One of his grandest discoveries was a method of weighing the heavenly
bodies by their action on each other. By means of this principle he
was able to compare the mass of the sun with the masses of those
planets that have moons, and also to compare the mass of our moon with
the mass of the earth.

Thus Newton, after having established his great principle, devoted his
splendid intellect to the calculation of its consequences. He proved
that if a body be projected with any velocity in free space, subject
only to a central force, varying inversely as the square of the
distance, the body must revolve in a curve which may be any one of the
sections of a cone--a circle, ellipse, parabola, or hyperbola; and he
found that those comets of which he had observations move in parabolae
round the Sun, and are thus subject to the universal law.

Newton realised that, while planets and satellites are chiefly
controlled by the central body about which they revolve, the new law
must involve irregularities, due to their mutual action--such, in
fact, as Horrocks had indicated. He determined to put this to a test
in the case of the moon, and to calculate the sun's effect, from its
mass compared with that of the earth, and from its distance. He proved
that the average effect upon the plane of the orbit would be to cause
the line in which it cuts the plane of the ecliptic (i.e., the line of
nodes) to revolve in the ecliptic once in about nineteen years. This
had been a known fact from the earliest ages. He also concluded that
the line of apses would revolve in the plane of the lunar orbit also
in about nineteen years; but the observed period is only ten
years. For a long time this was the one weak point in the Newtonian
theory. It was not till 1747 that Clairaut reconciled this with the