Small Planetary Satellites Research Articles

Orientation of Figures of Small Planetary Satellites During Chaotic Rotation

The effect of the preferred orientation of the largest axis of the satellite’s figure toward the planet during chaotic rotation is considered by means of numerical experiments. It has been found that the effect is most noticeable in the chaotic dynamics of small satellites with an orbital eccentricity e ≤ 0.005; this may impede the identification of the chaotic rotation of the satellite if the observation series is not sufficiently long. It is shown that the effect is present in the possible chaotic rotational dynamics of 30% of the known small satellites of the planets of the Solar System.

Identification of new orbits to enable future mission opportunities for the human exploration of the Martian moon Phobos

One of the paramount stepping stones towards NASA׳s long-term goal of undertaking human missions to Mars is the exploration of the Martian moons. Since a precursor mission to Phobos would be easier than landing on Mars itself, NASA is targeting this moon for future exploration, and ESA has also announced Phootprint as a candidate Phobos sample-and-return mission. Orbital dynamics around small planetary satellites are particularly complex because many strong perturbations are involved, and the classical circular restricted three-body problem (R3BP) does not provide an accurate approximation to describe the system׳s dynamics. Phobos is a special case, since the combination of a small mass-ratio and length-scale means that the sphere-of-influence of the moon moves very close to its surface. Thus, an accurate nonlinear model of a spacecraft׳s motion in the vicinity of this moon must consider the additional perturbations due to the orbital eccentricity and the complete gravity field of Phobos, which is far from a spherical-shaped body, and it is incorporated into an elliptic R3BP using the gravity harmonics series-expansion (ER3BP-GH). In this paper, a showcase of various classes of non-keplerian orbits is identified and a number of potential mission applications in the Mars–Phobos system are proposed: these results could be exploited in upcoming unmanned missions targeting the exploration of this Martian moon. These applications include: low-thrust hovering and orbits around Phobos for close-range observations; the dynamical substitutes of periodic and quasi-periodic Libration Point Orbits in the ER3BP-GH to enable unique low-cost operations for space missions in the proximity of Phobos; their manifold structure for high-performance landing/take-off maneuvers to and from Phobos’ surface and for transfers from and to Martian orbits; Quasi-Satellite Orbits for long-period station-keeping and maintenance. In particular, these orbits could exploit Phobos’ occulting bulk and shadowing wake as a passive radiation shield during future manned flights to Mars to reduce human exposure to radiation, and the latter orbits can be used as an orbital garage, requiring no orbital maintenance, where a spacecraft could make planned pit-stops during a round-trip mission to Mars.

Conditions for appearance of strange attractors in rotational dynamics of small planetary satellites

The conditions for the origination of strange attractors in the rotational dynamics of small planetary satellites when they reach a neighborhood of a synchronous resonance separatrix in the course of tidal evolution of the rotary motion are investigated by means of numerical experiments. It is assumed that a satellite has an arbitrary shape and moves along a fixed orbit in the gravitational field of a point-like mass; its rotational axis is orthogonal to the orbit plane. By calculating Lyapunov exponents, the regions of the values of problem parameters have been found where a strange attractor exists. The possibility of the appearance strange attractor in the rotational dynamics of real small planetary satellites is considered.

Survey of Spacecraft Trajectory Design in Strongly Perturbed Environments

A S KEPLER pointed out centuries ago, the motion of a spacecraft governed by a gravitating point mass is a wellbehaved conic section. In the low-energy regime, the conic section transcribes an ellipse and the motion is periodic and stable. Furthermore, the gravitational potential of a spherical mass with radially symmetric density is identical to that of a simple point mass located at the center of the sphere. Despite the fact that many perturbations are important when considering high-precision Earthorbiting applications, all perturbations combined are generally less than one part in a thousand compared with the dominant two-body term due to a spherical Earth. Therefore, the motion of a low-Earthorbiting ballistic spacecraft is very near periodic, and changes to the qualitative motion are slowly time-varying. For these reasons, the near-Earth environment indeed can be considered dynamically benign when compared with a great number of other locations of interest for space missions in our solar system. For the purposes of this paper, we will therefore consider strongly perturbed environments as those exotic locales beyond the near-Earth environment where perturbations to the Kepler two-body problem are no longer small. Notable examples of space missions in such highly perturbed dynamical environments include lunar missions; grand tours of the solar system and planetary satellite systems propelled by gravityassisted flybys; orbiters around major planetary satellites such as Jupiter’s Galilean moons and Saturn’s Titan and Enceladus; and missions to very small and irregular-shaped bodies such as comets, asteroids, and small planetary satellites. Drawing from common models such as patched conics of interplanetary missions and the restricted three-body problem (RTBP) of the libration point missions, this paper is organized in terms of the dominant perturbation forces on a spacecraft. The focus of this survey includes the wide-reaching perturbations that permeate globally the spacecraft environment over the course of a mission. Included are the third-body (TB) nonspherical gravity (NSG) and solar radiation pressure (SRP) perturbations. In their simplified forms, each of the main perturbations can be expressed as part of an autonomous and conservative dynamical system. Therefore, the ensuing analyses can benefit from a host of tools and insights including integrals of motion and system averaging that assist fast numerical methods and the recovery of equilibria and secular trends. Mission destinations of interest to the space science and space flight communities are discussed according to their respective dynamic environments. Special attention is given to orbit mechanics and its impact on mission and trajectory design techniques in the context of past and planned space missions to these dynamically rich environments. Mission classes and design techniques considered include lowand high-altitude orbiters, grand tour trajectories, patched conics, gravity-assistedflybys, Tisserand graphs, three-body models, periodic orbits, orbit averaging, and stable/unstable manifold design. A main result of this survey is a mission design reference (see Table 1 and the associated Fig. 1) that quantifies the absolute and relative importance of the main perturbations terms in the dynamic environments of many target bodies. It is acknowledged that atmospheric drag can induce extreme spacecraft heating and torques in the case of aerobraking, aerocapture, or entry decent and landing for missions to bodies with significant atmospheres such as Earth, Mars, Venus, or Titan. However, such extreme drag-related events are generally restricted to brief mission phases and can often be treated as nonpropellant propulsion (energy reducing) sources in the overall mission trajectory design. Therefore, atmospheric drag is not included in the scope of the paper. Finally, in the context of asteroids and comets, it is worth noting that small forces such as the Yarkovski and Yarkovsky–O’Keefe–Radzievskii– Paddacky (YORP) effects (arising mainly from imbalanced thermal radiation) and outgassing are important in the consideration of longterm small body orbital and spin rate evolution [1]. However, their indirect perturbations on the short-term dynamics of a nearby spacecraft are too small to warrant consideration in the current scope. For further information on the details and relative importance of dynamical perturbations on spacecraft in both the Earth and interplanetary environments, see [2–4].

How do the small planetary satellites rotate?

AbstractWe investigate the problem of the typical rotation states of the small planetary satellites from the viewpoint of the dynamical stability of their rotation. We show that the majority of the discovered satellites with unknown rotation periods cannot rotate synchronously, because no stable synchronous 1:1 spin-orbit state exists for them. They rotate either much faster than synchronously (those tidally unevolved) or, what is much less probable, chaotically (tidally evolved objects or captured slow rotators).

Secular Perturbations near Mean Motion Resonances

In this work we attempt to make progress into assessing the importance of secular interactions between planetary satellites. In recent years, discrepancies have been observed in the expected positions of small planetary satellites (Bosh & Rivkin, 1996; Roddier et al., 1998). The existing ephemerides-producing algorithms for these objects assume fixed, elliptical and inclined orbits whose rate of precession is determined by oblateness alone. Even though the masses of these satellites are quite small relative to the planet (∼ 10−9 – 10−10) their small mutual separations and the existence of much larger satellites further out leaves open the possibility that in some cases at least the fixed-orbit assumption is only a crude approximation to reality. Two important dynamical mechanisms through which these orbits may evolve are resonant or secular interactions. In order to explore the possibility of the latter we have set up a simple planar system where an satellite in a circular orbit around a spherical planet is perturbing a massless particle which moves in proximity to various mean motion resonances. We aim to examine the effect of the resonance on the particle’s reference orbit by measuring the secular frequency. The effects of oblateness have not been taken into account as they are adequately modeled by orbit-fitting theories and can thus be readily subtracted.

The gravitational potential of a homogeneous polyhedron or don't cut corners

A polyhedron can model irregularly shaped objects such as asteroids, comet nuclei, and small planetary satellites. With minor effort, such a model can incorporate important surface features such as large craters. Here we develop closed-form expressions for the exterior gravitational potential and acceleration components due to a constant-density polyhedron. An equipotential surface of Phobos is illustrated.

A General Formulation for the Distribution of Impacts and Ejecta from Small Planetary Satellites

Small planetary satellites and ring moons are the source of dust rings around each of the giant planets, and presumably Mars, by cratering impacts from interplanetary material. The relative velocities of planetary satellites and interplanetary impactors lead to an anisotropic flux of impactors onto planetary satellites. The anistropy in the impactor flux seen from the frame of the satellite results in an anisotropic production of dust from the surface of the satellite. This anisotropy can have observable consequences for the distribution of material in dust rings. In this paper, an expression for the angular distribution of meteoroid ejecta from impacts onto a single moon or ring particle orbiting a planet with arbitrary obliquity is derived. I allow for any distribution of orbits of the impactors by using a Monte Carlo approach for the micrometeoroid orbits. Ejecta distributions are prograde due to the enhanced impact velocity on the leading face of the target. Ejecta orbits are therefore concentrated in the region exterior to the source satellite. Orbitally averaged ejecta distributions are weakly dependent on the planetary obliquity. Ejecta distributions vary with orbital season for planets with a significant obliquity. The orbitally averaged ejecta distribution is weakly dependent on the orbital distribution of the impactor population, largely due to the smearing effect of the assumed ejects "phase function." The impact velocity of micrometeoroids in the frame of the satellite is correlated with the orbital element distribution of the micrometeoroid population, allowing the orbital elements of interplanetary dust to be inferred from dust impact experiments, such as those on Galileo and Cassini. Dust rings derived from micrometeoroid ejecta from small planetary satellites may show seasonal variations in the vertical distribution of dust as the planet orbits the Sun.

The Dust Torus around Phobos Orbit

Impact ejecta from the surfaces of some small planetary satellites (such as martian moon Phobos) should give rise to dust belts surrounding the satellites' orbits. The mechanism of dust belt formation is, principally, as follows. A satellite is subjected to impacts of meteoroids with encounter velocities of about 10 km sec.-1. The total mass of the ejecta is 3 to 4 orders of magnitude greater than the mass of a projectile. A great number of excavated particles is thrown to planetocentric trajectories close to the satellite orbit. This results in the generation of a dust toroid with an axial line coinciding with the orbit of the parent body. Simultaneously the grains are removed from the torus by the satellite. For not very small grains, their removal by the satellite is the major loss mechanism, so that the matter injection into the torus and the reaccretion come to a dynamical equilibrium at the increased density level.We study this mechanism in detail, construct the general model of a dust torus, and apply it to the Phobos case as the most typical and important in view of the martian space missions planned for the near future. Postulating a stationary meteoroidal flux to the Phobos surface and assuming the most probable regolith properties and impact parameters, we specify the model and, performing semianalitical evaluations, come to the following conclusions. The total mass of the Phobos dust belt is several times 104 kg. The lifetime of a particle inside the torus should be about 1 year. The matter density reaches a maximal value at the Phobos orbit, being 106 to 107 times the background density of the interplanetary medium. The geometry of the equidensity curves in the meridional section of the torus is investigated. All estimations are probably within one order of magnitude accuracy due to the physical data uncertainties and errors of the simulation.Our results are valid for macroscopic particles, greater than about 100 μm in size. The fine-dust component of the belt, affected strongly by radiative forces and charging, should be the subject of a separate study.Ways of refining the model and directions of further investigation are discussed.