XXVI
§ 58. The two forces being equal and acting perpendic
ularly upon each other, the course will be a circle.
§ 59. If the Centripetal force be stopped all of a sud
den, the body in consequence of inertia will pursue its course
in the direction of the tangent. For example: if the gravity of
the earth would cease to attract, everything on the surface of
the earth would be projected even the whole mass of the earth
would be scattered in pieces in the universe.
§ 60. The greater the radius of the course and the mass
of the body and the smaller the line of revolution, the greater
the Centripetal and Centrifugal forces will be.
§ 61. An important application of curvilinear motion is the
fly-wheel (351, 4) used for imparting an uniform motion (§ 30).
For this purpose its vis invertiae must be as great as possible,
hence a large radius and a great mass are wanted.
§ 62. The rotations of the moon round the earth and of
the planets round the sun are also curvilinear motions. Newton
assumed and (1682) proved that the Centripetal force active in
the rotation of the moon is the earth's gravitation.
§ 63. The three celebrated laws of Kepler (1571-1630)
are the following:
1). The courses of planets are ellipses and the sun is situat
ed in one of their foci.
