On Perceived Positions and Field Directions
Fig. 1 depicts a particle at time t=0. The particle has always moved along the negative x-axis with a constant speed of .95c. xr is the retarded position with respect to the indicated observer.
Retarded Particle Position
Assuming the only particle-emitted photons that can reach the observer at time t=0 are those emitted when the particle is at point xr, xr is where the particle will be observed (i.e. seen) to be at time t=0. But the inertial frame’s clocks (the origin clock in particular) will indicate that the particle is at the origin at time t=0.
These facts lead to an interesting "disconnect." For let us suppose that the particle is charged, and that the observer measures the particle’s electric field at time t=0. Since the electric field of a constant-velocity point charge points away/toward the charge at any moment, the electric field vector, at the observer’s position, and at time t=0, will point away/toward the origin … a result consistent with what the origin clock indicates. But the observer sees the particle to the left of the origin! Evidently the adage, "Don’t believe everything you see," applies.
What if the particle also has a large mass and the observer measures its gravitational field at time t=0? One obvious guess would be that the gravitational field would also point toward the origin … a result that would certainly be consistent with the idea that Maxwellian formulas also apply to a particle’s gravitational field (with an "orthogravic" or "gravitomagnetic" field factored in). Of course one should not rule out the possibility that, although the particle’s mass and charge exist at a common point, the gravitational field does not point toward the particle when its velocity is constant.
If the Maxwellian analogies apply to mass-mass interactions, then due caution is suggested in modeling systems of gravitationally interacting bodies. For the gravitational interactions might not always agree with the positions observed through a telescope (for example). The star positions that we observe from an Earth-bound telescope are retarded positions, and the gravitational field centers might be displaced from those positions at any moment in time.