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1.
V. A. Shefer 《Solar System Research》2005,39(3):239-246
The motion of minor Solar System bodies having close encounters with major planets is described using the model of motion within the framework of the perturbed restricted three-body problem. The actual motion of a minor body is represented as a combination of two motions, namely, the motion of a fictitious attracting center with a variable mass and the motion with respect to the fictitious center. The position and mass of the fictitious center are chosen so that, when the minor body collides with any of the primaries, the fictitious center carries into the center of inertia of the colliding body and the mass of the fictitious center becomes identical to the mass of this body. The regularizing KS-transformation and Sundman’s time transformation were applied to coordinates and velocities. As a result, a system of differential equations of motion that are quasilinear within the nearest vicinity of each of the primary attracting bodies was obtained. These equations are characterized by a numerical behavior during the encounters of the minor body with the primaries that is essentially better than that of the initial equations of motion. The motion of comets Brooks 2 and Gehrels 3, which have fairly close encounters with Jupiter, is simulated.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 3, 2005, pp. 272–280.Original Russian Text Copyright © 2005 by Shefer. 相似文献
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V. A. Shefer 《Astronomy Letters》2007,33(4):270-282
We suggest a new approach to solving the problem of finding the orbit of a celestial body from its three spatial position vectors and the corresponding times. It allows most of the perturbations in the motion of a celestial body to be taken into account. The approach is based on the theory of intermediate orbits that we developed previously. We construct the orbit the motion along which is a combination of two motions: the motion of a fictitious attracting center whose mass varies according to Mestschersky’s first law and the motion relative to the fictitious center. The first motion is generally parabolic, while the second motion is described by the equations of the Gylden-Mestschersky problem. The constructed orbit has such parameters that their limiting values at any reference epoch define a superosculating intermediate orbit with a fourth-order tangency. We have performed a numerical analysis to estimate the accuracy of approximating the perturbed motion of two minor planets, 145 Adeona and 4179 Toutatis, by the orbits computed using two-position procedures (the classical Gauss method and the method that we suggested previously), a three-position procedure based on the Herrick-Gibbs equation, and the new method. Comparison of the results obtained suggests that the latter method has an advantage. 相似文献
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V. A. Brumberg 《Celestial Mechanics and Dynamical Astronomy》1978,18(4):319-336
For treating the perturbed two-body problem in rectangular coordinates a new method is developed. The method is based on the reduction of the variational equations of the two-body problem with arbitrary elements to the Jordan system. The equations of perturbed motion rewritten in the quasi-Jordan form are subjected to a transformation excluding fast variables and leading to a system governing the long term evolution of motion. The method may be easily extended to the problem of the heliocentric motion of the major planets. For performing this method on computer it is suitable to use facilities of Poissonian and Keplerian processors. 相似文献
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V. A. Shefer 《Solar System Research》2013,47(1):38-49
Two new methods are described for finding the orbit of a small celestial body from three or more pairs of angular measurements and the corresponding time points. The methods are based on, first, the approach that has been developed previously by the author to the determination, from a minimum number of observations, of intermediate orbit considering most of the perturbations in the bodies’ motion and, second, Herget’s algorithmic procedure enabling the introduction of additional observations. The errors of orbital parameters calculated by the proposed methods are two orders of magnitude smaller than the corresponding errors of the traditional approach based on the construction of an unperturbed Keplerian orbit. The thus-calculated orbits of the minor planets 1566 Icarus, 2002 EC1, and 2010 TO48 are used to compare the results of Herget’s multiposition procedure and the new methods. The comparison shows that the new methods are highly effective in the study of perturbed motion. They are particularly beneficial if high-precision observational data covering short orbital arcs are available. 相似文献
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Based on the theory of intermediate orbits developed earlier by the author of this paper, a new approach is proposed to the solution of the problem of finding the orbit of a celestial body with the use of two position vectors of this body and the corresponding time interval. This approach makes it possible to take into account the main part of perturbations. The orbit is constructed, the motion along which is a combination of two motions: the uniform motion along a straight line of a fictitious attracting center, whose mass varies according to the first Meshchersky law, and the motion around this center. The latter is described by the equations of the Gylden–Meshchersky problem. The parameters of the constructed orbit are chosen so that their limiting values at any reference epoch determine a superosculating intermediate orbit with third-order tangency. The accuracy of approximation of the perturbed motion by the orbits calculated by the classical Gauss method and the new method is illustrated by an example of the motion of the unusual minor planet 1566 Icarus. Comparison of the results obtained shows that the new method has obvious advantages over the Gauss method. These advantages are especially prominent in cases where the angular distances between the reference positions are small. 相似文献
8.
Analysis of the potential field and equilibrium points of irregular-shaped minor celestial bodies 总被引：4，自引：0，他引：4
The equilibrium points of the gravitational potential field of minor celestial bodies, including asteroids, comets, and irregular satellites of planets, are studied. In order to understand better the orbital dynamics of massless particles moving near celestial minor bodies and their internal structure, both internal and external equilibrium points of the potential field of the body are analyzed. In this paper, the location and stability of the equilibrium points of 23 minor celestial bodies are presented. In addition, the contour plots of the gravitational effective potential of these minor bodies are used to point out the differences between them. Furthermore, stability and topological classifications of equilibrium points are discussed, which clearly illustrate the topological structure near the equilibrium points and help to have an insight into the orbital dynamics around the irregular-shaped minor celestial bodies. The results obtained here show that there is at least one equilibrium point in the potential field of a minor celestial body, and the number of equilibrium points could be one, five, seven, and nine, which are all odd integers. It is found that for some irregular-shaped celestial bodies, there are more than four equilibrium points outside the bodies while for some others there are no external equilibrium points. If a celestial body has one equilibrium point inside the body, this one is more likely linearly stable. 相似文献
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P. Kenneth Seidelmann B. A. Archinal M. F. A’hearn A. Conrad G. J. Consolmagno D. Hestroffer J. L. Hilton G. A. Krasinsky G. Neumann J. Oberst P. Stooke E. F. Tedesco D. J. Tholen P. C. Thomas I. P. Williams 《Celestial Mechanics and Dynamical Astronomy》2007,98(3):155-180
Every three years the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the
directions of the poles of rotation and the prime meridians of the planets, satellites, minor planets, and comets. This report
introduces improved values for the pole and rotation rate of Pluto, Charon, and Phoebe, the pole of Jupiter, the sizes and
shapes of Saturn satellites and Charon, and the poles, rotation rates, and sizes of some minor planets and comets. A high
precision realization for the pole and rotation rate of the Moon is provided. The expression for the Sun’s rotation has been
changed to be consistent with the planets and to account for light travel time 相似文献
10.
V. P. Tomanov 《Kinematics and Physics of Celestial Bodies》2007,23(5):196-206
We analyze our earlier data on the numerical integration of the equations of motion for 274 short-period comets (with the period P<200 yr) on a time interval of 6000 yr. As many as 54 comets had no close approaches to planets, 13 comets passed through the Saturnian sphere of action, and one comet passed through the Uranian sphere of action. The orbital elements of these 68 comets changed by no more than ±3 percent in a space of 6000 yr. As many as 206 comets passed close to Jupiter. We confirm Everhart’s conclusion that Jupiter can capture long-period comets with q = 4–6 AU and i < 9° into short-period orbits. We show that nearly parabolic comets cross the solar system mainly in the zone of terrestrial planets. No relationship of nearly parabolic comets and terrestrial planets was found for the epoch of the latest apparition of comets. Guliev’s conjecture about two trans-Plutonian planets is based on the illusory excess of cometary nodes at large heliocentric distances. The existence of cometary nodes at the solar system periphery turns out to be a solely geometrical effect. 相似文献
11.
John D. Hadjidemetriou 《Astrophysics and Space Science》1976,40(1):201-224
Several families of the planar general three-body problem for fixed values of the three masses are found, in a rotating frame of reference, where the mass of two of the bodies is small compared to the mass of the third body. These families were obtained by the continuation of a degenerate family of periodic orbits of three bodies where two of the bodies have zero masses and describe circular orbits around a third body with finite mass, in the same direction.The above families represent planetary systems with the body with the large mass representing the Sun and the two small bodies representing two planets or comets. One section of a family is shown to represent the Jupiter family of comets and also a model for the Sun-Jupiter-Saturn system is found.The stability analysis revealed that stability exists for small masses and small eccentricities of the two planets. Planetary systems with relatively large masses and eccentricities are proved to be unstable. In particular, the Jupiter family of comets, for small masses of the two small bodies, and the Sun-Jupiter-Saturn system are proved to be stable. Also, it was shown that resonances are not necessarily associated with instabilities. 相似文献
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T.C. Van Flandern 《Icarus》1981,47(3):480-486
The recent evidence that many minor planets may have satellites, together with recently iscovered physical, chemical, and lightcurve similarities between minor planets and comets, lead naturally to the question, “Might comets have satellites also?” This paper explores several puzzling features of comets which do not fit easily into conventional cometary models, but which can be satisfactorily explained if it is assumed that comets have a full range of gravitationally bound masses, from dust size to the size of the nucleus, in orbit around the principal nucleus. This discussion also implies a higher probability of destruction of a spacecraft near a comet than is usually assumed. 相似文献
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From 146 B.C. to 1760 A.D., 363 sets of cometary observations for a total 88 different comets were recorded in Chinese Ancient Records of Celestial Phenomena. According to those records, we reduced apparent positions and mean equatorial coordinates (epoch 2000.0) for all more than three times recorded comets. Taking into account the perturbations of all nine planets and using the numerical method of N-body problem, the orbits of correlative comets were calculated. For thirty different comets, new orbits are presented for the first time. 相似文献
14.
C. Beaugé 《Celestial Mechanics and Dynamical Astronomy》2004,88(1):51-68
In this communication we present an analytical model for the restricted three-body problem, in the case where the perturber is in a parabolic orbit with respect to the central mass. The equations of motion are derived explicitly using the so-called Global Expansion of the disturbing function, and are valid for any eccentricity of the massless body, as well as in the case where both secondary masses have crossing orbits. Integrating the equations of motion over the complete passage of the perturber through the system, we are then able to construct a first-order algebraic mapping for the change in semimajor axis, eccentricity and inclination of the perturbed body.Comparisons with numerical solutions of the exact equations show that the map yields precise results, as long as the minimum distance between both bodies is not too small. Finally, we discuss several possible applications of this model, including the evolution of asteroidal satellites due to background bodies, and simulations of passing stars on extra-solar planets. 相似文献
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E.D. Kuznetsov 《Planetary and Space Science》1997,45(12):1595-1606
The equation for calculation of the required accuracy of the perturbing bodies motion theories is obtained. The equation relates the accuracy required to take into account perturbing acceleration, acting on the perturbed body, with the accuracy of the motion theory of the perturbing body. The solutions for estimation of the required accuracy both for the inner and the external cases in the spherical coordinates are coincided. The solution for the calculation of the required accuracy for the general case (combining the inner and the external cases) in Cartesian coordinates is obtained. The special cases for the solution in Cartesian coordinates are studied. As an example, the estimations of the required accuracy of the motion theories of the solar system planets for some perturbed bodies (the near-Earth asteroid 4179 Toutatis, the main belt asteroid 208 Larcimosa, the trojan asteroid 588 Achilles, the centaur asteroid 5145 Pholus, the Kuiper belt asteroid 1995 QZ9, the comet Halley) are obtained. The conditions of the use of the obtained results are discussed. 相似文献
16.
D. Nesvorný F. Thomas S. Ferraz-Mello A. Morbidelli 《Celestial Mechanics and Dynamical Astronomy》2002,82(4):323-361
We develop a formalism of the non-singular evaluation of the disturbing function and its derivatives with respect to the canonical variables. We apply this formalism to the case of the perturbed motion of a massless body orbiting the central body (Sun) with a period equal to that of the perturbing (planetary) body. This situation is known as the co-orbital motion, or equivalently, as the 1/1 mean motion commensurability. Jupiter's Trojan asteroids, Earth's co-orbital asteroids (e.g., (3753) Cruithne, (3362) Khufu), Mars' co-orbital asteroids (e.g., (5261) Eureka), and some Jupiter-family comets are examples of the co-orbital bodies in our solar system. Other examples are known in the satellite systems of the giant planets. Unlike the classical expansions of the disturbing function, our formalism is valid for any values of eccentricities and inclinations of the perturbed and perturbing body. The perturbation theory is used to compute the main features of the co-orbital dynamics in three approximations of the general three-body model: the planar-circular, planar-elliptic, and spatial-circular models. We develop a new perturbation scheme, which allows us to treat cases where the classical perturbation treatment fails. We show how the families of the tadpole, horseshoe, retrograde satellite and compound orbits vary with the eccentricity and inclination of the small body, and compute them also for the eccentricity of the perturbing body corresponding to a largely eccentric exoplanet's orbit.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
17.
In the following paper we argue that each wind-driving star in relative motion with respect to the ambient interstellar medium experiences a force exerted on its central wind-generating body. The exact magnitude of this force depends on the actual geometry of the counterflow configuration of stellar and interstellar winds for a particular kinematic situation which is especially sensitive to whether the interstellar flow is subsonic or supersonic. It will, however, be demonstrated here that this force is of an accelerating nature, i.e., it operates like a rocket-motor, as long as the peculiar motion of the wind-driving star with respect to the ambient interstellar medium remains subsonic.Here we use a specific analytical model to describe theoretically the specific counterflow configuration for the case of the solar system in a subsonic peculiar motion with respect to the local interstellar medium assuming irrotational and incompressible flows. We can work out a quantitative number for the accelerating force governing the Sun's motion at present. The net reaction force exerted on the solar body is then mediated by the asymmetric boundary conditions to which the distant solar wind field has to adapt.Next we study the indirect action of such a force on orbiting Keplerian objects like planets, planetesimals and comets. Since this force only influences the central solar body, but not the planets themselves, the problem is different from the treatment of a constant perturbation force perturbing the Keplerian orbits. We present a perturbation analysis treating the action of a corresponding position-dependent perturbation force resulting in secular changes of the orbital elements of Keplerian objects. It is found that changes are accumulating more rapidly in time the closer to the sun the orbiting bodies are. Main axis and perihelion distances are systematically increasing. Especially pronounced are changes in the perihelion position angle of the objects. For solar wind mass losses larger than the Sun's present value by a factor of 1000 (T-Tauri phase of the Sun,) the migration periods calculated for the planet Mercury are of the same order of magnitude as that for corresponding general relativistic migration. 相似文献
18.
There exist many comets with near-parabolic orbits in the Solar System. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable (Oort, 1950). The theory assumes that there is a cometary cloud at a distance 103 – 105 AU from the Sun and that perturbing forces from planets or stars make orbits of some of these comets become of near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the Solar System forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighbourhood of any separatrix i.e. the trajectory with zero frequency of the unperturbed motion of an Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study on near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion (Petrosky, 1988). In this paper we derive a similar mapping directly and discuss its dynamical characters. 相似文献
19.
I. V. Tupikova 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):129-144
A new mathematically correct approach to construct an averaging procedure for the motion of a massless body around the central body perturbed by fully interacting planets is developed and the errors of the standard solution are discussed. The new technique allows to combine the advantages of the Hamiltonian representation with the usage of standard osculating elements in combination with all the standard expansions of the perturbing functions. The main idea is to introduce new additional variables conjugate to all the standard elements and to work in a corresponding super phase space. In this way, the number of variables is doubled at first, but one has to deal with only one Hamiltonian. The artificially introduced variables disappear from the final averaged equations as well as from the transformation formulae connecting the osculating and the mean elements. 相似文献
20.
Ya. S. Yatskiv L. V. Rykhlova V. K. Taradiy 《Kinematics and Physics of Celestial Bodies》2016,32(5):213-217
Astronomical research in the Elbrus Region are conducted in the wide international cooperation. They are implemented in under the aegis of the International Association of Academies of Sciences in collaboration with the Euro-Asiatic Association of Universities. Authors outline the important scientific results obtained in the fields of fundamental, applied, and search studies within the international astronomical programs at the Terskol Peak Observatory. They refer to the problem of the identification of diffuse interstellar bands, studies of the star light-curve, detection of optical residuals of gamma-ray bursts, determination of the kinematic and physical characteristics of minor bodies of the Solar System (asteroids and comets), as well as investigation of space objects of technogenic origin in the near-Earth space environment. 相似文献