Precession of a Freely Rotating Rigid Body. Inelastic Relaxation in the Vicinity of Poles

When a solid body is freely rotating at an angular velocity ${\bf \Omega}$, the ellipsoid of constant angular momentum, in the space $\Omega_1, \Omega_2, \Omega_3$, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from principal. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behaviour, because an infinitesimally small deviation of the body's shape from a rotational symmetry (i.e., a small difference between the largest and second largest moments of inertia) yields libration: the precession trajectory is not a circle but an ellipse. In this article we show that often the most effective internal dissipation takes place at twice the frequency of the body's precession. Applications to precessing asteroids, cosmic-dust alignment, and rotating satellites are discussed.Comment: 47 pages, 1 figur

29P/Schwassmann-Wachmann: A Rosetta Stone for Amorphous Water Ice and CO <-> CO2 Conversion in Centaurs and Comets?

Centaur 29P/Schwassmann-Wachmann 1 (SW1) is a highly active object orbiting in the transitional Gateway region (Sarid et al. 2019) between the Centaur and Jupiter Family Comet regions. SW1 is unique among the Centaurs in that it experiences quasi-regular major outbursts and produces CO emission continuously; however, the source of the CO is unclear. We argue that due to its very large size (approx. 32 km radius), SW1 is likely still responding, via amorphous water ice (AWI) conversion to crystalline water ice (CWI), to the rapid change in its external thermal environment produced by its dynamical migration from the Kuiper belt to the Gateway Region at the inner edge of the Centaur region at 6 au. It is this conversion process that is the source of the abundant CO and dust released from the object during its quiescent and outburst phases. If correct, these arguments have a number of important predictions testable via remote sensing and in situ spacecraft characterization, including: the quick release on Myr timescales of CO from AWI conversion for any few km-scale scattered disk KBO transiting into the inner system; that to date SW1 has only converted between 50 to 65% of its nuclear AWI to CWI; that volume changes upon AWI conversion could have caused subsidence and cave-ins, but not significant mass wasting or crater loss on SW1; that SW1s coma should contain abundant amounts of CWI CO2-rich icy dust particles; and that when SW1 transits into the inner system within the next 10,000 years, it will be a very different kind of JFC comet.Comment: 29 Pages, 3 Figures, 2 Tables, accepted 16-Sept-2022 by the Planetary Science Journal Corrected proof version 26-Oct-202

Asteroids. From Observations to Models

We will discuss some specific applications to the rotation state and the shapes of moderately large asteroids, and techniques of observations putting some emphasis on the HST/FGS instrument.Comment: to appear in LNP; 28pages; written in 2003; Winter School "Dynamique des Corps Celestes Non Ponctuels et des Anneaux", Lanslevillard (FRANCE

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

Outgassing-induced effects in the rotational state of comet 67P/Churyumov---Gerasimenko during the Rosetta mission

The new target of the Rosetta mission is comet 67P/Churyumov Gerasimenko (hereafter 67P/C G). In order to support the planning of the mission, in particular the strategy during the mapping and landing phases, we have performed numerical simulations of the rotational evolution of a comet in the orbit of 67P/C G. In these simulations, the currently known observational constraints have been taken into account and a large set of initial conditions were considered. For most of the simulations, we observe that the sublimation-induced torques produce significant changes in the rotational parameters of a 67P/C G-like comet. Typical rates of change for the spin period from the rendezvous up to the end of the nominal mission range from 0.001 to 0.05hday depending on different circumstances as described in the text. At perihelion, rates of change of the orientation of the angular momentum vector amount to about 0.01 0.1degday. These simulations suggest that a specific strategy should be defined in order to monitor likely variations of the rotational parameters. As an example we show a possible optimized schedule for observations with the OSIRIS instrument to determine the rotational parameters of comet 67P/C G and their possible evolution

R- And J-Band Photometry Of Comets 2P/Encke And 9P/Tempel 1

Near-simultaneous R- and J-band photometric measurements of the short-period Comets 2P/Encke and the Deep Impact mission target 9P/Tempel 1 were obtained. The resulting R - J colors are + 0.82 ± 0.08 mag and + 1.46 ± 0.13 mag for Encke and Tempel 1, respectively. Tempel 1\u27s color is redder than the solar R - J color index of +0.76. The Tempel 1 observations directly detected the nucleus while the Encke observations likely suffered from coma contamination. © 2005 Elsevier Inc. All rights reserved

R- And J-Band Photometry Of Comets 2P/Encke And 9P/Tempel 1

Near-simultaneous R- and J-band photometric measurements of the short-period Comets 2P/Encke and the Deep Impact mission target 9P/ Tempel 1 were obtained. The resulting R-J colors are +0.82 ± 0.08 mag and +1.46 ± 0.13 mag for Encke and Tempel 1, respectively. Tempel 1\u27s color is redder than the solar R-J color index of +0.76. The Tempel 1 observations directly detected the nucleus while the Encke observations likely suffered from coma contamination. © 2005 Elsevier Inc. All rights reserved