17 0.15 40 0.32 0.28 0.24 0.20 0.17 45 0.35 0.30 0.26 0.21 0.18 50 0.38 0.33 0.29 0.24 0.20 55 0.43 0.37 0.33 0.26 0.22 60 0.49 0.42 0.37 0.30 0.25 62 0.52 0.45 0.40 0.32 0.27 64 0.56 0.48 0.43 0.34 0.29 66 0.60 0.52 0.46 0.37 0.31 68 0.65 0.57 0.50 0.40 0.34 70 0.72 0.62 0.55 0.44 0.37 71 0.75 0.65 0.57 0.46 0.39 72 0.79 0.69 0.60 0.49 0.41 73 0.84 0.72 0.64 0.52 0.43 74 0.89 0.77 0.68 0.55 0.46 75 0.94 0.82 0.72 0.58 0.49 76 1.01 0.87 0.77 0.62 0.52 77 1.08 0.94 0.82 0.67 0.56 78 1.16 1.01 0.89 0.72 0.60 79 1.26 1.10 0.97 0.78 0.66 80 1.38 1.20 1.06 0.85 0.72 81 1.52 1.32 1.16 0.94 0.79 82 1.70 1.47 1.29 1.05 0.88 83 1.91 1.65 1.46 1.18 0.99 84 2.18 1.89 1.66 1.34 1.13 85 2.53 2.20 1.93 1.56 1.31 244 Appendix A: Atmospheric Extinction Tables z h = 0 h = 0.5 h = 1 h = 2 h = 3 86 3.01 2.61 2.30 1.86 1.56 87 3.69 3.20 2.82 2.28 1.91 88 4.72 4.09 3.60 2.91 2.45 89 6.44 5.58 4.91 3.97 3.34 90 9.80 8.50 7.49 6.05 5.08 Table A.3 “Summer” atmospheric extinction in magnitudes for various elevations above sea level (h, in km) z h = 0 h = 0.5 h = 1 h = 2 h = 3 1 0.32 0.26 0.22 0.17 0.14 10 0.32 0.27 0.23 0.17 0.14 20 0.34 0.28 0.24 0.18 0.15 30 0.37 0.30 0.26 0.20 0.16 40 0.41 0.34 0.29 0.22 0.18 45 0.45 0.37 0.32 0.24 0.19 50 0.49 0.41 0.35 0.26 0.21 55 0.55 0.46 0.39 0.30 0.24 60 0.63 0.53 0.45 0.34 0.27 62 0.68 0.56 0.48 0.36 0.29 64 0.72 0.60 0.51 0.39 0.31 66 0.78 0.65 0.55 0.42 0.34 68 0.85 0.70 0.60 0.45 0.36 70 0.93 0.77 0.65 0.50 0.40 71 0.97 0.81 0.69 0.52 0.42 72 1.02 0.85 0.72 0.55 0.44 73 1.08 0.90 0.76 0.58 0.47 Appendix A: Atmospheric Extinction Tables 245 z h = 0 h = 0.5 h = 1 h = 2 h = 3 74 1.15 0.95 0.81 0.61 0.49 75 1.22 1.01 0.86 0.65 0.53 76 1.30 1.08 0.92 0.70 0.56 77 1.40 1.16 0.99 0.75 0.60 78 1.51 1.25 1.07 0.81 0.65 79 1.64 1.36 1.16 0.88 0.71 80 1.79 1.49 1.26 0.96 0.77 81 1.97 1.64 1.39 1.06 0.85 82 2.19 1.83 1.55 1.18 0.95 83 2.47 2.06 1.75 1.32 1.07 84 2.82 2.35 1.99 1.51 1.22 85 3.28 2.73 2.32 1.76 1.41 86 3.90 3.25 2.75 2.09 1.68 87 4.78 3.98 3.38 2.56 2.06 88 6.11 5.09 4.32 3.28 2.63 89 8.33 6.93 5.89 4.47 3.59 90 12.68 10.56 8.97 6.80 5.47 Appendix B: The Phase Angle of a Comet Dusty comets display a significant phase effect at large phase angles due to the forward scattering of sunlight from small particles within their comas. A smaller effect, due to back- scattering, is also evident at very small phase angles, that is to say, when the comet is almost opposite the Sun in the sky. Phase angles may be calculated as follows: C α ∆ r E R S In the above diagram: S = Sun E = Earth C = Comet R = Radius vector of Earth (i.e., the distance from Earth to Sun) r = Radius vector of comet (i.e., distance of comet from Sun) Δ = Geocentric distance of comet α = Phase angle. The phase angle is defined by © Springer International Publishing Switzerland 2017 247 D.A.J. Seargent, Visually Observing Comets, Astronomer’s Pocket Field Guide, DOI 10.1007/978-3-319-45435-1 248 Appendix B: The Phase Angle of a Comet CosraD=+22- Rr2 / 2 D () Alternatively, the phase angle may be calculated by sin/()12aD= ()12//Ö-()()Rr+ ()Rr+-DDr Appendix C: “Lost” Short-Period Comets Short-period comets can become “lost” for several reasons. The reason may simply be that the orbit of a particular comet was not sufficiently well determined at its discovery appari- tion and the calculated period was therefore inaccurate. For a comet with a relatively long period (say, a few decades rather than a few years), this type of error can be quite large. Other comets have become lost due to drastic alterations in their orbits resulting from close approaches to one of the large planets, most frequently Jupiter, whereas others appear to have been abnormally lustrous at their discovery apparition and returned to their normal meager brightness subsequently.