he
general name of a centripetal force, as it is a force which is directed
to some centre; and, as it regards more particularly a body in that
centre, we call it circum-solar, circum-terrestrial, circum-jovial.

_Centre-Seeking Forces_

That by means of centripetal forces the planets may be retained in
certain orbits we may easily understand if we consider the motions of
projectiles, for a stone projected is by the pressure of its own weight
forced out of the rectilinear path, which, by the projection alone, it
should have pursued, and made to describe a curve line in the air; and
through that crooked way is at last brought down to the ground, and the
greater the velocity is with which it is projected the further it goes
before it falls to earth. We can, therefore, suppose the velocity to be
so increased that it would describe an arc of 1, 2, 5, 10, 100, 1,000
miles before it arrived at the earth, till, at last, exceeding the
limits of the earth, it should pass quite by it without touching it.

And because the celestial motions are scarcely retarded by the little or
no resistance of the spaces in which they are performed, to keep up the
parity of cases, let us suppose either that there is no air about the
earth or, at least, that it is endowed with little or no power of
resisting.

And since the areas which by this motion it describes by a radius drawn
to the centre of the earth have previously been shown to be proportional
to the times in which they are described, its velocity when it returns
to the point from which it started will be no less than at first; and,
retaining the same velocity, it will describe the same curve over and
over by the same law.

But if we now imagine bodies to be projected in the directions of lines
parallel to the horizon from greater heights, as from 5, 10, 100, 1,000
or more miles, or, rather, as many semi-diameters of the earth, those
bodies, according to their different velocity and the different force of
gravity in different heights, will describe arcs either concentric with
the earth or variously eccentric, and go on revolving through the
heavens in those trajectories just as the planets do in their orbs.

As when a stone is projected obliquely, the perpetual deflection thereof
towards the earth is a proof of its gravitation to the earth no less
certain than its direct descent when suffered to fall freely from rest,
so the deviation of bodies moving in free spaces from rectilinea