ecast of the destiny
which, after the lapse of ages, awaits the earth-moon system.

It seems natural to enquire how far the influence of tides can have
contributed towards moulding the planetary orbits. The circumstances are
here very different from those we have encountered in the earth-moon
system. Let us first enunciate the problem in a definite shape. The
solar system consists of the sun in the centre, and of the planets
revolving around the sun. These planets rotate on their axes; and
circulating round some of the planets we have their systems of
satellites. For simplicity, we may suppose all the planets and their
satellites to revolve in the same plane, and the planets to rotate about
axes which are perpendicular to that plane. In the study of the theory
of tidal evolution we must be mainly guided by a profound dynamical
principle known as the conservation of the "moment of momentum." The
proof of this great principle is not here attempted; suffice it to say
that it can be strictly deduced from the laws of motion, and is thus
only second in certainty to the fundamental truths of ordinary geometry
or of algebra. Take, for instance, the giant planet, Jupiter. In one
second he moves around the sun through a certain angle. If we multiply
the mass of Jupiter by that angle, and if we then multiply the product
by the square of the distance from Jupiter to the sun, we obtain a
certain definite amount. A mathematician calls this quantity the
"orbital" moment of momentum of Jupiter.[46] In the same way, if we
multiply the mass of Saturn by the angle through which the planet moves
in one second, and this product by the square of the distance between
the planet and the sun, then we have the orbital moment of momentum of
Saturn. In a similar manner we ascertain the moment of momentum for each
of the other planets due to revolution around the sun. We have also to
define the moment of momentum of the planets around their axes. In one
second Jupiter rotates through a certain angle; we multiply that angle
by the mass of Jupiter, and by the square of a certain line which
depends on his internal constitution: the product forms the "rotational"
moment of momentum. In a similar manner we find the rotational moment of
momentum for each of the other planets. Each satellite revolves through
a certain angle around its primary in one second; we obtain the moment
of momentum of each satellite by multiplying its mass into the angle
described