A scientific analysis of stopping the spin of Discovery One spaceship

[Leo Liu]

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.

 

[.Scott]

It has the potential to work. It should be a two step process.
1) Bring the axis of rotation back to the long axis.
2) Bring all of the angular momentum back to the centrifuge.

So it might require more than just turning those motors on. You would likely need to power them forward and backwards to get the result. The biggest thing working against them is the huge ratio between the length and width of the spacecraft .

 

[Leo Liu]

1) Bring the axis of rotation back to the long axis.
2) Bring all of the angular momentum back to the centrifuge.

But since the angular momentum of the system is conserved, we need to add some energy to the system to achieve this. How would you do it?

 

[.Scott]

It's okay to add energy to the system if you can also "brake" the system later to burn it off.
When you first start to spin up the centrifuge, it will act like a gyroscope and (assuming sufficient power) will move the axis of rotation to where you want it. But at that point, the entire craft will most likely be spinning on that axis - the centrifuge one way and the rest of the craft the other. So you will probably need to brake it until the spacecraft is not longer spinning - leaving only the centrifuge in motion.

Of course, at that point thrusters might be useful in adjusting the rotation. But since the spacecraft started out with the correct angular momentum before it was abandoned, once the craft is made stable, the centrifuge should be rotating at about the right speed.

In the video, that craft appears to be tumbling at about 1 revolution per 40 seconds. Converting that angular momentum to the rotation of a smaller mass and much smaller diameter would be interesting. Without doing any calculations, I suspect that the centrifuge will end up delivering well more than 1 G.