- #1

Leo Liu

- 353

- 156

I have been reading 2010: The Year We Make Contact, a sci-fi book belonging to a classic series by Arthur Clarke. The book involves a myraid of scientific concepts so I think it is worth it to verify if the scenes would be feasible in the real word. In this thread I'd like to focus on the scene in which a group of cosmonauts trying to cramp the rotation the abandoned Discovery One spaceship on the orbit around a moon of Jupiter.

After the spaceship is abandoned, the rotating artificial gravity generator (cyan highlight) transfers the residual angular momentum to the hull through frictional torque. In the end, the whole spaceship rotates about the axis that possesses the maxium rotational inertia so that the total rotational energy is the lowest according to this equation:

$$K_{rot}=\frac{L^2}{2I}>K'_{rot}=\frac{L^2}{2I'}$$

This motion is well illustrated in the flim -- the Discovery rotates about the axis perpendicular to the long and slim hull and at the midpoint:

(Timestamp: 1m28s)

and portrayed in the book:

Walter Curnow knew that as an abstract principle; but he did not really feel it in his bones until he saw the entire hundred-metre length of Discovery turning end-over-end, while Leonov kept at a safe distance. Years ago, friction had braked the spin of Discovery's carousel, thus transferring its angular momentum to the rest of the structure. Now, like a drum-majorette's baton at the height of its trajectory, the abandoned ship was slowly tumbling along its orbit.

The windmilling motion of the spaceship poses a big problem to the team who then decides to solve it by restarting the artificial gravity carousel:

I'm not after gravity, though it will be useful to have some aboard. If we can get the carousel running again, it will mop up the ship's spin — stop it tumbling. Then we'll be able to couple our airlocks together, and cut out EVAs. That will make work a hundred times easier.

However, I doubt this strategy would work in reality since the spin momentum is not on the same axis as the axis about which the ship tumbles. By doing so the ship would gain an extra component of angular momentum. My reasoning is shown in the picture below (pardon my bad drawings):

Key:

1. The spaceship spins about axis 1 and has angular momentum ##\vec L_1##.

2. The carousel begins spinning and the hull gains ##\vec L_2## while the angular momentum of the system remains unchanged.

3. Due to the windmilling motion, the direction of ##\vec L_2## changes with time. The change is ##\Delta \vec L_2=\vec L_2(t+\Delta t)-\vec L_2(t)##.

4. We know that the torque is the rate of change of the angular momentum, so there is a torque acting on the hull pointing in the same direction as ##\Delta \vec L_2##.

5. This torque makes the hull spin around axis 2 and thus gains additional angular momentum.

It is unclear to me how the artificial gravity removes ##\vec L_1## like a charm. And I wonder if my concern is valid. Plus, why would't they just turn on the main thruster and tilt the nuzzle or use the RCS to create a force component and therefore a torque against the spin?

Thanks.

Last edited: