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1.
V. Carruba 《Monthly notices of the Royal Astronomical Society》2009,398(3):1512-1526
In this work, I conduct a preliminary analysis of the Phocaea family region. I obtain families and clumps in the space of proper elements and proper frequencies, study the taxonomy of the asteroids for which this information is available, analyse the albedo and absolute magnitude distribution of objects in the area, obtain a preliminary estimate of the possible family age, study the cumulative size distribution and collision probabilities of asteroids in the region, the rotation rate distribution and obtain dynamical map of averaged elements and Lyapunov times for grids of objects in the area.
Among my results, I identified the first clump visible only in the frequency domain, the (6246) Komurotoru clump, obtained a higher limit for the possible age of the Phocaea family of 2.2 Byr, identified a class of Phocaea members on Mars-crossing orbits characterized by high Lyapunov times and showed that an apparently stable region on time-scales of 20 Myr near the ν6 secular resonance is chaotic, possibly because of the overlapping of secular resonances in the region. The Phocaea dynamical group seems to be a real S-type collisional family, formed up to 2.2 Byr ago, whose members with a large semimajor axis have been dynamically eroded by the interaction with the local web of mean-motion and secular resonances. Studying the long-term stability of orbits in the chaotic regions and the stability of family and clumps identified in this work remain challenges for future works. 相似文献
Among my results, I identified the first clump visible only in the frequency domain, the (6246) Komurotoru clump, obtained a higher limit for the possible age of the Phocaea family of 2.2 Byr, identified a class of Phocaea members on Mars-crossing orbits characterized by high Lyapunov times and showed that an apparently stable region on time-scales of 20 Myr near the ν
2.
Patrick Michel Christiane Froeschlé Paolo Farinella 《Celestial Mechanics and Dynamical Astronomy》1997,69(1-2):133-147
In the last three years we have carried out numerical and semi-analytical studies on the secular dynamical mechanisms in the
region (semimajor axis a < 2 AU) where the NEA orbits evolve. Our numerical integrations (over a time span of a few Myr) have
shown that: (i) the linear secular resonances with both the inner and the outer planets may play an important role in the
dynamical evolution of NEAs; (ii) the apsidal secular resonance with Mars could provide an important dynamical transport mechanism
by which asteroids in the Mars-crossing region eventually achieve Earth-crossing orbits; (iii) in this region, due to the
interaction with the terrestrial planets, the Kozai resonance can occur at small inclinations, with the argument of perihelion
ω librating around 0° or 180°, providing a temporary protection mechanism against close approaches to the planets.
The location of the linear secular resonances in this zone has also been obtained by an automatic procedure using a semi-numerical
method valid for all values of the inclinations and eccentricities of the small bodies, and also in the case of libration
of the argument of perihelion. A map of the secular resonances in the (a, i) plane shows — in agreement with the numerical
integrations — that all the resonances with the terrestrial and giant planets are present, and also that some of them overlap.
Thus the way is now open to fully take into account secular resonances in modelling the dynamical evolution of NEAs.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
To try to understand the dynamical and collisional evolution of the Hungaria asteroids we have built a large catalog of accurate synthetic proper elements. Using the distribution of the Hungaria, in the spaces of proper elements and of proper frequencies, we can study the dynamical boundaries and the internal structure of the Hungaria region, both within a purely gravitational model and also showing the signature of the non-gravitational effects. We find a complex interaction between secular resonances, mean motion resonances, chaotic behavior and Yarkovsky-driven drift in semimajor axis. We also find a rare occurrence of large scale instabilities, leading to escape from the region. This allows to explain the complex shape of a grouping which we suggest is a collisional family, including most Hungaria but by no means all; we provide an explicit list of non-members of the family. There are finer structures, of which the most significant is a set of very close asteroid couples, with extremely similar proper elements. Some of these could have had, in a comparatively recent past, very close approaches with low relative velocity. We argue that the Hungaria, because of the favorable observing conditions, may soon become the best known sub-group of the asteroid population. 相似文献
4.
O. Miloni S. Ferraz-Mello C. Beaugé 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):89-111
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
5.
Mean orbital elements are obtained from osculating ones by removing the short periodic perturbations. Large catalogues of
asteroid mean elements need to be computed, as a first step in the computation of proper elements, used to study asteroid
families. The algorithms for this purpose available so far are only accurate to first order in the masses of the perturbing
planet; the mean elements have satisfactory accuracy for most of the asteroid belt, but degraded accuracy in the neighbourhoods
of the main mean motion resonances, especially the 2:1. We investigate a number of algorithms capable of improving this approximation;
they belong to the two classes of Breiter-type methods and iterative methods. The former are obtained by applying some higher
order numerical integration scheme, such as Runge–Kutta, to the differential equation whose solution is a transformation removing
the fast angular variables from the equations; they can be used to compute a full second order theory, however, only if the
full second order determining function is explicitly computed, and this is computationally too cumbersome for a complicated
problem such as the N-body. The latter are fixed point iterative schemes, with the first order theory as an iteration step,
used to compute the inverse map from mean to osculating elements; formally the method is first order, but because they implement
a fixed frequency perturbation theory, they are more accurate than conventional single iteration methods; a similar method
is already in use in our computation of proper from mean elements. Many of these methods are tested on a sample of asteroid
orbits taken from the Themis family, up to the edge of the 2:1 resonance, and the dispersion of the values of the computed
mean semimajor axis over 100 000 years is used as quality control. The results of these tests indicate that the iterative
methods are superior, in this specific application, to the Breiter methods, in accuracy and reliability. This is understood
as the result of the cancellations occurring between second order perturbation terms: the incomplete second order theory,
resulting from the use of a Breiter method with the first order determining function only, can be less accurate than complete,
fixed frequency theories of the first order. We have therefore computed new catalogues of asteroid mean and proper elements,
incorporating an iterative algorithm in both steps (osculating to mean and mean to proper elements). This new data set, significantly
more reliable even in the previously degraded regions of Themis and Cybele, is in the public domain.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
T. A. Heppenheimer 《Celestial Mechanics and Dynamical Astronomy》1979,20(3):231-241
The solution of Brouwer and van Woerkom (1950), for reduction to prope, elements of asteroidal osculating elements at epoch, is extended to the range of semimajor axes, 0.1<a<55 AU. The locations and strengths of secular resonances are noted. 相似文献
7.
Time evolution of the interplanetary dust particle under the action of the solar electromagnetic radiation (Poynting-Robertson effect) is investigated. Evolution of the initially circular orbit in terms of the orbital elements present in the standard equations for their secular changes is considered. It is pointed out that the osculating eccentricity is practically constant during the motion in spite of generally accepted opinion that the standard equations for the secular changes of orbital elements represent time evolution of the osculating elements. 相似文献
8.
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
9.
Both the Poynting-Robertson drag and resonant orbits appear to be very important for the motion of small grains in the early solar system. While orbital resonances are very often stable and tend to force bodies into noncircular orbits, the Poynting-Robertson drag produces secular variations in the semimajor axis and tends to circularize the orbits. We study numerically the competition between the Poynting-Robertson drag and the gravitational interaction of grains with Jupiter near the 2/1 resonance. Computations are based on the plane-restricted problem. Numerical investigations show that the grains always cross the resonance region without any oscillation, except in the special case where the grains were initially inside the resonance. In both cases the variations of the osculating elements exhibit a drastic step, which can be explained by Greenberg's and Schubart's theories. 相似文献
10.
Lin-Sen Li 《Astrophysics and Space Science》2012,340(2):323-330
Perturbative post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the parameterized post-Newtonian theoretical framework. The results obtained are applied to the Einstein and Brans–Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The post-Newtonian effects are calculated and discussed for six extrasolar planets. 相似文献
11.
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. 相似文献
12.
Yoshihide Kozai 《Icarus》1980,41(1):89-95
As the classical linear theory of secular perturbations for asteroids is known not to be adequate for computing the perturbations of asteroids with high eccentricities and/or inclinations, a seminumerical method to calculate the secular perturbations by including higher-degree terms in the disturbing function has been developed. It is here applied to asteroids with small values of , since the secular variations as well as their deviations from the results derived by the classical linear theory are generally large for such asteroids. It is found that the arguments of perihelion for five of the numbered asteroids are librating around 90 or 270°. For asteroids with less than 0.85 the results of the secular variations are tabulated. Also the stability of such orbits is discussed by comparing the orbital properties of short-periodic comets with them. Generally speaking, orbits of the asteroids are more stable than those of the short-periodic comets, and asteroids with librating arguments of perihelion are more stable than those with circular coplanar orbits although their orbital elements are changed more by secular perturbations. 相似文献
13.
T. A. Heppenheimer 《Celestial Mechanics and Dynamical Astronomy》1980,22(3):297-304
It is proposed that the Kirkwood Gaps are primordial, representing regions where asteroids failed to form by accretion. A brief scenario is presented to indicate the main features of a model for the early history of the asteroids. An analytical treatment is given for the effects of a solar nebula upon the eccentricity-pumping of asteroids, due to secular perturbations and to commensurability-type resonances associated with Jupiter. It is shown that nebular effects promote growth of main-belt asteroids; but in commensurability regions, growth is inhibited. A discussion is given of two related problems: the origin of asteroidal eccentricities and inclinations, and the likelihood that Jupiter suffered major changes in its semimajor axis during its formation. It is suggested that in view of these problems, the present theory should not be taken as necessarily correct, but should be regarded as illustrative of viewpoints which in time may yield a correct theory. 相似文献
14.
Michèle Moons 《Celestial Mechanics and Dynamical Astronomy》1996,65(1-2):175-204
The study of mean motion resonance dynamics was motivated by the search for an explanation for the puzzling problem of the Kirkwood gaps. The most important contributions in this field within the last 32 years are reviewed here. At the beginning of that period, which coincides with the first long-term numerical investigations of resonant motion, different hypotheses (collisional, gravitational, statistical and cosmological) to explain the origin of the gaps were still competing with each other. At present, a general theory, based on gravitational mechanisms only, is capable of explaining in a uniform way all the Kirkwood gaps except the 2/1 one. Indeed, in the 4/1, 3/1, 5/2 and 7/3 mean motion commensurabilities, the overlap of secular resonances leads to almost overall chaos where asteroids undergo large and wild variations in their orbital elements. Such asteroids, if not thrown directly into the Sun, are sooner or later subject to strong close encounters with the largest inner planets, the typical time scale of the whole process being of the order of a few million years. Unfortunately, this mechanism is not capable of explaining the 2/1 gap where the strong chaos produced by the overlapping secular resonances does not attain orbits with moderate eccentricity, of low inclination and with low to moderate amplitude of libration. In the light of the most recent studies, it appears that the 2/1 gap is the global consequence of slow diffusive processes. At present, the origin of these processes remains under study. 相似文献
15.
Zoran Knežević 《Celestial Mechanics and Dynamical Astronomy》1989,46(2):147-158
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
16.
Peter Musen 《Celestial Mechanics and Dynamical Astronomy》1971,4(3-4):378-396
This paper derives the contributionF
2
* by the great inequality to the secular disturbing function of the principal planets. Andoyer's expansion of the planetary disturbing function and von Zeipel's method of eliminating the periodic terms is employed; thereby, the corrected secular disturbing function for the planetary system is derived. An earlier solution suggested by Hill is based on Leverrier's equations for the variation of elements of Jupiter and Saturn and on the semi-empirical adjustment of the coefficients in the secular disturbing function. Nowadays there are several modern methods of eliminating periodic terms from the Hamiltonian and deriving a purely secular disturbing function. Von Zeipel's method is especially suitable. The conclusion is drawn that the canonicity of the equations for the secular variation of the heliocentric elements can be preserved if there be retained, in the secular disturbing function, terms only of the second and fourth order relative to the eccentricity and inclinations.The Krylov-Bogolubov method is suggested for eliminating periodic terms, if it is desired to include the secular perturbations of the fifth and higher order in the heliocentric elements. The additional part of the secular disturbing functionF
2
* derived in this paper can be included in existing theories of the secular effects of principal planets. A better approach would be to preserve the homogeneity of the theory and rederive all the secular perturbations of principal planets using Andoyer's symbolism, including the part produced by the great inequality. 相似文献
17.
For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams. 相似文献
18.
19.
Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study
the secular effects of two non-coplanar planets which are not in mean–motion resonance. By means of Lie transformations (which
introduce an action–angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body
problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements,
the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This
study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations
of the linear Laplace–Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial
values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital
planes.
Anne-Sophie Libert is FNRS Research Fellow. 相似文献
20.
Electromagnetic Radiation and Motion of a Particle 总被引：2，自引：2，他引：0
Jozef Klačka 《Celestial Mechanics and Dynamical Astronomy》2004,89(1):1-61
We consider the motion of uncharged dust grains of arbitrary shape including the effects of electromagnetic radiation and
thermal emission. The resulting relativistically covariant equation of motion is expressed in terms of standard optical parameters.
Explicit expressions for secular changes of osculating orbital elements are derived in detail for the special case of the
Poynting-Robertson effect. Two subcases are considered: (i) central acceleration due to gravity and the radial component of
radiation pressure independent of the particle velocity, (ii) central acceleration given by gravity and the radiation force
as the disturbing force. The latter case yields results which may be compared with secular orbital evolution in terms of orbital
elements for an arbitrarily shaped dust particle. The effects of solar wind are also presented.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献