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.
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