Page:The evolution of worlds - Lowell.djvu/289

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NOTES 247 �for the case of no action, the other terms being insensible �r> �for the satellites in the table, since in all r < �400 �Supposing, now, the particles within the orbit of the planet to be equally distributed according to their major axes, then as the velocity of any one of them, taking R r = R approx. as unity, is ���the mean velocity of all of those which may encounter the satellite is, at the point of collision, ����= 0.754; �that is, just over three-quarters of the planet's speed in its orbit. �If we suppose the particles to be equally distributed in space, we shall have more with a given major axis in pro- portion to that axis, and our integral will become ����= 0.792 of the planet's orbital speed. ��� �