Gyron Field—gravitational analogue of magnetic force

Abstract

AN electrostatic field E in a stationary coordinate system, when referred to a moving coordinate system, can produce both an electric field E^*, and a magnetic field B^*. If v is the uniform velocity of motion, perpendicular to E, then by the usual Lorentz transformation: where β=v/c. Consider two stationary point masses, m₁ and m₂, with respective electric charges q₁ and q₂. Suppose that the particles are located at 0, r/2, 0 and 0, −r/2, 0 in a system of Cartesian coordinates. If the masses and charges are chosen so that the force of electrostatic repulsion exactly balances that of gravitational attraction, then where G is the constant of gravitation and ɛ₀ is the electrical permittivity of space. Positive signs indicate repulsion and negative signs attraction.