Orbital Perturbation Analysis Near Binary Asteroid Systems

Icarus, 2021

We obtained thorough photometric observations of two binary near-Earth asteroids (66391) Moshup = 1999 KW4 and (88710) 2001 SL9 taken from 2000 to 2019. We modeled the data and derived physical and dynamical properties of the binary systems. For (66391) 1999 KW4, we derived its mutual orbit's pole, semimajor axis and eccentricity that are in agreement with radar-derived values (Ostro et al. [2006]. Science, 314, 1276-1280). However, we found that the data are inconsistent with a constant orbital period and we obtained unique solution with a quadratic drift of the mean anomaly of the satellite of 0✿65 ✝ 0✿16 deg/yr 2 (all quoted uncertainties correspond to 3✛). This means that the semimajor axis of the mutual orbit of the components of this binary system, determined ❛ = 2✿548 ✝ 0✿015 km by Ostro et al. (2006), increases in time with a mean rate of 1✿2 ✝ 0✿3 cm/yr. For (88710) 2001 SL9, we determined that the mutual orbit has a pole within 10 ✍ of (▲❀ ❇) = (302 ✍ ❀ 73 ✍) (ecliptic coordinates), and is close to circular (eccentricity ❁ 0✿07). The data for this system are also inconsistent with a constant orbital period and we obtained two solutions for the quadratic drift of the mean anomaly: 2✿8 ✝0✿2 and 5✿2 ✝ 0✿2 deg/yr 2 , implying that the semimajor axis of the mutual orbit of the components (estimated ❛ ✘ 1✿6 km) decreases in time with a mean rate of 2✿8✝0✿2 or 5✿1 ✝ 0✿2 cm/yr for the two solutions, respectively. The expanding orbit of (66391) 1999 KW4 may be explained by mutual tides interplaying with binary YORP (BYORP) effect (McMahon, J., Scheeres, D. [2010]. Icarus 209, 494-509). However, a modeling of the BYORP drift using radar-derived shapes of the binary components predicted a much higher value of the orbital drift than the observed one. It suggests that either the radar-derived shape model of the secondary is inadequate for computing the BYORP effect, or the present theory of BYORP overestimates it. It is possible that the BYORP coefficient has instead an opposite sign than predicted; in that case, the system may be moving into an equilibrium between the BYORP and the tides. In the case of (88710) 2001 SL9, the BYORP effect is the only known physical mechanism that can cause the inward drift of its mutual orbit. Together with the binary (175706) 1996 FG3 which has a mean anomaly drift consistent with zero, implying a stable equilibrium between the BYORP effect and mutual body tides (Scheirich et al. [2015]. Icarus 245, 56-63), we now have three distinct cases of well observed binary asteroid systems with their long-term dynamical models inferred. They indicate a presence of all the three states of the mutual orbit evolution-equilibrium, expanding and contracting-in the population of near-Earth binary asteroids.

Journal of Physics: Conference Series, 2010

In this work we studied the stable regions around four binary asteroids in the main asteroid belt. The studied systems were (107) Camilla, (22) Kallipe, (45) Eugenia and (762) Pulcova. The stability was characterized with three motion indicators: relative Lyapunov indicator, maximum eccentricity, and maximum difference of eccentricities. The survay covered the P type orbits, where satellite moves around both primaries. On the basis of our work it can be decided, in which system the discovery of a third component can be expected.

One of the most important aspects when dealing with a Potentially Hazardous Object (PHO) is the accurate determination of its dynamical state. In particular, the determination of orbital and rotational perturbations is important to propagate accurately the heliocentric orbital path of an asteroid or a comet, and to be more precise in the impact risk determination and related uncertainty containment. The paper discusses the analysis and study of the motion of an irregularly-shaped celestial body, with particular attention to its complex three-dimensional rotational dynamics: the rotation state, nutation and precession motions are considered while modelling. All perturbations , relevant to the case of study, are included in the dynamical model, from the classical to the more complex, such as the Solar Radiation Pressure (SRP), the third body gravitational effect (presence of the Sun), the YORP effect and the internal dis-sipation of energy. In addition, particular attention has been paid to accurately model the shape of the asteroid: simple spherical models demonstrated to possess low accuracy when the asteroid or the comet is not spherically shaped. Irregular shapes represent, indeed, one of the most important aspects to compute the disturbances affecting the dynamics of these objects. The study has been performed by considering different characteristic shapes for typical irregular bodies: from the quasi-spherical, to the dog-bone and the elongated shapes. The perturbations due to external sources are modelled numerically. The sources of disturbances are then ranked and different criteria to propagate rotational motion have been derived depending on the shape of the observed asteroid. Even if the simulation results have been verified on selected asteroids dynamics, the presented methods and approach apply to the dynamical propagation of any kind of asteroid or comet.

The study of the dynamical environment near an asteroid pair has become an extremely relevant topic to design trajectories for future missions design. This study analyzes the dynamical environment in the proximity of a binary asteroid system and develops some useful tools to design trajectories about the asteroid couple, exploiting convenient dynamical properties of three-body systems. The interaction between two different three-body systems is analyzed and a convenient dynamical environment is defined in the vicinity of the asteroid pair by introducing the concept of Surface Of Equivalence (SOE). A possible trajectory design method is shown, using invariant manifolds associated to the Circular Restricted Three-Body Problem and multi-dimensional Poincaré maps. An example of a suitable trajectory for the lift-off/landing of a spacecraft from the primary asteroid is finally shown.

Proceedings of the International Astronomical Union

We apply Kholshevnikov metrics defined in the space of Keplerian orbits to search for asteroids in close orbits. We showed that the Yarkovsky effect was required to take into account accurately to carry out precise simulation of dynamical evolution of the asteroid pairs. Determination of physical and rotational parameters of asteroids is needed to solve this problem.

The paper discusses the analysis and the study of the motion around irregular celestial bodies, with particular attention to the representation of their gravitational influence and the characterization of their complex non-principal axis rotational dynamics. The study has been performed considering different characteristic shapes for typical NEO asteroids: from the simple, almost spherical, to more complex shapes, such as the dog-bone and the elongated ones. The gravitational attraction of these irregular objects has been modeled, through accurate shape discretization, with a constant density polyhedron or an ensemble of point masses. All perturbations, relevant to the case of study, are included in the model, such as the Solar Radiation Pressure (SRP) and the third body gravitational effect (presence of the Sun).

Bulletin of the American Astronomical Society, 2001

The dynamical problem of a binary asteroid system is posed and its stability discussed. In the general binary asteroid problem we consider the motion of two bodies of arbitrary mass distribution as they move relative to each other. Basic results from the classical n-body problem can still apply to such a system and some basic concepts continue to hold. Specifically, the total energy of the system, now including both rotational and translational energy, controls whether the system may ultimately disrupt under its own interactions. Whether or not an excess of positive energy (contained for example in the rotational motion of an asteroid) can be transferred to a positive excess of energy in the translational motion depends on the amount of spin-orbit coupling that can occur between the bodies. Some methods for estimating the amount of energy and angular momentum transfer between rotational and translational motions are introduced. These methods can be used to develop constraints on the long-term stability of a binary asteroid system. This research was funded by a grant from NASA's Office of Space Science, Planetary Geology and Geophysics Program.

Icarus, 2008

Near-Earth Asteroid (66391) 1999 KW4 was the subject of the recently published first extensive radar imaging, shape and mutual orbit modeling, and physical and dynamical characterization of a binary asteroid. In this paper we present in detail our numerical simulation of KW4 behind that work. Our propagations of the system with some variation in estimated parameters cover the set of KW4's possible current dynamical states consistent with the body models and other information obtained directly from the observations. We also apply our implementation of this simulation capability to address some of the dynamical mechanisms by which KW4 may be moved into the more energetically excited of those possible current states, particularly solar gravity interaction. Through comparison of the results with certain features of the observation data, we conclude that the actual KW4 system is not in the most energetically relaxed configuration but must be moderately excited. The system occupies a generalized Cassini state 2 which is different from that considered in most previously published treatments of Cassini states in that it involves co-precession of the primary's spin frame and the mutual orbit rather than co-precession of a satellite's spin frame and that satellite's orbit about the primary. We present a simple analytical theory describing the system's dynamics, which should be applicable to any other binary systems, of which KW4 is representative, in which a massive, roughly oblate primary is spinning rapidly relative to the rate of its mutual orbit with an on-average synchronous, elongated secondary. We examine separately both the effect of the larger binary component's oblateness, and the effect of the smaller component's roughly triaxial ellipsoid shape. The simple analytical formulae obtained agree with full-detail numerical simulation results, and can be used for remote estimation of binary mass properties from observed system motion.

Celestial Mechanics and Dynamical Astronomy, 2016

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Dynamical Systems, 2005

The purpose of this paper is to describe the general setting for the application of techniques from geometric mechanics and dynamical systems to the problem of asteroid pairs. It also gives some preliminary results on transport calculations and the associated problem of calculating binary asteroid escape rates. The dynamics of an asteroid pair, consisting of two irregularly shaped asteroids interacting through their gravitational potential is an example of a full body problem or FBP in which two or more extended bodies interact. One of the interesting features of the binary asteroid problem is that there is coupling between their translational and rotational degrees of freedom. General FBPs have a wide range of other interesting aspects as well, including the 6-DOF guidance, control, and dynamics of vehicles, the dynamics of interacting or ionizing molecules, the evolution of small body, planetary, or stellar systems, and almost any other problem where distributed bodies interact with each other or with an external field. This paper focuses on the specific case of asteroid pairs using techniques that are generally applicable to many other FBPs. This particular full 2-body problem (F2BP) concerns the dynamical evolution of two rigid bodies mutually interacting via a gravitational field. Motivation comes from planetary science, where these interactions play a key role in the evolution of asteroid rotation states and binary asteroid systems. The techniques that are applied to this problem fall into two main categories. The first is the use of geometric mechanics to obtain a description of the reduced phase space, which opens the door to a number of powerful techniques such as the energy-momentum method for determining the stability of equilibria and the use of variational integrators for greater accuracy in simulation. Secondly, techniques from computational dynamical systems are used to determine phase space structures important for transport phenomena and dynamical evolution.