NO. l6 METEOR-ORBITS IX THE SOLAR SYSTEM VOX NIESSL 1/ 



and therefore the longitude of the radiant point in the ecliptic or the 

 apex of the earth's annual motion is O ' — 90° . 



Finally the heliocentric velocity of the earth at the distance r from 



the sun is given by the expression a/ 1. 



The quantities A', /?', v', A, /3, v are connected by the three equations 



2/C0S;Ssin(O' — A)=t;'cos^' sin(0' — A') — a/ ^ — i, 

 ^;coSi8cos(0'-A)='!/cos/?'cos (O'-A'), 

 V sm jB = z)' sin /?', 



(20) 



from which A, j8 and v can be found. 



If we desire only the magnitude of the heliocentric velocity, we 

 obtain that from the equation 



^2 = ^'2+/2 _i^_2z/ J ^ -I .cos/8'-sin(O'-A0, (21) 



and we obtain the semi-major axis of the respective meteor orbits 

 from equation 



a= — ^. {22) 



2 — r'lr 



This orbit, therefore, either an ellipse or hyperbola according as a is 



• <i 2 



either positive or negative, or according as ^'^ ^ -^ . 



The parabola corresponds to a = 00, and hence we obtain the special 

 limiting case v~= ~ . 



Sometimes from the periodical return of an especially rich shower 

 of meteors (such as the Leonids), one deduces a well-known radiant 

 A', p', and the time of revolution [/ of a dense swarm of meteors and 

 these can therefore be considered as given or known. In such a case 

 in order to compute the remaining elements of the orbit, we have 



a=U\ (23) 



and thence also v. Then the three equations (20) give us v' , A and jB, 

 from which the elements of the orbits of the stream can be deduced 

 according to the following method : 



Let i be the inclination of the heliocentric orbit of the meteor to 

 the ecliptic ; r be the angle of the tangent on this orbit to the radius 

 vector r of the earth's orbit at its node with the meteor orbit ; let p 

 be the semi-parameter of the meteor orbit; let e be the excentricity 

 of the meteor orbit ; let q be the perihelion distance of the meteor's 



