THE ORIGIN OF THE EARTH. 



73 



Fig. 29. — Diagram illustrating the condition under which collisions may take place 

 in elliptical orbits of the planetary type. S represents the solar mass at the 

 center of the system, E the planetary nucleus, B its orbit, p a planetesimal in 

 the orbit A , smaller than B, and P a planetesimal in the orbit C, larger than 

 B. The case has been so chosen as to represent at once the smallest and the 

 largest orbits of typical eccentricity that can come into contact with the orbit of 

 the planetary nucleus. The minimum extreme is found when the aphelion point 

 of the small ellipse A coincides with the perihelion point of the orbit of the 

 planetary nucleus B. In no other position can the orbit A touch the orbit B. 

 The maximum extreme is found where the aphelion point of B coincides with 

 the perihelion point of C. In no other position can these orbits touch. Be- 

 tween these limiting phases, represented by the orbits A and C, there are an 

 indefinite number of possible planetesimal orbits that might cut the orbit B, 

 but in all case's, except where the orbits were like B, conjunction could arise 

 only when a more or less aphelion portion of an inner orbit touched or crossed a 

 more or less perihelion portion of B. If the orbits were equal, the velocities at 

 the crossings would be equal and the rotating effects would be nil, or neutralized, 

 and if they were nearly equal, the difference would be slight, so that the effective 

 cases are those of the extreme classes represented. Further explanation is given 

 in the text. 



