The Earth's BeginningBall, Robert S. (Robert Stawell)
Science
The Earth's Beginning
Ball, Robert S. (Robert Stawell)
Krakatoa (Indonesia); Nebular hypothesis
It will illustrate the application of the argument to take a particular
case in which a system of particles is revolving round a central sun in
circular orbits, all of which lie in the same plane. Let us suppose
that, while the moment of momentum of the system of particles is to
remain unaltered, one of the particles is to be shifted into a plane
which is inclined at an angle of 60° to the plane of the other orbits;
it can easily be seen that an area in the new plane, when projected down
into the original plane, will be reduced to half its amount. Hence, as
the moment of momentum of the whole system is to be kept up, it will be
necessary for the particle to have a moment of momentum in the circle
which it describes in the new plane which is double that which it had in
the original plane. It follows that the radius of the circle in the new
plane must be four times the radius of the circle which defined the
orbit of the particle in the old plane. The energy of the particle in
this orbit is therefore correspondingly greater, and thus the energy of
the whole system is increased. This illustrates how a system, in which
the circular orbits are in different planes, requires more energy for a
given moment of momentum than would suffice if the circular orbits had
all been in the same plane. So long as the orbits are in different
planes there will still remain a reserve of energy for possible
dissipation. But the dissipation is always in progress, and hence there
is an incessant tendency towards a flattening of the system by the
mutual actions of its parts.
It may help to elucidate this subject to state the matter as follows:
The more the system contracts, the faster it must generally revolve;
this is the universal law when disturbing influences are excluded. Take,
for instance, the sun, which is at this moment contracting on account of
its loss of heat. In consequence of that contraction it is essential
that the sun shall gradually turn faster round on its axis. At present
the sun requires twenty-five days, four hours and twenty-nine minutes
for each rotation. That period must certainly be diminishing, although
no doubt the rate of diminution is very slow. Indeed, it is too slow for
us to observe; nevertheless, some diminution must be in progress.
Applying the same principle to the primitive nebula, we see, that as the
contraction of the original volume proceeds, the speed with which the
several parts will rotate must increase.
Public-domain text, read in full here on John Shaqi.
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