High precision model of precession and nutation of the asteroids (1) Ceres, (4) Vesta, (433) Eros, (2867) Steins, and (25143) Itokawa

Abstract

Context. Several asteroids have recently been visited by spacecrafts that give us precious information and new constraints on their physical and rotational properties. In parallel, there are already several well-established theories to model the rotational motion of a rigid body, but accurate models of the rotational motion of asteroids have been poorly investigated so far. Aims. We aim to model the rotational motion of the asteroids (1) Ceres, (4) Vesta, (433) Eros, (2867) Steins, and (25143) Itokawa with high precision. Their physical parameters have been or will be (in the case of Ceres) better constrained by data from space missions. We concentrate in particular on the motion of their spin axis in space, a component that is generally not studied. Methods. We used Kinoshita's theory, based on a Hamiltonian approach for the rotation of a rigid body. We deduced an analytical model for determining the precession rate and the nutation coefficients for the set of five asteroids selected above. Results. For each asteroid considered we make a summary of the rotational and physical characteristics necessary for our calculations, and we give both the precession rate and accurate tables of nutation. Results show a very high precession rate for (25143) Itokawa, of more than one degree per decade (ψ = −(461.52 ± 6.57) /yr), and rather high ones for (433) Eros and (2867) Steins. We present the complete tables of nutation for both (1) Ceres and (4) Vesta, and give the peak-to-peak amplitudes for the five asteroids. At last, we show the curves described by the spin axis in space. Results agree with previous ones for (4)Vesta and (433) Eros. Conclusions. In this paper we show that it is possible to accurately compute the combined precession-nutation motion of asteroids that are well constrained by observational data as we do for a set of five asteroids. This enables one to understand the rotational behavior of their spin axis in space and constitutes an interesting step toward knowing of their rotational evolution and its consequences on their history. This work should serve as a basis for more extended ones dealing with the long-term rotational dynamics of the asteroids studied.

Cooperative planning for multi-site asteroid visual coverage

“…In addition to the gravity and solar radiation perturbations, proximity asteroid missions should also consider precession, nutation, and Yarkovsky-O'Keefe-Radzievskii-Paddack effects on the asteroid's spin rate and orbital evolution. For simplicity in this article, but without a loss of generality, these asteroid spin rate affecting factors are not considered as these have a very small and negligible effect on the asteroid's spin rate [40,41] over the considered duration of the observation mission, i.e. ranging in couple of asteroid days.…”

Stable periodic orbits for spacecraft around minor celestial bodies

“…The physical and shape model of asteroid 433 Eros used here is generated by data from Gaskell [31] with the polyhedral model [25,26]. The overall dimensions of asteroid 433 Eros are 36×15×13 km [32], the estimated bulk density is 2.67 g m −3 [32,33], the rotational period is 5.27025547 h [32] and the moment of inertia is 17.09×71.79×74.49 km 2 [33]. The modeling of 433 Eros employed 99846 vertices and 196608 faces [31].…”

Gravity field and solar component of the precession rate and nutation coefficients of Comet 67P/Churyumov–Gerasimenko

“…The general theoretical framework to model the rotation of a given celestial body as the comet 67P has been constructed by Kinoshita (1977). Starting from this framework Petit et al (2014) have proposed formulae, valid up to order 4 in e, for the precession rate ψ, the nutation of the longitude of the node ∆ψ, and the oscillations of the obliquity ∆ε. These formulae were successfully applied on celestial bodies with well defined physical constraints, as (1) Ceres, (4) Vesta, (433) Eros, (2867) Steins and (25143) Itokawa.…”

“…At this point, we provide the general formula for the precession rate up to order 16 in e, while we only summarize the formulae for ∆ψ, ∆ε up to 4th order in e (but still use 16th order formulae in our calculations). The precession rate up to order 16, according to Petit et al (2014), is given by: where the constant K together with its possible ranges during one orbital period of the comet is given by…”

“…A statistical analysis of the obliquities, precession rates, and nutation coefficients for a set of 100 asteroids has been performed by Lhotka et al (2013). Moreover the determination of these fundamental rotational parameters for 5 asteroids, that have been targets for past space missions, has been done by Petit et al (2014). These studies are based on a theory of rigid body dynamics constructed by Kinoshita (1977) and were implemented for an asteroid in the case of Eros in Souchay et al (2003); Souchay & Bouquillon (2005).…”