Posted 13 December 2013 - 07:25 PM
If Mercury and Jupiter were exactly the same distance from the Sun, in exactly opposite directions, and moving at exactly the same angular velocity, and there were no other gravitational influences involved, the orbits would not be stable over a long period, because the center of mass of the entire system would change relative to the three. The system's mass would be the sum of the three bodies, and the center of that mass would be offset slightly towards Jupiter since its mass is greater than Mercury's. Therefore Jupiter would be closer to the center of mass of the system, and orbit slightly faster, so it would catch up with Mercury.
If both bodies were the exact same distance from the center of mass, then they would orbit at the same velocity in a stable orbit, although Mercury would always be thousands of miles closer to the Sun than Jupiter would.