Table 1. — Astronomical constants and formulas. 



[From original sources.] 



Mean distance, earth to sun = 92,897,416 statute miles* 



Mean distance, earth to moon = 238,857 statute miles* 



Radius of earth, equatorial = 3,963.34 statute miles.* 



Radius of earth, polar = 3,949.99 statute miles.* 



Ratio of mass of moon to that of earth =1:81. 45. f 



Ratio of mass of sun to that of earth =333,432:1.1 



Eccentricity of earth's orbit 



= 0.016,751,04-0.000,041,80 T -0.000,000,126 T^.^^ 

 Eccentricity of moon's orbit =0.054,899,720.$ 



Inclination of earth's orbit to plane of ecliptic: 



= 23° 27' 8.26" -46.845" r-0.005,9" ^2+0.001,81" T^.f 

 Inclination of moon's orbit to plane of ecliptic =5° 08' 43.354,6". J 



Mean longitude of sun 



= 279° 41' 48.04" +129,602,768.13" T + 1.089" T^.f 

 Longitude of solar perigee 



= 281° 13' 15.0" +6,189.03" 7 + 1.63" T2+0,012" T^.j 

 Mean longitude of moon 



= 270° 26' 14.72" + (1336 rev. +1,108,411.20") r+9.09" T2-j_o.006,8" T^.f 

 Longitude of lunar perigee 



=334° 19' 40.87" + (ll rev. +392,515.94") 7-37.24" 7'2_o.045" T^.f 

 Longitude of moon's node 



= 259° 10' 57.12" -(5 rev. +482,912.63") 7 + 7.58" 72+O.OO8" T^.f 



True longitude of moon in its orbit (in radians) 

 = mean longitude (in radians) 



+2e sin (s—p) +| e^ sin 2{s—p) (elliptic inequality). 



+^me sin {s—2h+p) (evectional inequality) . 



+-V-TO^ sin 2{s—h) (variational inequality) , || 



Reciprocal of true distance of moon from earth 

 = reciprocal of mean distance 



+a'e cos is — p)+a'e^ cos 2{s — p) (elliptic inequality). 



+-^a'me cos {s—2h+p) (evectional inequality) . 



+a'm^ cos 2(8 — h) (variational inequality). |1 



r = Number of Julian centuries (36525 days) from Greenwich mean noon on 

 December 31, 1899. 



e = Eccentricity of moon's orbit. 



s = Mean longitude of moon. 



p = Mean longitude of lunar perigee. 



h = Mean longitude of sun. 



m = Ratio of mean motion of the sun to that of the moon. 

 a' = Reciprocal of product of moon's mean distance by (1 — e^). 



* American Ephemeris for year 1923, p. xvi. 



t Astronomical Papers for the American Ephemeris, by Simon Newcomb : Vol. VI , pp. 9-11, and Vol. IX, 

 pt. 1, p. 224. 

 J The Solar Parallax and Related Constants, by William Harkness, p. 140. 

 1 An Elementary Treatise on the Lmiar Theory, by Hugh Godfrey, 4th ed., p. 53. 



172 



