Is emission-less propulsion possible? I believe it is...

[muriel_volestrangler]

81. OK, some numbers for position (Python? Why Python? This is a physics problem, not a numerical procedure)

The man (and his tether system) has mass 100kg, and the combined "bullets" from the railgun .5kg. Velocity and position are measured relative to an external static point. The bullets are caught and returned by the tether at the end of an arm.

After firing, 100kg is moving right at 1m/s, and .5kg left at 200 m/s
Total momentum is 100 * 1 - .5 * 200 = 0

Say it takes 1 second for the bullets to reach the tether, so the man moves 1m (measured relative to the outside static point), and the bullet 200m - so the length of the arm is 201m (the end of the arm also moved 1m right in that second, so to meet the bullets moving left after 1 second, it must be 200 + 1 metres long)

After "reflection" of the bullets, say they do lose a little kinetic energy in the process. Say they are now .5kg moving right at 190 m/s (relative to the external static point)

Then the 100kg man must be moving left at .5/100*190=0.95 m/s, and the relative speed of the bullets to the man (and arm) is 190+0.95=190.95 m/s

This then lasts for (201/190.95) seconds before the bullets reach the man again

In this time, the man moves left .95*201/190.95= 1m (exactly)

The bullet is reabsorbed, and we're back where we started, in both position and momentum.

As others have said, during the process, the combined man/bullet system is reconfigured around the centre of mass, so a part of the system (such as the man) is seen to move - first right, then left, but when the mass is finally distributed as it was at the start, the net movement of the man (and bullet) has been zero.