602 Table 756 



MISCELLANEOUS ASTRONOMICAL DATA AND FORMULAE 



If 8 = declination, t, hour angle measured west from meridian, h, altitude, <p, latitude 

 and A, azimuth measured from S. point through W. Then 



sin h = sin <f> sin 5 + cos cos 8 cos t 1 

 cos h cos A = — cos <t> sin 5 -f- sin <p cos 8 cos t f given 5, t , <p 

 cos h sin A= cos 8 sin /J 



sin S = sin sin h — cos <t> cos h cos /4 1 

 cos 8 cos £ = cos 4> sin & + sin <p cos /z cos A r given h,A,<p 

 cos 5 sin f = cos h sin A J 



Refraction.— ,- i n (") = [983 X (barometer in in.)/(46o + t° F.)] tanZ, where Z = 

 zenith distance. Error < 1", Z < 75 , ordinary t and pressure. 



Twilight. — Considered to end when 1st mag. star is visible in zenith. Lasts until sun 

 is about 18 below horizon; lat. 40 , equivalent to about 1^ to 2 hr. ; latitude > 50 , lasts 

 until midnight. 



Dip of horizon. — In minutes of arc = V elevation in ft. 



Horizon. — Distance at sea is approximately, miles = V (f )/r in feet; no account taken of 

 refraction, actual distance greater. 



Date line. — 180 from meridian of Greenwich. Ships crossing it from the east, skip a 

 day ; going east, count same day twice. 



Velocity, equatorial point on earth. — Because of rotation: 1000 mi./hr. = 1500 ft./sec. 

 = 1600 km/m = 450 m/sec. In orbit : 18.5 mi. /sec. = 30 km/sec. 



latitude variation. — Direction of axis of the earth in space is invariable but a variation 

 in latitude is caused by a shift of the earth's body about this axis. There are two com- 

 ponents, one, annual (narrow ellipse, varying in form and position, about 10 m long on 

 the earth's surface) probably meteorological in origin; the other, circular, about 8 m in 

 diameter, period 433 days, due to noncoincidence of axis of figure and of rotation. 



Magnitudes. — (Apparent, m). The light of an average 1st magnitude star was found 

 to be physically 100 times as intense as that of a 6th. V I0 ° or 2 -5 12 has been adopted as 

 the light ratio between two stars differing in magnitude by unity (log™ 0.400 = 2.512). 

 If hi = approximate brightness of star of magnitude m, In of n, then, ln/lm= (2.^\2) m ~ n 

 whence 



m — n = 2.5 (log In — log l m ) ; if h= brightness mag. star log (logw/logo) = — 0.4m. 



Magnitudes. — ("Absolute," M.) The "absolute" magnitude of a star is its magni- 

 tude reduced to a standard distance, 10 parsecs (Int. Astron. Union, 1922). M — w = 2.5 

 (log amt. light rec'd)/(log amt. if at unit distance) =5 log /> — 5 log /> where p, pa 

 are observed parallax and that for standard distance; /> = o.i ■'• M=m -\- 5 + 5 log p. 

 j3 Orionis, M= — 5.5 is brightest star. 



Color index. — We have visual, photographic, and bolometric (radiometric) magnitudes. 

 The zero of the photographic scale is taken so that both the photographic and visual scale 

 coincide, on the average, for stars of spectrum class AO and 111 = 5.5 to 6.5. Difference 

 of magnitudes on the two scales is the color index, photovisual is + for red, — for blue stars 

 and may amount to -f- 2.0 mag. 



Heat index. — Radiometric (heat or bolometric), zero taken to agree with Class AO, 

 (radiometric — visual magnitude) = head index, -f- for red stars. 



Purkinje effect. — Two colored lights appearing equally bright at a certain brightness, 

 when brightness decreased equally physically, the bluer appears brighter. 



Smithsonian Tables 



