Paper: Spin-orbit coupling and chaotic rotation for circumbinary bodies

Posted: August 21, 2015 by tchannon in Astrophysics

A paper of interest to some Talkshop readers

Spin-orbit coupling and chaotic rotation for circumbinary bodies
Application to the small satellites of the Pluto-Charon system



Alexandre C. M. Correia, Adrien Leleu, Nicolas Rambaux and Philippe Robutel
Open access, published 20 August 2015


We investigate the resonant rotation of circumbinary bodies in planar quasi-circular orbits. Denoting nb and n the orbital mean motion of the inner binary and of the circumbinary body, respectively, we show that spin-orbit resonances exist at the frequencies n ± k?/2, where ? = nb – n, and k is an integer. Moreover, when the libration at natural frequency has the same magnitude as ?, the resonances overlap and the rotation becomes chaotic. We apply these results to the small satellites in the Pluto-Charon system, and conclude that their rotations are likely chaotic. However, the rotation can also be stable and not synchronous for small axial asymmetries.

The A&A site showed a related work which also might be of interest, 2011 paper on Venus LoD.

The various contributions in Venus rotation rate and LOD

Post by Tim

  1. oldbrew says:

    Whenever they say ‘chaotic’ it means ‘we don’t understand how it works’ 😉

    Example: Saturn’s moon Hyperion.
    ‘It is distinguished by its irregular shape, its chaotic rotation, and its unexplained sponge-like appearance. It was the first non-round moon to be discovered.’ – Wikipedia

    It turns out that instead of having synchronous rotation (orbit period = rotation period) like most moons in the solar system, Hyperion has a rotation period of 13.1 days. All they have to do is compare that to its orbit period of 21.276 days.

    Result: it’s either a 13:21 ratio or 8:13 (Fibonacci numbers), depending on how accurate the ‘13.1 days’ is. It’s not as chaotic as they think.

    Letter to Nature: ‘Chaotic rotation of Hyperion?’

    ‘These data conclusively show that the 13.1-day period found by Thomas et al. was not due to coherent rotation.’

    Sure about that? It was 1986 so ideas should have moved on.

  2. M Simon says:

    Whenever they say ‘chaotic’ it means ‘we don’t understand how it works’

    It means “we can’t make predictions”. You can understand how something works and still not be able to predict what it will do.

  3. Paul Vaughan says:

    OB wrote:
    “Whenever they say ‘chaotic’ it means ‘we don’t understand how it works’”

    True …but they’ll try to have you believe otherwise …and if you’re independently capable of competently doing diagnostics firsthand you’ll be aware that their reasoning is based on beloved false assumptions (conveniently invoked to render the model math tractable).

  4. oldbrew says:

    When a probe whizzes past Pluto-Charon and their small moons at high speed there isn’t enough time to study their behaviour in any great detail. Rotation data might be interesting though.

    This recent research re moon Kerberos found something in its frequency analysis and commented:
    ‘The 3/2 harmonic is unexplained.’

  5. tchannon says:

    A fair point oldbrew, inadequate data is a science normalism. Astronomy particularly tries to use less than the minimum sample rate, in this case I have no idea.

    There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.” — Twain

  6. oldbrew says:

    The barycentric motion of exoplanet host stars: tests of solar spin-orbit coupling (2010)
    – M. A. C. Perryman, T. Schulze-Hartung

    ‘The study provides the basis for independent investigations of the widely-studied but unproven suggestion that the Sun’s motion is somehow linked to various indicators of solar activity. We show that, because of the nature of their barycentric motions, the host stars HD168443 and HD74156 offer particularly powerful tests of this hypothesis.’