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1.
A new theory for the calculation of proper elements, taking into account terms of degree four in the eccentricities and inclinations, and also terms of order two in the mass of Jupiter, has been derived and programmed in a self contained code. It has many advantages with respect to the previous ones. Being fully analytical, it defines an explicit algorithm applicable to any chosen set of orbits. Unlike first order theories, it takes into account the effect of shallow resonances upon the secular frequencies; this effect is quite substantial, e.g. for Themis. Short periodic effects are corrected for by a rigorous procedure. Unlike linear theories, it accounts for the effects of higher degree terms and can thus be applied to asteroids with low to moderate eccentricity and inclination; secular resonances resulting from the combination of up to four secular frequencies can be accounted for. The new theory is self checking : the proper elements being computed with an iterative algorithm, the behaviour of the iteration can be used to define a quality code. The amount of computation required for a single set of osculating elements, although not negligible, is such that the method can be systematically applied on long lists of osculating orbital elements, taken either from catalogues of observed objects or from the output of orbit computations. As a result, this theory has been used to derive proper elements for 4100 numbered asteroids, and to test the accuracy by means of numerical integrations. These results are discussed both from a quantitative point of view, to derive an a posteriori accuracy of the proper elements sets, and from a qualitative one, by comparison with the higher degree secular resonance theory.  相似文献   

2.
《Icarus》1986,68(1):55-76
The accuracy and reliability of the proper orbital elements used to define asteroid families are investigated by simulating numerically the dynamical evolution of families assumed to arise from the “explosion” of a parent object. The orbits of the simulated family asteroids have then been integrated in the frame of the elliptic restricted three-body problem Sun-Jupiter-asteroid, for times of the order of the circulation periods of perihelia and nodes. By filtering out short-periodic perturbations, we have monitored the behavior of the proper eccentricities and inclinations, computed according to the linear secular perturbation theory. Significant long-period variations have been found especially for families having nonnegligible eccentricities and/or inclinations (like the Eos family), and strong disturbances due to the proximity of mean motion commensurabilities with Jupiter have been evidenced (for instance, in the case of the Themis family). These phenomena can cause a significant “noise” on the proper eccentricities and inclinations, probably affecting in some cases the derived family memberships. They can also give rise to a spurious anisotropy in the fragment ejection velocity fields computed from the dispersion in proper elements observed in each family, and this could explain the puzzling anisotropies of this kind actually found in real families by D. Brouwer (1951, Astron. J. 56, 9–32) and by V. Zappalà, P. Farinella, Z. Knežević, and P. Paolicchi (1984), Icarus 59, 261–285).  相似文献   

3.
The analytical solution for the perturbations of an artificial satellite due to the zonal part of the geopotential is presented. The Hamiltonian is fully normalized up to the second order by a single averaging transformation and the generating function is given explicitly. The formulas allow an arbitrarily high degree of geopotential harmonics to be included. The transformation from mean to osculating variables or vice versa is performed by means of a numerical method proposed by the author in a previous paper (Breiter,1997): periodic perturbations are computed by means of a Runge-Kutta method of order 2 instead of being explicitly derived from a generator. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

4.
For the orbits with low to moderate inclination and eccentricity, in the asteroid main belt, the analytically computed proper elements are accurate to a level very close to the best result achievable by any analytical theory. This fundamental limitation results from the infinite web of resonances and because of the occurrence of chaotic motions. Still, there are some regions of the belt in which these proper elements are of degraded accuracy, thus preventing a reliable definition of asteroid families and detailed studies of the dynamical structure. We have used a different method to compute asteroid proper elements, following the approach introduced in the LONGSTOP project to describe the secular dynamics of the major outer planets. By applying purely numerical techniques, we produced so-called synthetic proper elements for a catalog of 10,256 asteroids with osculating semimajor axes between 2.5 and 4.0AU.The procedure consisted of simultaneous integration of asteroid and planetary orbits for 2Myr, with online filtering of the short-periodic perturbations. The output of the integration was spectrally resolved, and the principal harmonics (proper values) extracted from the time series. For each asteroid we have also tested the accuracy and stability in time of the proper elements, and estimated the maximum Lyapunov Characteristic Exponent to monitor the chaotic behaviors. This provided information on the reliability of the data for each orbit, in particular allowing to select 1,852 cases for an extended integration (10Myr) of the orbits showing instability. The results indicate that for more than half of the cases the proper elements have a time stability improved by more than a factor 3 with respect to the elements computed by the previous analytical theory. But of course there are also unstable cases for which the proper elements are less accurate and reliable, the extreme examples being 23 orbits exhibiting hyperbolic escape from the solar system. This form of escape from the asteroid belt could be responsible for a significant mass loss over the age of the solar system.  相似文献   

5.
P. Pravec  D. Vokrouhlický 《Icarus》2009,204(2):580-588
We have studied statistical significance of asteroid pairs residing on similar heliocentric orbits with distances (approximately the current relative encounter velocity between orbits) up to in the five-dimensional space of osculating elements. We found candidate pairs from the Hungaria zone through the entire main belt as well as outside the main belt, one among Hildas and one in the Cybele zone. We first determined probability that the candidate pairs are just coincidental couples from the background asteroid population. Those with estimated probability <0.3 were further investigated. In particular we computed synthetic proper elements for the relevant asteroids and used them to determine the three-dimensional distance of the members in candidate pairs. We consider small separation in the proper-element space as a signature of a real asteroid pair; conversely, cases with large separation in the proper-element space were rejected as spurious. Finally, we provide a list of candidate pairs that appear real, genetically related, to facilitate targeted studies, such as photometric and spectroscopic observations. As a by-product, we discovered six new compact clusters of three or more asteroids. Initial backward orbit integrations suggest that they are young families with ages <2 Myr.  相似文献   

6.
Abstract— Criteria for finding asteroid families (Zappala et al. 1995) are applied to a large (205,770 member) data set of asteroid orbital elements. The cases of the Eunomia and Themis families are considered as examples. This is combined with the cratering criteria for catastrophic disruption of small bodies in the solar system (Leliwa‐Kopystyński et al. 2008). We find that the Eunomia parent body itself was not catastrophically disrupted in the family‐generating impact event; after impact, the current body contains as much as 70% of its primordial mass. However, by contrast with Eunomia, the present mass of 24 Themis is only about 21% of that of its primordial body. Limits are placed on the sizes of the impactors in both examples, and for the case of Eunomia, the radius of the just sub‐critical crater (which may be present on 15 Eunomia) is predicted as <58 km.  相似文献   

7.
After several decades of frustrating results showing a generally poor agreement among different asteroid family classifications, recent studies based on high accuracy proper elements, as well as on objective statistical methods of cluster analysis have largely improved the situation. Now, a number of asteroid families have been recognized on the basis of different methods of cluster analysis, using asteroid proper elements data sets computed by means of different theories. For these reasons, they should be considered of very high reliability. Moreover, spectroscopic observations confirm in some cases these results, indicating surface compositions of the family members in agreement with a geochemically plausible parent body. However, in particular zones of the belt, like the Flora region, further efforts should be performed in order to establish the real consistence of the resulting clusterings of objects. In addition, the size distribution and the taxonomic types of some well established families seem to indicate particular features of the family sample when compared with the field objects. We recall that asteroid families, in the framework of asteroid collisional evolution, are of the highest importance for understanding the mechanisms of injection of fragments into the Earth-crossing zone through mean-motion and secular resonances and, as a consequence, for evaluating the impact rate on Earth of asteroidal objects.  相似文献   

8.
A new semianalytical theory of asteroid motion is presented. The theory is developed on the basis of Kaula's expansion of the disturbing function including terms up to the second order with respect to the masses of disturbing bodies. The theory is constructed in explicit form that gives the possibility to study separately the influence of different perturbations in the dynamics of minor planets. The mean-motion resonances with major planets as well as mixed three-body resonances can also be taken into account. For the non-resonant case the formulas obtained can be used for deriving the second transformation to calculate the proper elements of an asteroid orbit in closed form with respect to inclinations and eccentricities. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

9.
The Hamiltonian of the second order with respect to the disturbing mass, as defined in the higher order-higher degree theory of asteroid secular perturbations by Yuasa (1973), is expressed in the heliocentric, ecliptic coordinate system. Errors found in the original paper with terms coming from the principal part of the disturbing function are removed, and corrected values of the coefficients are computed. The importance of second-order perturbations and the improvement in the accuracy of proper element determination, achieved by using the newly-obtained coefficients, are demonstrated. Finally, a table of the secular frequencies as functions of the semimajor axis is given, and compared with the analogous one by Kozai (1979).  相似文献   

10.
Collisional evolution studies of asteroids indicate that the initial asteroid population at the time mean collisional velocities were pumped up to ～5 km/sec was only modestly larger than it is today; i.e., the asteroid belt was already depleted relative to the mean surface density elsewhere in the planetary region. Numerical simulations of the collisional evolution of hypothetical initial asteroid populations have been run, subject to three constraints: they must (a) evolve to the present observed asteroid size distribution, (b) preserve Vesta's basaltic crust, and (c) produce at least the observed number of major Hirayama families. A “runaway growth” initial asteroid population distribution is found to best satisfy these constraints. A new model is presented for calculating the fragmental size distribution for the disruption of large, gravitationally bound bodies in which the material strength is increased by hydrostatic self-compression. This model predicts that large asteroid behave as intrinsically strong bodies, even if they have had a history of being collisionally fractured. This model, when applied to the breakup of the Themis and Eos family parent bodies, gives size distributions in reasonably good agreement with those observed.  相似文献   

11.
The orbital evolutions of the asteroid 3040 Kozai and model asteroids with similar orbits have been investigated. Their osculating orbits for an epoch 1991 December 10 were numerically integrated forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all inner planets, Jupiter, and Saturn.The orbit of the asteroid Kozai is stable. Its motion is affected only by long-period perturbations of planets. With change of the argument of perihelion of the asteroid Kozai, the evolution of the model asteroid orbits changes essentially, too. The model orbits with the argument of perihelion changed by the order of 10% show that asteroids with such orbital parameters may approach the Earth orbit, while asteroids with larger changes may even cross it, at least after 10,000 years. Long-term orbital evolution of asteroids with these orbital parameters is very sensitive on their angular elements.  相似文献   

12.
Trajectories of satellites under the influences of earth oblateness and air drag are derived by the asymptotic method in nonlinear mechanics. Based on the assumptions: (1) the dominant oblateness factor of the earth is the second harmonic (J 2), (2) a non-rotating, spherically symmetric atmosphere and an exponential distribution of atmospheric density, (3) original elliptical orbits being of small eccentricity, closed-form solutions for the improved first order approximation are obtained. After finding the osculating orbital elements of the resulting trajectories, we expose the behavior of osculating orbits at various inclinations.  相似文献   

13.
Based on Williams' work and rewritten in action angle variables, a method for the calculation of proper elements is here presented. The averaging over the long periodic terms is performed by the semi numerical method developed by Henrard (1990); no series expansion in eccentricity or inclination of the asteroid is used which allows calculating proper elements for highly inclined orbits. Conversely, the theory is truncated at the first degree in the eccentricity and the inclination of the perturbing planets. A few tests about accuracy and consistency are presented.  相似文献   

14.
The Eos asteroid family is the third most populous, after Themis and Koronis, and one of the largest non-random groups of asteroids in the main belt. It has been known and studied for decades, but its structure and history still presented difficulties to understand. We first revise the Eos family identification as a statistical cluster in the space of proper elements. Using the most to-date catalogue of proper elements we determine a nominal Eos family, defined by us using the hierarchical-clustering method with the cut-off velocity of 55 m/s, contains some 4400 members. This unforeseen increase in known Eos asteroids allows us to perform a much more detailed study than was possible so far. We show, in particular, that most of the previously thought peculiar features are explained within the following model: (i) collisional disruption of the parent body leads to formation of a compact family in the proper element space (with characteristic escape velocities of the observed asteroids of tens of meters per second, compatible with hydrocode simulations), and (ii) as time goes, the family dynamically evolves due to a combination of the thermal effects and planetary perturbations. This model allows us to explain sharp termination of the family at the J7/3 mean motion resonance with Jupiter, uneven distribution of family members about the J9/4 mean motion resonance with Jupiter, semimajor axis distribution of large vs small members in the family and anomalous residence of Eos members inside the high-order secular resonance z1. Our dynamical method also allows us to estimate Eos family age to . Several formal members of the Eos family are in conflict with our model and these are suspected interlopers. We use spectroscopic observations, whose results are also reported here, and results of 5-color wide-band Sloan Digital Sky Survey photometry to prove some of them are indeed spectrally incompatible with the family.  相似文献   

15.
The dependence of the cumulative number of numbered asteroids (up to 3720) on their absolute magnitude is investigated. The differential mass index k is derived from these relations for fainter asteroids. A steeper slope (2.2 < k < 2.4) is found in the four most populous asteroid familes (Flora, Koronis, Eos and Themis) and a flatter slope (1.3 < k < 1.6) for non-family asteroids. This indicates that there are two different asteroid populations in the asteorid belt. Total masses of the asteroid families may be greater than it is commonly accepted.  相似文献   

16.
In this paper, we present the mathematical basis for the calculation of proper elements for asteroids in 3:2 mean-motion resonance with Jupiter from their osculating Keplerian elements. The method is based on a new resonant Lie-series perturbation theory (Ferraz-Mello, 1997, 2002), which allows the construction of formal solutions in cases where resonant and long-period angles appear simultaneously. For the disturbing function, we used the Beaugé’s expansion (Beaugé, 1996), adapted to include short period terms. In this paper, the theory is restricted to the planar case and only the perturbations due to Jupiter are considered.  相似文献   

17.
The Solar System dust bands discovered by IRAS are toroidal distributions of dust particles with common proper inclinations. It is impossible for particles with high eccentricity (approximately 0.2 or greater) to maintain a near constant proper inclination as they precess, and therefore the dust bands must be composed of material having a low eccentricity, pointing to an asteroidal origin. The mechanism of dust band production could involve either a continual comminution of material associated with the major Hirayama asteroid families, the equilibrium model (Dermott et al. (1984) Nature 312, 505–509) or random disruptions in the asteroid belt of small, single asteroids (Sykes and Greenberg (1986) Icarus 65, 51–69). The IRAS observations of the zodiacal cloud from which the dust band profiles are isolated have excellent resolution, and the manner in which these profiles change around the sky should allow the origin of the bands, their radial extent, the size-frequency distribution of the material and the optical properties of the dust itself to be determined. The equilibrium model of the dust bands suggests Eos as the parent of the 10° band pair. Results from detailed numerical modeling of the 10° band pair are presented. It is demonstrated that a model composed of dust particles having mean semimajor axis, proper eccentricity and proper inclination equal to those of the Eos family member asteroids, but with a dispersion in proper inclination of 2.5°, produces a convincing match with observations. Indeed, it is impossible to reproduce the observed profiles of the 10° band pair without imposing such a dispersion on the dust band material. Since the dust band profiles are matched very well with Eos, Themis and Koronis type material alone, the result is taken as strong evidence in favor of the equilibrium model. The effects of planetary perturbations are included by imposing the appropriate forced elements on the dust particle orbits (these forced elements vary with heliocentric distance). A subsequent model in which material is allowed to populate the inner solar system by a Poynting-Robertson drag distribution is also constructed. A dispersion in proper inclination of 3.5° provides the best match with observations, but close examination of the model profiles reveals that they are slightly broader than the observed profiles. If the variation of the number density of asteroidal material with heliocentric distance r is given by an expression of the form 1/rτ then these results indicate that γ < 1 compared with γ = 1 expected for a simple Poynting-Robertson drag distribution. This implies that asteroidal material is lost from the system as it spirals in towards the Sun, owing to interparticle collisions.  相似文献   

18.
The orbital evolution of the near-Earth asteroid (NEA) 30825 1990 TG1 has been studied by numerical integration of the equations of its motion over the 100 000-year time interval with allowance for perturbations from eight major planets and Pluto, and the variations in its osculating orbit over this time interval were determined. The numerical integrations were performed using two methods: the Bulirsch-Stoer method and the Everhart method. The comparative analysis of the two resulting orbital evolutions of motion is presented for the time interval examined. The evolution of the asteroid motion is qualitatively the same for both variants, but the rate of evolution of the orbital elements is different. Our research confirms the known fact that the application of different integrators to the study of the long-term evolution of the NEA orbit may lead to different evolution tracks.  相似文献   

19.
We explore the correlation between an asteroid’s taxonomy and photometric phase curve using the H, G12 photometric phase function, with the shape of the phase function described by the single parameter G12. We explore the usability of G12 in taxonomic classification for individual objects, asteroid families, and dynamical groups. We conclude that the mean values of G12 for the considered taxonomic complexes are statistically different, and also discuss the overall shape of the G12 distribution for each taxonomic complex. Based on the values of G12 for about half a million asteroids, we compute the probabilities of C, S, and X complex membership for each asteroid. For an individual asteroid, these probabilities are rather evenly distributed over all of the complexes, thus preventing meaningful classification. We then present and discuss the G12 distributions for asteroid families, and predict the taxonomic complex preponderance for asteroid families given the distribution of G12 in each family. For certain asteroid families, the probabilistic prediction of taxonomic complex preponderance can clearly be made. In particular, the C complex preponderant families are the easiest to detect, the Dora and Themis families being prime examples of such families. We continue by presenting the G12-based distribution of taxonomic complexes throughout the main asteroid belt in the proper element phase space. The Nysa–Polana family shows two distinct regions in the proper element space with different G12 values dominating in each region. We conclude that the G12-based probabilistic distribution of taxonomic complexes through the main belt agrees with the general view of C complex asteroid proportion increasing towards the outer belt. We conclude that the G12 photometric parameter cannot be used in determining taxonomic complex for individual asteroids, but it can be utilized in the statistical treatment of asteroid families and different regions of the main asteroid belt.  相似文献   

20.
We identified the family of the binary asteroid 423 Diotima consisting of 411 members in the phase space of orbital elements—semimajor axes a (or mean motions n), eccentricities e, and inclinations i—by using an electronic version of the ephemerides of minor planets EMP-2003 containing osculating orbital elements for 34992 asteroids of the main belt. The 9/4 resonance with Jupiter clearly separates the family of 423 Diotima from the family of Eos, which, according to EMP for 2003, contains 1204 asteroids.  相似文献   

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