[TML] Asteroid Mining (was Molding Ships)

[Jerry W Barrington]

On 10/4/07 10:06 AM, Timothy Little wrote:

> There is one other complication: Smallish asteroids are rather
> irregular and for some values of angular momentum (those more closely
> aligned with the mid-length axis of the inertial ellipsoid) will
> tumble chaotically.  If the asteroid is tumbling to begin with, I'm
> sure you can see how the simple mechanism described will fail.
> 
> For a visual experience of tumbling motion, find an smallish dense
> object with quite different length, width, and thickness. (E.g. 9V
> battery)  First throw it in the air spinning it "flat" about the
> shortest axis.  It may wobble, but will have fairly regular spin.
> Next spin it about the long axis: again it will probably wobble, but
> regularly.  Finally spin it about the "middle" axis: during its
> rotation it will *irregularly* flip about the other axes.
> 
> There are unlikely to be any asteroids with spin axis aligned exactly
> with angular momentum axis.  This could be a problem, since the
> simplistic mechanism described transfers angular momentum along the
> spin axis, not the axis of angular momentum.
> 
> Even for those that do not initially tumble, uncertainty in the
> moments of inertia with offset torque axis will lead to increasingly
> magnified difference in axis between angular momentum and angular
> velocity.  This will tend to shift the angular momentum axis toward a
> chaotic spin state (tumble).  (This is easily derivable from second
> year undergraduate physics, but still verifiable from many other
> sources if my credentials are not impressive enough)
> 
> 
> In short, a passive system applied to an irregular body as described
> will most likely lead to a more irregular tumbling rotation in the
> later stages, which may tangle the line - and in some cases may
> actually return angular momentum to the asteroid, speeding it up
> again.  It is nowhere near as simple as the writer makes it sound!
> 
> It is much easier for artificial satellites, of known and controllable
> dynamical characteristics and initial conditions - and even they don't
> pretend you can just wrap it in string and let rotational dynamics
> sort themselves out.

Umm...  No.

Nothing in space "tumbles" like that.  In freefall, you have a fixed angular
momentum about a fixed spin axis thru the center of gravity.  (For the
purists yes, there are gravity effects that can cause wobble, but not on
this sort of time/size scale.)  The spin axis *IS* the angular momentum
axis, by definition!

To make sure the string unwinds properly, you may have to build a "spool"
around the spin axis, but that's a pretty simple project.  And the use of 2
equal weights on opposite sides, as described, keeps the torque aligned to
the axis of spin, so no offset torque problem.