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Astron. Astrophys. 356, 747-756 (2000)

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1. Introduction

In recent years the scientific community has focused on the study of small solar system bodies, due to the information that they contain about the formation and evolution of the solar system. After an initial phase characterized by flybys to comets and asteroids by major planetary missions (Galileo, CASSINI) or by dedicated missions (GIOTTO, Sakigate & Suisei, Vega1 & 2), a series of rendezvous-missions are being planned to allow extended and detailed exploration of these bodies. NEAR, ROSETTA and MUSES-C will orbit for several months around a comet or asteroid to study in detail their morphology, physical properties and evolution with time. When a spacecraft is in close proximity to such a small body it is exposed to the risk of being hit by particles trapped in long-lifetime orbits around the body. Small particles (on the order of millimeters to centimeters) can be injected into temporary capture orbits after cratering impacts or intense cometary outgassing, since in this size range the solar radiation pressure significantly influences the dynamical evolution of the particles and may transition them into orbits with lifetimes on the order of hundreds of days or longer.

Small energy cratering events, capable of lofting a significant amount of ejecta off of a small body, occur frequently on asteroids and could also occur on comets that spend a significant amount of their orbit in the main belt, like comet Wirtanen, the target of the ROSETTA mission. Outgassing phenomena on a comet surface during a perihelion passage can also eject large amounts of dust from the surface that can be trapped in temporary orbits, forming a cloud surrounding the nucleus of the comet.

An interesting experiment that will simulate an impact event on the surface of a comet is represented by the Deep Impact experiment (Meech et al. 1999). The Deep Impact (DI) Discovery mission is designed to release a 500 kg impactor that will collide with comet Tempel 1 at a relative speed of about 10 km/s. This experiment, intended to probe the material strength of the comet and to reveal the inner composition of the nucleus, mimics a natural cratering event on the surface of the comet. Ejecta from such a cratering event may re-impact on the surface of the nucleus, escape on hyperbolic orbits, or be trapped in temporary orbits around the nucleus. Images taken after the impact may allow initial orbit parameters of crater fragments to be determined, leading to a model of the subsequent dynamical evolution of the ejecta blankets.

Numerical calculations of simulated ejecta blankets from impacts on the asteroid Ida have been performed by Geissler et al. (1996) via direct numerical integration of the equations of motion. However, their study is limited to the effects of non-sphericity and rotation of the asteroid on the trajectory of particles launched from an impact site. In this paper we consider ejecta with diameters on the order of centimeters and smaller. In this size range the solar radiation pressure force is, by far, the leading perturbing force. Richter & Keller (1995) re-derived an analytic closed form solution (denoted as RPA) to the equations of motion for a dust particle moving around a spherical body (in an eccentric orbit around the sun) and perturbed by the radiation pressure (see Mignard & Hénon 1984 for an earlier discussion of this solution). This solution predicts the evolution of the orbital elements of a dust particle and can be used to estimate the time spent orbiting around the comet before re-impact on the comet surface occurs.

Since we are dealing with dust ejected on nearly rectilinear orbits with very large eccentricity, we first tested the RPA solution against the numerical solution in this range of eccentricity. Once we define the limits of applicability for the RPA approximation, we analytically derive the conditions for dust particles to become trapped in orbit about the comet (or asteroid) and the lifetime of these orbits as a function of ejection speed and particle size. We show that the lifetime of the dust particles depends strongly on their size and on the ejection velocity. The maximum particle size which can be trapped into orbit around the comet can be computed as a function of ejection site, particle size, and ejection speed.

One limitation of our approach for computing ejecta orbits is that the RPA solution does not include all the possible perturbations to the dynamics of a dust particle. When close to the comet surface, the particle orbit may deviate significantly from the RPA solution due to gravity and outgassing, while far from the comet the solar tide may strongly perturb the solution. Thus, we also discuss the possible effects of these perturbations to first order. Future analysis of this problem will improve the characterization of these effects and include them into one general model.

Since we cannot analyse all the possible configurations of cratering events on asteroids or comets, we concentrate our study on the DI experiment. Both the analytical predictions and numerical simulations are assumed to have similar initial conditions to the DI experiment.

In Sect. 2 we discuss the basic mechanics of how the solar radiation pressure (SRP) force can cause particles to become captured. In Sect. 3 we discuss the effect of the averaging approximation and other perturbations on these mechanics. In Sect. 4 we apply our model to the Deep Impact crater experiment to compute global conditions for particle trapping. Finally, in Sect. 5 we discuss the results and give conclusions.

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© European Southern Observatory (ESO) 2000

Online publication: April 10, 2000
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