CENTRAL FORCES. Forces which pro duce on a moving body an acceleration toward a fixed point called the 'centre of force.' Il lustrations are afforded by the motion of a stone whirled in a sling, by the motion of the moon with reference to the earth. or of the earth with reference to the sun. It is evident, since the line of action of the force is through a fixed point. that the moving body will always move in a definite plane. and that the moment of the force around a line through the fixed point per pendicular to this plane being zero, there is no change in the angular momentum around this line. (See SIEruANtes.) This leads at once to whot is called the principle of the 'conserva tion of areas.' or the statement that, if a radius vector he drawn from the fixed point to the MoN lug body, it mill describe equal areas in equal intervals of thine; thus, the nearer the body is to the centre, the greater must be its speed.
It can be slioNNn further that, if the force is an attraction varying inversely as the square of the distance flout the centre to the body, the orbit of the body w will be an ellipse, hyperbola or parabola, depending upon the conditions under which the motion may be regarded as being started, the centre of the force being a focus.
If the orbit is it may be shown that the square of the period of revolution of the body in its orbit is proportioned to the cube of the major axis of the ellipse. See Tait and Steele, Dynamics of it Po rt (Loudon. 1S561.
The great astronomer Kepler, hi 1609, by a careful consideration of the observations Tycho Brahe oil the motions of the planets, de duced the fact that these motions obeyed the three laws stated above; that is, they satisfy the conservation of areas. their orbits are elliptical about the sun as a focus, and the squares of their periods are proportional to the eubes of the major axis of the whit. These are, therefore, often called 'Kepler's laws.' Sir Isaac Newton sonic years later showed that these laws were a neces sary consequence of his principle of universal gravitation, which states that any two particle of matter act upon each other with a force of attraction which varies directly as the product of the masses of the particles and inversely as the square of their distance apart. and of the further principle that a large spherical body acts upon outside points as if its matter were con centrated at its centre.