Preface: On Earth, with the help of gravity, I can easily tie a wrench to a rope, then spin it around, lasso-style, and let go at any time to send the wrench and rope flying away from me in the air. I want to know if something similar is possible in space.
I know that movement through space is accomplished by delta-v, which typically means to get somewhere you must leave something behind. I'm just trying to figure out if that must always be the case.
Let's say I am only six feet away from my space ship when I realize that I forgot to attach the tether. The tether is perhaps twenty feet long, and is on a spool connected to my suit. I have no means to puncture my suit, and I am moving with exactly zero relative velocity to my space ship. Suppose I was using my MMU, and it just ran out of fuel right as I caught up to the space ship, but remained six feet from it. Now, I want to reach the space ship, which has plenty of grippy surfaces on it that I can use to get back inside as long as I can reach them. I also have a very massive wrench. Do I have any options?
Let's say I attach the wrench to the tether, spool out all 20 feet of the tether, but then grab it such that the wrench is attached about three feet from my hand. That leaves 17 feet of slack from my hand to the point where it is attached to my suit. Now, I want to shove (throw) the wrench toward the ship with all of my might. That's going to move me away from the ship by some amount, but then I want to try to start the wrench spinning in a lasso-style movement perpendicular to the ship (i.e. circle's radius would go from me out toward the ship). Assuming I can get the wrench moving lasso-style, I would let go of the tether just as the wrench was moving toward the ship, and then let it pull the cable and me along with it. When this happens in space, would I be flung in the opposite direction with equal force?
The idea I'm going for is that I can inject a lot of energy into the rotational movement of the wrench with my lasso technique. I'm burning calories doing this, so I'm not creating energy. I'm converting my stored energy into kinetic energy in the rotating lasso system. Is that even possible to do in space? Am I violating any laws of physics by trying to use angular momentum to induce a linear velocity?
I understand that if I throw the wrench, then pull the wrench, I will end up with a net movement of zero relative to my initial point. If the wrench has a sufficiently smaller mass to mine, then perhaps I could make the wrench move away from me fast enough to reach the space ship before I move more than the length of the tether away, and hope to hook something on the ship. Maybe the wrench could have a magnet on it. I don't know. Perhaps I have a gyroscope with me that I can hold onto for starting the lasso-maneuver.