rth concerning
Eros. The importance of this coincidence is that it tends to revive a
remarkable theory of the origin of the asteroids which has long been in
abeyance, and, in the minds of many, perhaps discredited.

This theory, which is due to Olbers, begins with the startling
assumption that a planet, perhaps as large as Mars, formerly revolving
in an orbit situated between the orbits of Mars and Jupiter, was
destroyed by an explosion! Although, at first glance, such a catastrophe
may appear too wildly improbable for belief, yet it was not the
improbability of a world's blowing up that led to a temporary
abandonment of Olbers's bold theory. The great French mathematician
Lagrange investigated the explosive force "which would be necessary to
detach a fragment of matter from a planet revolving at a given distance
from the sun," and published the results in the Connaissance des Temps
for 1814.

"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 firs