I am reasonably familiar with conventional elliptical orbits under gravity but how do they change as orbital velocities get very fast and start approaching the speed of light? let us initially neglect any energy losses due to gravitational radiation. I have been searching the web for some time for help on this subject and have found nothing of any use except the statement that relativistic effects cause the perihelion of mercury to move slightly An object with a particular mass will accelerate and become "heavier" (or more difficult to accelerate) as it aproches its closest point to the object it is orbiting. does this effective mass increase change the greavitational forces on the object and what about the angular momentum? As nobody mentions any significant changes to the standard elliptical shape of an object orbiting another of much heavier mass I presume that this does not change and that the main changes are in the way the interplay between potential and kinetic energy operates as orbital velocites get significant to the velocity of light.