“Applying his results to the earth, Lagrange found that if the velocity of the detached fragment exceeded that of a cannon ball in the proportion of 121 to 1 the fragment would become a comet with a direct motion; but if the velocity rose in the proportion of 156 to 1 the motion of the comet would be retrograde.  If the velocity was less than in either of these cases the fragment would revolve as a planet in an elliptic orbit.  For any other planet besides the earth the velocity of explosion corresponding to the different cases would vary in the inverse ratio of the square root of the mean distance.  It would therefore manifestly be less as the planet was more distant from the sun.  In the case of each of the four smaller planets (only the four asteroids, Ceres, Pallas, Juno, and Vesta, were known at that time), the velocity of explosion indicated by their observed motion would be less than twenty times the velocity of a cannon ball."[6]

[Footnote 6:  Grant’s History of Physical Astronomy, p. 241.]

Instead, then, of being discredited by its assumption of so strange a catastrophe, Olbers’s theory fell into desuetude because of its apparent failure to account for the position of the orbits of many of the asteroids after a large number of those bodies had been discovered.  He calculated that the orbits of all the fragments of his exploded planet would have nearly equal mean distances, and a common point of intersection in the heavens, through which every fragment of the original mass would necessarily pass in each revolution.  At first the orbits of the asteroids discovered seemed to answer to these conditions, and Olbers was even able to use his theory as a means of predicting the position of yet undetected asteroids.  Only Ceres and Pallas had been discovered when he put forth his theory, but when Juno and Vesta were found they fell in with his predictions so well that the theory was generally regarded as being virtually established; while the fluctuations in the light of Vesta, as we have before remarked, led Olbers to assert that that body was of a fragmental shape, thus strongly supporting his explosion hypothesis.

Afterward, when the orbits of many asteroids had been investigated, the soundness of Olbers’s theory began to be questioned.  The fact that the orbits did not all intersect at a common point could easily be disposed of, as Professor Newcomb has pointed out, by simply placing the date of the explosion sufficiently far back, say millions of years ago, for the secular changes produced by the attraction of the larger planets would effectively mix up the orbits.  But when the actual effects of these secular changes were calculated for particular asteroids the result seemed to show that “the orbits could never have intersected unless some of them have in the meantime been altered by the attraction of the small planets on each other.  Such an action is not impossible, but it is impossible to determine it, owing to the great number of these bodies and our ignorance of their masses."[7]