268. The Moon’s path being concave to the Sun throughout, demonstrates
that her gravity towards the Sun, at her conjunction, exceeds her
gravity towards the Earth. And if we consider that the quantity of
matter in the Sun is almost 230 thousand times as great as the quantity
of matter in the Earth, and that the attraction of each body diminishes
as the square of the distance from it increases, we shall soon find,
that the point of equal attraction where these two powers would be
equally strong, is about 70 thousand miles nearer the Earth than the
Moon is at her Change. It may now appear surprising that the Moon does
not abandon the Earth when she is between it and the Sun, because she is
considerably more attracted by the Sun than by the Earth at that time.
But this difficulty vanishes when we consider, that the Moon is so near
the Earth in proportion to the Earth’s distance from the Sun, that she
is but very little more attracted by the Sun at that time than the Earth
is; and whilst the Earth’s attraction is greater upon the Moon than the
difference of the Sun’s attraction upon the Earth and her (and that it
is always much greater is demonstrable) there is no danger of the Moon’s
leaving the Earth; for if she should fall towards the Sun, the Earth
would follow her almost with equal speed. The absolute attraction of the
Earth upon a drop of falling rain is much greater than the absolute
attraction of the particles of that drop upon each other, or of it’s
center upon all parts of it’s circumference; but then the side of the
drop next the Earth is attracted with so very little more force than
it’s center, or even it’s opposite side; that the attraction of the
center of the drop upon it’s side next the Earth is much greater than
the difference of force by which the Earth attracts it’s nearer surface
and center: on which account the drop preserves it’s round figure, and
might be projected about the Earth by a strong circulating wind so as to
be kept from falling to the Earth. It is much the same with the Earth
and Moon in respect to the Sun; for if we should suppose the Moon’s
Orbit to be filled with a fluid Globe, of which all the parts would be
attracted towards the Earth in it’s center, but the whole of it much
more attracted by the Sun; one part of it could not fall to the Sun
without the other, and a sufficient projectile force would carry the
whole fluid Globe round the Sun. A ship, at the distance of the Moon,
sailing round the Earth on the surface of the fluid Globe, could no more
be taken away by the Sun when it is on the side next him, than the Earth
could be taken away from it when it is on the opposite side; which could
never happen unless the Earth’s projectile motion were stopt; and if it
were stopt, the Ship with the whole fluid Globe, Earth and all together,
would as naturally fall to the Sun as a drop of rain in calm air falls
to the Earth. Hence we may see, that the Earth is in no more danger of
being left by the Moon at the Change, than the Moon is of being left by
the Earth at the Full: the diameter of the Moon’s Orbit being so small
in comparison of the Sun’s distance, that the Moon is but little more or
less attracted than the Earth at any time. And as the Moon’s projectile
force keeps her from falling to the Earth, so the Earth’s projectile
force keeps it from falling to the Sun.
[Sidenote: Fig. III.]
269. All the curves which Jupiter’s Satellites describe, are different
from the path described by our Moon, although these Satellites go round
Jupiter, as the Moon goes round the Earth. Let _ABCDE_ &c. be as much of
Jupiter’s Orbit as he describes in 18 days from _A_ to _T_; and the
curves _a_, _b_, _c_, _d_ will be the paths of his four Moons going
round him in his progressive motion.
[Sidenote: The absolute Path of Jupiter and his Satellites delineated.