. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . 09° 25 55, SS = d= 46° 044. log cos P = tanp = 05279161-log tan m = 109° 2555. m = log cos SD = cosp = colog cos m = cos d = PROBLEMS OF SPHERICAL ASTRONOMY. 345 (5) Given the right ascension and declination of a star; tofind its latitude and longitude. Let V be the vernal equinox, S the star, VD, VL thethe equator and the ecliptic, SD, SLperpendicular to VD, VL. ThenVD = right ascension = a, SD = dec-l
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . 09° 25 55, SS = d= 46° 044. log cos P = tanp = 05279161-log tan m = 109° 2555. m = log cos SD = cosp = colog cos m = cos d = PROBLEMS OF SPHERICAL ASTRONOMY. 345 (5) Given the right ascension and declination of a star; tofind its latitude and longitude. Let V be the vernal equinox, S the star, VD, VL thethe equator and the ecliptic, SD, SLperpendicular to VD, VL. ThenVD = right ascension = a, SD = dec-lination = 8, VL == longitude = A,SL = latitude = I. Denote the ob-liquity of the ecliptic DVL by <o,and the angle DVS by 6. From the right triangles SVD,SVL we get cot 6 = sin a cot S . (1) tanA = cos (0 — <d) tana sec 6 (2) sinZ= sin (0 — co) sin 8 cosec0 (3) From (1), 0 is determined; and from (2) and (3), X andI are determined. Ex. Given the right ascension of a star 5h 6m , andits declination 45° 51 N.; to find its longitude andlatitude, the obliquity of the ecliptic being 23° 27 a = 76° 40 = 45° 51 = 46° 38 11 .8a) == 23° 27 0-o> = 23° = 79° 58 Z = 22° log sin a = cot 8 = log cot 0 = log cos (0 - o>) = log tan a = cologcos0 = log tanX = log sin (0 - o>) = log sin 8 = cologsinfl= log sin I = 346 SPHERICAL TRIGONOMETRY. EXAMPLES. 1. Find the apparent time of sunrise at a place whoselatitude is 40° 42, when the suns declination is 17° 49 N. Ans. 4h 56m. 2. Given the latitude of a place = 40° 36 , the hourangle of a star=46°, and its declination = 23° 4 ;to find its azimuth and altitude. Ans. Azimuth = 80° 23 4 .47, altitude = 47° 15 3. Find the altitude and azimuth of a star to an observerin latitude 38° 53 N., when the hour angle of the star is3k
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
