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How well or accurately can we measure the tumble of space debris?

I know that we can make ground-based measurements based on light curve data acquired by telescopes. Can tumble be measured from radar data?

What percentage of space debris do we already have tumble data for?

Primarily, I am wondering if there are currently any space-based methods for analyzing tumble.

uhoh
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Jonathan L.
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  • related in Astronomy SE: DAMIT how do they get 3D shape and rotational trajectory of a tumbling asteroid from photometry? but of course different; as you point out radar reflections will be different than light since the wavelengths can be of order the same size as macroscopic features on the object. cf. Star-shaped artifacts in SAR images of the “Suez Canal traffic jam seen from space” – uhoh Jun 20 '21 at 09:47
  • You measure a periodic light curve with a telescope. If the period is not too large ( more than days up to weeks) or to small ( less than milliseconds ) the period may be caused by tumbling. But the light curve does not tell the axis of tumbling.

    A periodic signal may be found in the intensity of the reflected radar signal.

     – Uwe Jun 22 '21 at 01:12
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    @Uwe I don't think tumbling is necessarily periodic, though I'm sure you can probably still figure out the motion making assumptions about the shape and reflectivity and gauging the principal moments of inertia. – Roger Wood Jun 22 '21 at 16:38
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    @RogerWood If there is conservation of angular momentum, how tumbling may be non periodic ? – Uwe Jun 22 '21 at 20:36
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    @Uwe I don't underand this very well, but, despite the conservation of angular momentum and rotational energy, the axis of rotation can still wander around within the body and the rpm can change (see Tennis Racket Theorem). The wandering around with respect to the body is called the "polhode" and it is periodic. But the wandering around of the axis with respect to fixed space (the "herpolhode") is not generally periodic. See also https://en.wikipedia.org/wiki/Poinsot%27s_ellipsoid – Roger Wood Jun 23 '21 at 02:32
  • @RogerWood I don't understand it either, but a way to get out of explaining it is to recall that the total angular momentum vector is some moment of inertia tensor $\mathbf{I}$ times some angular rotation vector $\mathbf{\overrightarrow{\omega}}$, and what might look like a simple rotation around one axis might actually be three rotations around three axes temporarily mimicking something simpler-looking. Thus both angular momentum and deceptive appearances are conserved simultaneously :-) – uhoh Jun 23 '21 at 04:13
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    I did some more digging. It seems the best tumble/rotational data comes from AIUB in Switzerland. They have a database of light curves for about 400 pieces of space debris throughout LEO, HEO, and GEO. They also catalogue some GLONASS objects. Silha et. al did a phenomenal study on it. Here's the link: https://www.sciencedirect.com/science/article/pii/S027311771730786X#b0025 – Jonathan L. Jun 23 '21 at 12:32
  • @uhoh hah, it's difficult to visualize something rotating around three axes simultaneously, but maybe that's the same as saying the axis of rotation can move with a certain angular velocity. Maybe when something precesses, it can be said to be rotating around two axes? – Roger Wood Jun 23 '21 at 20:56
  • @RogerWood it's offered only as "a way to get out of explaining it" :-) – uhoh Jun 24 '21 at 00:03
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    @JonathanL. excellent! It's always okay to answer your own question in Stack Exchange. If you feel it's only a partial answer just mention that in the beginning. – uhoh Jun 24 '21 at 00:04

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