NO. l6 METEOR-ORBITS IN TilK SOLAR SYSTEM — VON NIESSL IQ 



upon the original cosmic velocity, all other orbital elements of the 

 same type and consequently also the co-ordinates of the apparent 

 radiant can have quite different values. 



Under such circumstances a comparison of different cases gives us 

 not the complex of those elements that are characteristic of the orbits 

 of planets and comets, but, according to what has already been said, 

 they give exclusively the magnitude and direction of the motion for 

 such large values of the radius vector p that relative to these even r 

 may be considered as almost negligibly small. Since such a portion 

 of the orbit is almost the same as the asymptote, we can take p= oo 

 for this distance. 



The direction, towards which this asymptote points on the celestial 

 sphere, whose longitude and latitude will be designated by / and b, 

 can be called the sidereal or cosmic point of departure of the meteor. 

 The determination of this point for different assumptions of a (i. e., 

 for corresponding z/s) for a given radiant point A', ft' is really our 

 most important object in reference to hyperbolic meteors. 



If w' is the true anomaly of the meteor orbit for the radius vector 

 p= CO and or the angle, which the direction of the asym])tote drawn 

 from the point (I, b) makes with the radius vector r at the node of 

 the orbit on the earth's orbit in complete analogy as to t in regard to 

 numeration and definition, then we obtain 



Qj. j£ cosw'=— - , a — w' — IV, (26) 



^l 



e 



rv- 



-m, (27) 

 TV' — 2 



. (T m sin T / o\ 



tan = ■ , (28) 



2 i-|-mcosT ^ ^ 



which is more convenient for the inverse determinations, also 



/^ \ 2-f- (rZ/^ — 2)C0S OP 



C0s{2r-<r)= ^^,^ , (29) 



while / and b are then determined from 



sin ( O — /) COS 6 = — sin a cos i, 



C0s(O — /)C0S &= — COScr, I (30) 



sin 6 = sin o- sin i. J 

 The velocity of entrance into the solar system (p= 00) is given by 



