Now this generalization finds immediate use in explaining certain
features of the solar system. In looking over the congruities it will
be seen that deviation from the principal plane of the system or
departure from a circular orbit is always associated with smallness
in size. The insignificant bodies are the erratic ones. Now it has
been shown mathematically in several different ways that when small
particles collect into a larger mass, the collisions tend to make
the resultant orbit of the combination both more circular and more
conformant to the general plane than its constituents. But we may see
this more forthrightly by means of the general principle enunciated
above. For in fact both results are direct outcomes of the conservation
of moment of momentum. Given a certain moment of momentum for the
system, the total energy of the bodies is least when they all move in
one plane. This is evident at once because the components of motion
at right angles to the principal plane add nothing to the moment
of momentum of the system. It is also least when the bodies all
revolve in circles about the centre of gravity. The circle has some
interesting properties which almost justify the regard paid to it by
the ancients as the only perfect figure. It encloses the maximum area
for a given periphery, so that according to the old legends, if one
were given as much land as he could enclose with a certain bull’s
hide, he should, after cutting the hide into strips, arrange these
along the circumference of a circle. Now this property of the circle
is intimately connected with the fact that a body revolving in a
circle has the greatest moment of momentum for the least expenditure
of energy. For under the same central force all ellipses of the same
longest diameters—major axes these are technically called—are described
in the same time, and with the same energy, and of all such, the circle
encloses the greatest area, which area measures the moment of momentum
[see NOTE 6].
Given a certain moment of momentum, then the energy is least when the
bodies all move in one plane and all travel in circles in that plane.
As energy is constantly being dissipated while any alteration among
the bodies is going on, to coplanarity and circularity of path all
the bodies must tend, if by collision they be aggregated into larger
masses. As in the present state of our system the small bodies travel
out of the general plane in eccentric ellipses while the big ones
travel in it in approximate circles, the facts indicate that the origin
of the larger masses was due to development by aggregation out of
smaller particles.
Public-domain text, read in full here on John Shaqi.
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