ipio.] 



SEE— ORIGIN OF ZONE OF ASTEROIDS. 



355 



As the orbits of the planets and satelHtes are essentially circular, we 

 may put r^a=i ; and then since 



I, 



k'- 



it follows that in these units z'-/k- = j. If instead of the velocity 

 appropriate to carry the attendant body around in its nearly circular 

 orbit, we substitute in (2) the fractional values of v-/k~ given in the 

 above table, as due to the rotation of the central mass postulated 

 by Laplace, we shall find that in all cases the semi-axis major of the 

 new orbit is about one-half that of the existing orbit. The largest 

 value results from the inner ring of Saturn, where the equation 

 would give 0=1/1.86^^0.54, the value of v^/k" in this case being 

 about 0.14. 



Table of Data Relating to the Solar System. 



9. The obvious meaning of this result is that if the planets and 

 satellites were projected along the tangents of their present orbits, 

 with such small squared velocities as shown in the table, they not 

 only would not pursue their present paths, but would in each case 

 fall towards the centers and describe orbits with semi-axes just about 

 one half. In other words, the projected satellites would pursue very 

 elongated ellipses having their aphelia at the existing orbits, but their 

 perihelia penetrating the central masses about which they now re- 

 volve. /// no case ivonld over lialf a revolution be possible without 

 collision, because the projected satellites zvoiild fall almost straight 

 to the center and he absorbed in the central mass. 



