Spacester's answer is correct, but he doesn't say what happens along the orbit. One can plot these things using some good approximations. I believe the equations are called the Clohesey-Wilshire equations (although my spelling is probably off. A good place to start is a book by Bate, Meuller, and White, with further apologies for spelling.)<br /><br />Assume the initial orbit is circular, although it doesn't matter much, and assume that the throw is at right angles to the astronaut's path. The projectile leaves his hand heading "down" towards the center of the earth. As said by others, going "on the inside track" it moves ahead, but eventually hits its new perigee. At that point it is moving in the same direction as the astronaut, but lower and going faster. Then the orbit radius increases until it is at the same altitude as the astronaut. Its at the same velocity, but out in front. It continues to rise towards its apogee, and slows down. Now its "above" the astronaut but going slower, so he's catching up. It then descends, gaining speed to macth that of the astronaut, but droping in altitude. After exactly one orbit it passes by the astronaut, heading down at the speed it was thrown, having made a pretty good approximation of a circle. <br /><br />Even if there was a measureable drag effect, it would pretty much effect both equally unless there was a dramatic difference in balistic coefficient, such as if the thrown object was a balloon. In that case, the circles would become loops, one per orbit, moving away from the astronaut in the direction of motion but losing altitude relative to the astronaut.