DPS Pasadena Meeting 2000, 23-27 October 2000
Session 13. Asteroids II - Discovery and Dynamics
Oral, Chairs: W. Merline, J. Burns, Tuesday, 2000/10/24, 8:30-10:00am, C106

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[13.01] Nutational Damping Revisited

J.A. Burns, I. Sharma (Cornell University)

Motivated by the recent detection of complex rotational states for several asteroids and comets, as well as by the ongoing and planned spacecraft missions to such bodies, which should allow their rotational states to be accurately determined, we revisit the problem of the nutational damping of small solar system bodies. The nutational damping of asteroids has been approximately analyzed by Prendergast (1958), Burns and Safronov (1973), and Efroimsky and Lazarian (2000). Many other similar dynamical studies concern planetary wobble decay (e.g., Peale 1973; Yoder and Ward 1979), interstellar dust grain alignment (e.g., Purcell 1979; Lazarian and Efroimsky 1999) and damping of Earth's Chandler wobble (Lambeck 1980).

Recall that rotational energy loss for an isolated body aligns the body's angular momentum vector with its axis of maximum inertia. Assuming anelastic dissipation, simple dimensional analysis determines a functional form of the damping timescale, on which all the above authors agree. However, the numerical coefficients of published results are claimed to differ by orders of magnitude. Differences have been ascribed to absent physics, to solutions that fail to satisfy boundary conditions perfectly, and to unphysical choices for the Q parameter. The true reasons for the discrepancy are unclear since, despite contrary claims, the full 3D problem (nutational damping of an anelastic ellipsoid) is analytically intractable so far. To move the debate forward, we compare the solution of a related 2D problem to the expressions found previously, and we present results from a finite element model. On this basis, we feel that previous rates for the decay of asteroidal tumbling (Harris 1994), derived from Burns and Safronov (1973), are likely to be accurate, at least to a factor of a few. Funded by NASA.

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