. Compendium of meteorology. Meteorology. GENERAL ASPECTS OF UPPER ATMOSPHERIC PHYSICS 249 The hour angle h of the sun at its rising at any height // may be obtained as follows. We have cos Z = sin 4> sin 5 + cos cos S cos h, where Z = zenith distance of the sun, 6 = declination of the sun, and <^ = latitude of the place of observation. From Fig. 2, Z = 90° + Fig. 2.—The height H at which the cjdindrical shadow cast by the earth cuts the zenith is given hy H = a( — 1). The effect of refraction—which accelerates the time of rising—has not been taken into account in the equation above.
. Compendium of meteorology. Meteorology. GENERAL ASPECTS OF UPPER ATMOSPHERIC PHYSICS 249 The hour angle h of the sun at its rising at any height // may be obtained as follows. We have cos Z = sin 4> sin 5 + cos cos S cos h, where Z = zenith distance of the sun, 6 = declination of the sun, and <^ = latitude of the place of observation. From Fig. 2, Z = 90° + Fig. 2.—The height H at which the cjdindrical shadow cast by the earth cuts the zenith is given hy H = a( — 1). The effect of refraction—which accelerates the time of rising—has not been taken into account in the equation above. The true zenith distance of the sun's centre when it rises at height H above the ground is given by Z = 90° + 6> + 50'. Here 34' has been allowed for horizontal refraction and 16' for the semidiameter of the sun. Now, at actual noon the apparent time is 12'" and the mean time is 12'' + t, where e is the equation of time. Hence the mean time t of sunrise at height H above the ground is given by t= 12^ + e-h. Similarly, the hour of sunset at H is given by t = 12'> + e + /i. The values of e and S may be obtained from the Nautical Almanac. Hence the hours of sunrise and sunset at different atmospheric levels may be calculated with the help of these equations. Curves in Figs. 3a and db delineate (after Ghosh [40]) the variation of the hour of sunrise with height for the whole year at intervals of about a fortnight for the latitude of Calcutta (22° 32' 48" N). Figure 4 depicts (after Bartels [10]) the height above which the atmosphere is illuminated by solar rays at midnight during the course of the year in the latitudes 40° to 90°. Useful curves depicting the hours of sunrise at dif- ferent latitudes on the surface of the earth and also at a given set of heights {, 50 km, 180 km, 250 km, and 500 km) are also given by Bartels [10]. (a) 400 r. Please note that these images are extracted from scanned page images that may have been digitally enhanced fo
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