Gravitational Field.
This method of obtaining from Coulomb’s law the expected expression for the force exerted by a moving electric charge is of special interest, since it suggests the possibility of obtaining from Newton’s law an expression for the gravitational force exerted by a moving mass.
Let us assume, in accordance with Newton’s law, that a stationary mass will act on any other mass with the force , where and are the masses which the particles would have if they were at rest, isolated, and at the absolute zero of temperature, and r the radius vector from to . The determination of the force exerted by a mass in uniform motion may now be carried out in exactly the same manner as for the force exerted by a moving charge. In fact in analogy to equations (24), (25), and (26), we may write–
(27) |
(28) |
(29) |
These are the components of the force with which a particle of "stationary" mass , in uniform motion in the X direction with the velocity , acts on another particle of "stationary" mass . Taking as the centre of coordinates, has the coordinates X, Y, and Z and the velocity . is the constant of gravitation, is placed equal to , and has been substituted for [1].
It may be noted that the particle must be in uniform motion, although the particle may have any motion, its instantaneous velocity being . It is unfortunate that the method does not also permit a determination of the force which an accelerated particle exerts. For cases, however, where the acceleration is slow enough to be neglected, it would
- ↑ These equations would accord with the electromagnetic theory of gravitation proposed by D. L. Webster, Proc. Amer. Acad. xlvii. p. 561 (1912).