The ONLY way to give myself momentum towards the station is to give something else momentum AWAY from it. I have to eject mass in the
direction away from the station.
If I weren't wearing this darn helmet, I could SPIT away from the station,
and that would do the job. But if I do that now, then I'll only move toward
the station for a very short time ... until the spit goes splat against the inside
of the helmet, and then I'll stop. I have to throw something that isn't connected
to me in any way, and it has to keep going.
The first thing to throw away is the empty jet pack. Right now, the total
momentum of the system of (me + jet-pack) is zero. When I THROW the
jet-pack, I'll give it momentum that way ==>, and in order for momentum to
be conserved, my body will get an equal amount of momentum this way <== .
The harder I throw the jet-pack away from the station, the more momentum
(speed) I get toward the station.
I can also look through my space-suit pockets and belt, for any tools,
cameras, ropes, hammers etc. that I brought out with me to do the work
during the spacewalk, and throw all of THAT stuff away from the station too.
The more mass I can throw away, and the faster I can throw it, the more
momentum I'll give myself in the opposite direction. If I have enough
disposable mass, I can be back inside in time for lunch.
