planet is moving.

These rules provide the methods for estimating all the moments of
momentum, so far as the revolutions in our system are concerned. For
the rotations somewhat more elaborate processes are required. Let us
think of a sphere rotating round a fixed axis. Every particle of that
sphere will of course describe a circle around the axis, and all these
circles will lie in parallel planes. We may for our present purpose
regard each atom of the body as a little planet revolving in a
circular orbit, and therefore the moment of momentum of the entire
sphere will be found by simply adding together the moments of momentum
of all the different atoms of which the sphere is composed. To perform
this addition the use of an elaborate mathematical method is required.
I do not propose to enter into the matter any further, except to say
that the total moment of momentum is the product of two factors--one
the angular velocity with which the sphere is turning round, while the
other involves the sphere's mass and dimensions.

To illustrate the principles of the computation we shall take one or
two examples. Suppose that two circles be drawn, one of which is
double the diameter of the other. Let two planets be taken of equal
mass, and one of these be put to revolve in one circle, and the other
to revolve in the other circle, in such a way that the periods of both
revolutions shall be equal. It is required to find the moments of
momentum in the two cases. In the larger of the two circles it is
plain that the planet must be moving twice as rapidly as in the
smaller, therefore its momentum is twice as great; and as the radius
is also double, it follows that the moment of momentum in the large
orbit will be four times that in the small orbit. We thus see that the
moment of momentum increases in the proportion of the squares of the
radii. If, however, the two planets were revolving about the same sun,
one of these orbits being double the other, the periodic times could
not be equal, for Kepler's law tells us that the square of the
periodic time is proportional to the cube of the mean distance.
Suppose, then, that the distance of the first planet is 1, and that of
the second planet is 2, the cubes of those numbers are 1 and 8, and
therefore the periodic times of the two bodies will be as 1 to the
square root of 8. We can thus see that the velocity of the outer body
must be less than that of the inner one, for while the length of the