150. From the uniform projectile motion of bodies in straight lines, and
the universal power of attraction, arises the curvilineal motions of all
the Heavenly bodies. If the body _A_ be projected along the right line
_ABX_, in open Space, where it meets with no resistance, and is not
drawn aside by any other power, it will for ever go on with the same
velocity, and in the same direction. For, the force which moves it from
_A_ to _B_ in any given time, will carry it from _B_ to _X_ in as much
more time; and so on, there being nothing to obstruct or alter it’s
motion. But if, when this projectile force has carried it, suppose to
_B_, the body _S_ begins to attract it, with a power duly adjusted, and
perpendicular to it’s motion at _B_, it will then be drawn from the
straight line _ABX_, and forced to revolve about _S_ in the Circle
_BYTU_. When the body _A_ comes to _U_, or any other part of it’s Orbit,
if the small body _u_, within the sphere of _U_’s attraction, be
projected as in the right line _Z_, with a force perpendicular to the
attraction of _U_, then _u_ will go round _U_ in the Orbit _W_, and
accompany it in it’s whole course round the body _S_. Here, _S_ may
represent the Sun, _U_ the Earth, and _u_ the Moon.
151. If a Planet at _B_ gravitates, or is attracted, toward the Sun, so
as to fall from _B_ to _y_ in the time that the projectile force would
have carried it from _B_ to _X_, it will describe the curve _BY_ by the
combined action of these two forces, in the same time that the
projectile force singly would have carried it from _B_ to _X_, or the
gravitating power singly have caused it to descend from _B_ to _y_; and
these two forces being duly proportioned, and perpendicular to one
another, the Planet obeying them both, will move in the circle
_BYTU_[30].
[Sidenote: Elliptical Orbits.