Bill and Bob are out on a little job that requires a space-walk. They are installing a new pump, which weighs about 150kg, for the heating unit for the Space Lab. They have an accident.

Gas pressure was built up in one of the lines on the old pump. This was Bob's mistake. He forgot to crack the fitting, and instead he cut the hose for quick removal. Bill flinched to avoid being slapped by the hose and he pushed himself away from the Lab at about 4 meters per second, and Bob was knocked off the platform in about the same direction as Bill. They were tethered together at the waist, and to the pump, which was pulled off the platform with Bob. Bill made a critical mistake when when he hit the accelerator on his backpack, sending himself and Bob in orbit around the pump. Bob followed up this blunder by doing the same thing. When they finally settled themselves into a quiet orbit around the pump, all the fuel in their jetpacks was gone. They are several hundred meters away from the Lab and the Shuttle, and the distance is increasing at about 5 meters per/second.

They only have about 30 minutes of air left. They quickly come to an agreement that they will not cut the tether between them in an attempt to hurl one or the other toward the Shuttle, for fear they would miss, and both be lost forever.

How can Bill and Bob reverse their direction and hope to 'steer' themselves back? Can they?

Each man is attached to the pump by 15 meters of cable. The pump is almost perfectly centered between them, and it wieghs 150kg.

We can assume there is no answer, or that there are many.

I just think this problem presents an interesting platform of thought.

Originally posted by Fluidity
How can Bill and Bob reverse their direction and hope to 'steer' themselves back? Can they?


If I read your scenario correctly, they can't. They can pull on the tethers and change their positions relative to the pump and to each other but they can't change the velocity of their common centre-of-mass.

Cheers,

Ron.

They have to take the chance of cutting the cable at some point, and the sooner the better. I personally would cut the cable, (If I were Bill), and start a centrifugal orbit of sufficient velocity to hurl myself toward the shuttle. Aiming is the hardest part, but it's the only chance. I should be able to 'feel' my alignment with the shuttle and the lab pretty well, since there is no gravity to confuse the sense of equilibrium allowed by centrifugal force.
All I would have to do then is let go when I am best aligned.
Bob would then have his own chance to hurl himself using the pump as his orbital mass. So, the chances of survival are increased by a factor of 2, as long as someone cuts the cable.

Oops, Bob might be doomed. If I throw him and the pump in the opposite direction, he might never build enough velocity to overcome that reaction. Well, I could be generous and take a little off my velocity to try to leave him a chance.

The pump's mass is 150kg, maybe it's heavy enough for two launches?