Retarded position

Einstein's equations admit gravity wave-like solutions. In the case of a moving point-like mass and in the linearized limit of a weak-gravity approximation these solutions of the Einstein equations are known as the Lienard-Wiechert gravitational potentials. The gravitational field at any point of space at some instant of time t is generated by the mass taken in the preceding (or retarded) instant of time s < t on its world-line at a vertex of the null cone connecting the mass and the field point. The position of the mass that generates the field is called the retarded position and the Lienard-Wiechert potentials are called the retarded potentials. The retarded time and the retarded position of the mass are a direct consequence of the finite value of the speed of gravity, the speed with which gravity propagates in space.

Note that for gravitational masses moving past each other in straight lines (or for that matter for electromagnetically charged objects), there is little or no retardation effect on the effect from them. So long as no radiation is emitted, conservation of momentum requires that forces between objects (either electromagnetic or gravitational forces) point at the object's true instantaneous and up to date positions, not their speed-of-light delayed retarded positions. However, since no information can be transmitted from such an interaction, such influences which seem to exceed that of the influence of light, cannot be used to violate principles of relativity.

See
* [http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html Does Gravity Travel at the Speed of Light?] in "The Physics FAQ"