Secular perturbations of asteroids in secular resonance

When the precessional rate of the orbital plane of an asteroid is nearly equal to that of Jupiter, the orbital inclination of the asteroid changes quite largely due to this near equality of their precessional rates, which is called a secular resonance. In the vicinity of the exact resonance the difference of their longitudes of nodes librates with quite a long period of order of 1×10⁶ yr. In this paper we treat this secular resonance by a method of semianalytical secular perturbations with use of numerical averaging for both non-resonant and resonant asteroids and show that the results by the semi-analytical treatment agrees qualitatively with those obtained by direct numerical integrations of asteroid's orbits.     

Secular spin dynamics of inner main-belt asteroids

Understanding the evolution of asteroid spin states is challenging work, in part because asteroids have a variety of orbits, shapes, spin states, and collisional histories but also because they are strongly influenced by gravitational and non-gravitational (YORP) torques. Using efficient numerical models designed to investigate asteroid orbit and spin dynamics, we study here how several individual asteroids have had their spin states modified over time in response to these torques (i.e., 951 Gaspra, 60 Echo, 32 Pomona, 230 Athamantis, 105 Artemis). These test cases which sample semimajor axis and inclination space in the inner main belt, were chosen as probes into the large parameter space described above. The ultimate goal is to use these data to statistically characterize how all asteroids in the main belt population have reached their present-day spin states. We found that the spin dynamics of prograde-rotating asteroids in the inner main belt is generally less regular than that of the retrograde-rotating ones because of numerous overlapping secular spin-orbit resonances. These resonances strongly affect the spin histories of all bodies, while those of small asteroids (?40 km) are additionally influenced by YORP torques. In most cases, gravitational and non-gravitational torques cause asteroid spin axis orientations to vary widely over short (?1 My) timescales. Our results show that (951) Gaspra has a highly chaotic rotation state induced by an overlap of the s and s₆ spin-orbit resonances. This hinders our ability to investigate its past evolution and infer whether thermal torques have acted on Gaspra's spin axis since its origin.     

Long periodic perturbations of Trojan asteroids

The motion of the Trojan asteroids is studied in the elliptic restricted three-body problem of the Sun-Jupiter-asteroid system. Long periodic perturbations of the orbital elements are discussed. Relations between dynamical parameters are considered and comparisons are made with Bien's and Schubart's results.     

Secular perturbations in general planetary theory

Based on a general planetary theory, the secular perturbations in the motion of the eight major planets (excluding Pluto) have been derived in polynomial form. The results are presented in the tables. The linear terms of second order with respect to the planetary masses and the nonlinear terms of first order up to the fifth (and partly seventh) degree with respect to eccentricities and inclinations were taken into account in the right-hand members of the secular system. Calculations were carried out by computer with the use of a system that performed analytic operations on power series with complex coefficients.

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Secular perturbations of fictitious satellites of uranus

Secular perturbations of fictitious satellites that are initially circular and in the equatorial plane of Uranus are discussed. Satellites located in the region where the solar perturbation is dominant become highly eccentric and inclined with respect to the equator, and have a possibility to collide with Uranus. Satellites located in the region where the oblateness perturbation is dominant keep the original eccentricity and the inclination. A scenario of a possible extinction of outer satellites of Uranus is also discussed.     

Secular resonances and the origin of eccentricities of Mars and the asteroids

A mechanism is treated for the origin of the eccentricities of the asteroids and of Mars: secular resonances associated with the dissipation of a primitive solar nebula. The nebula is modeled as a two-dimensional disk; a closed-form, convergent integral is derived to represent its disturbing function. Dissipation of this nebula gives rise to “excitation waves”, produced by the variable location of the secular resonances, which can excite the eccentricity of Mars, and scatter asteroidal eccentricities through the observed ranges. By requiring that these ranges match the observed values as a functions of semimajor axis, one infers: (a) the primordial eccentricities of Jupiter and Saturn initially had amplitudes different from present-day values, but these amplitudes approached the present values toward the end of nebular dissipation; (b) the nebular dissipation time scale may have been of the order of (few) × 10⁴ years as the dissipation neared completion (but this depends on the validity of linear equations which model the inherently nonlinear asteroidal eccentricity pumping); (c) it is reasonable to propose a common origin for the eccentricies of Mars and the asteroids. A simple extension of the model also accounts for the quasi-Gaussian distribution of the number density of asteroidal eccentricities.     

Numerical investigation of motions of resonant asteroids in the three-dimensional space

Motions of asteroids in mean motion resonances with Jupiter are studied in three-dimensional space. Orbital changes of fictitious asteroids in the Kirkwood gaps are calculated by numerical integrations for 10⁵ – 10⁶ years. The main results are as follows: (1) There are various motions of resonant asteroids, and some of them are very complicated and chaotic and others are regular. (2) The eccentricity of some asteroids becomes very large, and the variation of the inclination is large while the eccentricity is large. (3) In the 3:1 resonance, there is a long periodic change in the variation of the inclination, when (7 : ) is a simple ratio (7: longitude of perihelion, : longitude of node). (4) In the 7:3 resonance, the variation of the inclination of some resonant asteroids is so large that prograde motion becomes retrograde. Some asteroids in the 7:3 resonance can collide with the Sun as well as with the inner planets.     

Application of the Brown-Shook model to the Kirkwood gaps and resonant asteroids

The mathematical model developed by Brown and Shook is used to explain the absence of asteroids in the Kirkwood gaps as well as the existence of some resonant asteroids with orbital periods commensurable to that of Jupiter. In addition, this model can possibly explain the biased number distributions at the commensurable positions of both resonant gaps and clusters. However, this resonant model is probably not applicable to the Saturnian ring system due to the possible cosmogonic plasma process during its formation.     

The resonant structure of Jupiter's Trojan asteroids – I. Long-term stability and diffusion

We study the global dynamics of the jovian Trojan asteroids by means of the frequency map analysis. We find and classify the main resonant structures that serve as skeleton of the phase space near the Lagrangian points. These resonances organize and control the long-term dynamics of the Trojans. Besides the secondary and secular resonances, that have already been found in other asteroid sets in mean motion resonance (e.g. main belt, Kuiper belt), we identify a new type of resonance that involves secular frequencies and the frequency of the great inequality, but not the libration frequency. Moreover, this new family of resonances plays an important role in the slow transport mechanism that drives Trojans from the inner stable region to eventual ejections. Finally, we relate this global view of the dynamics with the observed Trojans, identify the asteroids that are close to these resonances and study their long-term behaviour.     

Numerical investigation on the orbital evolution of 1:2 resonant asteroids between Jupiter and Saturn

According to some investigations (Lecar and Franklin, 1973; Franklin et al., 1989; Soper et al., 1990) asteroids cannot remain for along time between Jupiter and Saturn. But as it is well known there is a near 5:2 commensurability between Jupiter and Saturn. So there might be a possibility that asteroids between Jupiter and Saturn could be trapped in a resonant relation.In order to investigate this possibility, the changes of orbital elements of an asteroid whose initial value of semi-major axis corresponds to that of a 1:2 resonant orbit were investigated by means of a double precision Cowell method. The integration routine was kindly supplied by Dr Yoshikawa.We considered first a planar restricted problem of three bodies, Sun-Jupiter-Asteroid, then a four body problem, Sun-Jupiter-Asteroid-Saturn. When integrating the equations of motion, short periodic terms were not eliminated and in the second test the interactions between Jupiter and Saturn were retained. Whether a close approach occured or not was not investigated. In every case a _j = 5.20, a _s = 9.54 and a = 8.26 were adopted as initial values of the semi-major axis of Jupiter, Saturn and Asteroid respectively.     

Photometry of asteroids

Photometry is one of the most efficient investigation techniques. It provided a large body of data on albedos, sizes, shapes, rotation, optical properties, and structural characteristics of asteroids and other minor bodies of the solar system. The contribution of photometry to the determination of asteroid parameters was most crucial. This review summarizes main results of asteroid studies in three most important areas: i) determination of the shape and rotation parameters of asteroids, ii) investigation of optical properties of asteroid surfaces, and iii) detection and investigation of binary asteroid systems.     

Near-Sun asteroids

As follows from dynamical studies, in the course of evolution, most near-Earth objects reach orbits with small perihelion distances. Changes of the asteroids in the vicinity of the Sun should play a key role in forming the physical properties, size distribution, and dynamical features of the near-Earth objects. Only seven of the discovered asteroids are currently moving along orbits with perihelion distances q < 0.1 AU. However, due to the Kozai–Lidov secular perturbations, the asteroids, having recently passed near the Sun, could by now have moved to orbits farther from the Sun. In this study, we found asteroids that have been recently orbiting with perihelion distances q < 0.1 AU. Asteroids may be on such orbits for hundreds to tens of thousands of years. To carry out astrophysical observations of such objects is a high priority.     

Tumbling asteroids

We present both a review of earlier data and new results on non-principal axis rotators (tumblers) among asteroids. Among new tumblers found, the best data we have are for 2002 TD₆₀, 2000 WL₁₀₇, and (54789) 2001 MZ₇—each of them shows a lightcurve with two frequencies (full terms with linear combinations of the two frequencies are present in the lightcurve). For 2002 TD₆₀, we have constructed a physical model of the NPA rotation. Other recent objects which have been found to be likely tumblers based on their lightcurves that do not fit with a single periodicity are 2002 NY₄₀, (16067) 1999 RH₂₇, and (5645) 1990 SP. We have done a statistical analysis of the present sample of the population of NPA rotators. It appears that most asteroids larger than ∼0.4 km with estimated damping timescales (Harris, 1994, Icarus 107, 209) of 4.5 byr and longer are NPA rotators. The statistic of two short-period tumblers (D=0.04 and 0.4 km) with non-zero tensile strength suggests that for them the quantity μQ/T, where μ is the mechanical rigidity, Q is the elastic dissipation factor, and T is a spin excitation age (i.e., a time elapsed since the last significant spin excitation event), is greater by two to four orders of magnitude than the larger, likely rubble-pile tumblers. Among observational conditions and selection effects affecting detections of NPA rotations, there is a bias against detection of low-amplitude (small elongation) tumblers.     

Taxonomy of asteroids

A taxonomic system was introduced by C. R. Chapman, D. Morrison, and B. Zellner [Icarus25, 104–130 (1975)], in which minor planets are classified according to a few readily observable optical properties, independent of specific mineralogical interpretations. That taxonomy is here augmented to five classes, now precisely defined in terms of seven parameters obtained from polarimetry, spectrophotometry, radiometry, and UBV photometry of 523 objects. We classify 190 asteroids as type C, 141 as type S, 13 as type M, 3 as type E, and 3 as type R; 55 objects are shown to fall outside these five classes and are designated U (unclassifiable). For the remaining 118, the data exclude two or more types but are insufficient for unambiguous classification. Reliable diameters, from radiometry or polarimetry or else from albedos adopted as typical of the types, are listed for 396 objects. We also compare our taxonomy with other ones and discuss how classification efforts are related to the interpretation of asteroid mineralogies.     

The resonant structure of Jupiter's Trojan asteroids – II. What happens for different configurations of the planetary system

In a previous paper, we have found that the resonance structure of the present Jupiter Trojan swarms could be split up into four different families of resonances. Here, in a first step, we generalize these families in order to describe the resonances occurring in Trojan swarms embedded in a generic planetary system. The location of these families changes under a modification of the fundamental frequencies of the planets and we show how the resonant structure would evolve during a planetary migration. We present a general method, based on the knowledge of the fundamental frequencies of the planets and on those that can be reached by the Trojans, which makes it possible to predict and localize the main events arising in the swarms during migration. In particular, we show how the size and stability of the Trojan swarms are affected by the modification of the frequencies of the planets. Finally, we use this method to study the global dynamics of the Jovian Trojan swarms when Saturn migrates outwards. Besides the two resonances found by Morbidelli et al. which could have led to the capture of the current population just after the crossing of the 2:1 orbital resonance, we also point out several sequences of chaotic events that can influence the Trojan population.     

Express identification of asteroids

A technique for the fast identification of detected asteroids directly after terminating their observations on a short topocentric arch is briefly described.     

Stability of binary asteroids

The restricted problem of 2+2 bodies is applied to the study of the stability and dynamics of binary asteroids in the solar system. Numerical investigation of the behavior of the orbital elements and the maximal Lyapunov characteristic number of binary asteroids reveal extensive regions where bounded quasiperiodic motion is possible. These regions are compared to the bounded regions which are predicted by the classical restricted problem of three bodies. Regions of bounded chaotic solutions are also found.     

Transient co-orbital asteroids

We analyze the orbital behavior of four new co-orbital NEOs and the Earth horseshoe object 2002 AA29. The new objects are 2001 CK32, a 3753 Cruithne-like co-orbital of Venus, 2001 GO2 and 2003 YN107, two objects with motion similar to 2002 AA29. 2001 CK32 is on a compound orbit. The asteroid reverses its path when the mean longitude difference is −50°. Its motion is chaotic. 2001 GO2 is an Earth HS orbiter with repeated transitions to the QS phase, the next occurring 200 years from now. The HS libration period is 190 years and the QS phases last 45 years. For 2002 AA29, our simulations permit us to find useful theoretical insights into the HS-QS transitions. Its orbit can be simulated with adequate accuracy for 4400 years into the future and 1483 years into the past. The new co-orbital 2003 YN107 is at present an Earth QS. It has entered this phase in 1997 and will leave it again in 2006, completing one QS cycle. Like 2002 AA29, it has frequent transitions between HS and QS. One HS cycle takes 133 years.     

Physical study of asteroids: Ligthcurves and rotational periods of six asteroids

V band photoelectric lightcurves and rotational periods are presented for six asteroids: 150 Nuwa, 203 Pompeja, 336 Lacaderia, 545 Messalina, 984 Gretia, and 1240 Fantasia. Except for 984 Gretia, none of these asteroids has been previously observed. The observations were obtained during September 1983 at the Astrophysical Observatory of Catania and are part of a program devoted to increase the present data set of asteroids' rotational properties. For 336 Lacaderia and 984 Gretia the magnitude-phase relations, in terms ofQ_v and β_v, were also obtained.