74 GEOLOGY. 



29) , can only come into contact with a planetary nucleus, E, in the orbit 

 B, at the point where it is farthest from the sun, or its aphelion point. 

 So likewise a planetesimal, P, in the large orbit, C, can only come into 

 contact with the planetary nucleus, E, at the point where the planetesimal 

 comes nearest to the sun, its perihelion. In the first case the planetary 

 nucleus is at its perihelion; in the second, at its aphelion. These are 

 chosen as limiting cases; between them there are innumerable possible 

 intermediate ones. The two selected are the most effective in their 

 results because the differences in the velocities are greatest, and hence 

 they may be regarded as embracing the whole and as representative. 



Now the vital point lies in the fact that, at the point of collision, the 

 body in the smaller orbit is moving slower than the one in the larger 

 orbit, though on the average it moves the faster. For example, the 

 planetesimal, P, at the points where alone it may come into contact 

 with the nucleus, E, is moving slower than E. If collision takes place 

 at all, E must overtake P. This may be demonstrated by the principles 

 of celestial mechanics, 1 but it may also be readily seen by inspection, 

 for at the point of contact E has a velocity sufficient to carry it 

 farther away from the sun through the larger orbit B, while the body 

 in the orbit A, from deficiency of velocity, falls back towards the 

 sun. At the points where the planetesimal, P, in the large orbit, can 

 alone come into collision with the nucleus, E, the case is reversed, and 

 the planetesimal, P, has the greater velocity, and must overtake E, if 

 there is any collision at all. 



The varying effects of the impacts on the rotation. — If the body 

 in the outer orbit were always to strike the outside of the body in the 

 inner orbit, as in the ideal cases illustrated, the impact would contribute 

 to forward rotation; but the orbits may cross one another, and the body 

 in the inner orbit may have passed the crossing before it is overtaken 

 by the body in the outer orbit, and so the inertia of the overtaken 

 body may be felt on the outer side of the nucleus and tend to produce 

 retrograde rotation. It is, therefore, necessary to take account of 

 two opposite classes of effects, and to estimate the residual influence 

 of all probable collisions. It will be seen at once that this residual 

 influence must be far less in magnitude than the sum of the force of all 

 impacts, for the opposing classes neutralize one another, and hence 



1 An elegant method of determining the velocity of a body at any point in its 

 elliptical orbit is given on p. 139 of Moulton's Celestial Mechanics. 



