Rantakivi, Gravitation III – Velocity-dependent force

General relativity gives the orbit of a celestial body as a solution to Euler's equations. The solution is a time-dependent position vector that minimizes the orbital length in curved space. The same Euler equations can also be viewed from another perspective. They can be interpreted as a group of equations for components parallel to the coordinate axes of the acceleration of the body as a function of the velocity and position of the body in a rectilinear Euclidean space. Accelerations can be solved numerically from the group of equations. Since the acceleration is the same as the force per unit mass, the result is the relativistic force acting on the object. In this way, the orbits of several bodies can be calculated simultaneously according to general relativity. The book presents a more detailed calculation algorithm, a program in the FORTRAN language and several calculated example cases.