So he was led by a similar phenomenon to precisely
the same opinion about Vesta that has lately been put forth 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.
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