Euler, Jacobi, and Missions to Comets and Asteroids

Whenever a freely spinning body is found in a complex rotational state, this means that either the body is a recent victim of an impact or a tidal interaction, or is a fragment of a recently disrupted progenitor. Another factor (relevant for comets) is outgassing. Due to impacts, tidal forces and outgassing, the asteroidal and cometary precession must be a generic phenomenon: while some rotators are in the state of visible tumbling, a much larger amount of objects must be performing narrow-cone precession not so easily observable from the Earth. The internal dissipation in a freely precessing top leads to relaxation (gradual damping of the precession) and sometimes to spontaneous changes in the rotation axis. Recently developed theory of dissipative precession of a rigid body reveals that this is a highly nonlinear process: while the body is precessing at an angular rate $\omega$, the precession-caused stresses and strains in the body contain components oscillating at other frequencies. Dependent upon the spin state, those frequencies may be higher or, most remarkably, lower than the precession rate. In many states dissipation at the harmonics is comparable to or even exceeds that at the principal frequency. For this and other reasons, in many spin states the damping of asteroidal and cometary wobble happens faster, by several orders, than believed previously. This makes it possible to measure the precession-damping rate. The narrowing of the precession cone through the period of about a year can be registered by the currently available spacecraft-based observational means. However, in the near-separatrix spin states a precessing rotator can considerably slow down its relaxation.Comment: 21 pages, 1 figur

Rotation State of Comet 103P/Hartley 2 from Radio Spectroscopy at 1 mm

The nuclei of active comets emit molecules anisotropically from discrete vents. As the nucleus rotates, we expect to observe periodic variability in the molecular emission line profiles, which can be studied through mm/submm spectroscopy. Using this technique we investigated the HCN atmosphere of comet 103P/Hartley 2, the target of NASA's EPOXI mission, which had an exceptionally favorable apparition in late 2010. We detected short-term evolution of the spectral line profile, which was stimulated by the nucleus rotation, and which provides evidence for rapid deceleration and excitation of the rotation state. The measured rate of change in the rotation period is +1.00 \pm 0.15 min per day and the period itself is 18.32 \pm 0.03 hr, both applicable at the epoch of the EPOXI encounter. Surprisingly, the spin-down efficiency is lower by two orders of magnitude than the measurement in comet 9P/Tempel 1 and the best theoretical prediction. This secures rotational stability of the comet's nucleus during the next few returns, although we anticipate a catastrophic disruption from spin-up as its ultimate fate.Comment: Accepted for publication in ApJ Letter

Relaxation of Wobbling Asteroids and Comets. Theoretical Problems. Perspectives of Experimental Observation

A body dissipates energy when it freely rotates about any axis different from principal. This entails relaxation, i.e., decrease of the rotational energy, with the angular momentum preserved. The spin about the major-inertia axis corresponds to the minimal kinetic energy, for a fixed angular momentum. Thence one may expect comets and asteroids (as well as spacecraft or cosmic-dust granules) stay in this, so-called principal, state of rotation, unless they are forced out of this state by a collision, or a tidal interaction, or cometary jetting, or by whatever other reason. As is well known, comet P/Halley, asteroid 4179 Toutatis, and some other small bodies exhibit very complex rotational motions attributed to these objects being in non-principal states of spin. Most probably, the asteroid and cometary wobble is quite a generic phenomenon. The theory of wobble with internal dissipation has not been fully developed as yet. In this article we demonstrate that in some spin states the effectiveness of the inelastic-dissipation process is several orders of magnitude higher than believed previously, and can be measured, by the presently available observational instruments, within approximately a year span. We also show that in some other spin states both the precession and precession-relaxation processes slow down considerably. (We call it near-separatrix lingering effect.) Such spin states may evolve so slowly that they can mimic the principal-rotation state.Comment: 2 figure

Disability Justice: An Audit Tool

This toolkit is aimed at helping Black, Indigenous and POC-led organizations (that are not primarily focused around disability) examine where they're at in practicing disability justice, and where they want to learn and grow. It includes questions for self-assessment, links to access tools, organizational stories and more

The Increasing Rotation Period of Comet 10P/Tempel 2

We imaged comet 10P/Tempel 2 on 32 nights from 1999 April through 2000 March. R-band lightcurves were obtained on 11 of these nights from 1999 April through 1999 June, prior to both the onset of significant coma activity and perihelion. Phasing of the data yields a double-peaked lightcurve and indicates a nucleus rotational period of 8.941 +/- 0.002 hr with a peak-to-peak amplitude of ~0.75 mag. Our data are sufficient to rule out all other possible double-peaked solutions as well as the single- and triple- peaked solutions. This rotation period agrees with one of five possible solutions found in post-perihelion data from 1994 by Mueller and Ferrin (1996, Icarus, 123, 463-477), and unambiguously eliminates their remaining four solutions. We applied our same techniques to published lightcurves from 1988 which were obtained at an equivalent orbital position and viewing geometry as in 1999. We found a rotation period of 8.932 +/- 0.001 hr in 1988, consistent with the findings of previous authors and incompatible with our 1999 solution. This reveals that Tempel 2 spun-down by ~32 s between 1988 and 1999 (two intervening perihelion passages). If the spin-down is due to a systematic torque, then the rotation period prior to perihelion during the 2010 apparition is expected to be an additional 32 s longer than in 1999.Comment: Accepted by The Astronomical Journal; 22 pages of text, 3 tables, 6 figure