共查询到20条相似文献，搜索用时 31 毫秒
1.
Martin Lara 《Celestial Mechanics and Dynamical Astronomy》2017,127(3):285-300
This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions. 相似文献
2.
This paper deals with the Restricted Three Body Problem (RTBP) in which we assume that the primaries are radiation sources
and the influence of the radiation pressure on the gravitational forces is considered; in particular, we are interested in
finding families of periodic orbits under theses forces.
By means of some modifications to the method of numerical continuation of natural families of periodic orbits, we find several
families of periodic orbits, both in two and three dimensions. As starters for our method we use some known periodic orbits
in the classical RTBP.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
3.
In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have
powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different types of symmetry
planes of the fixed cube, periodic orbits are obtained using the method of the Poincaré surface of section. While in general
positions, periodic orbits are found by the homotopy method. The results show that periodic orbits exist extensively in symmetry
planes of the fixed cube, and also exist near asymmetry planes that contain the regular Hex cross section. The stability of
these periodic orbits is determined on the basis of the eigenvalues of the monodromy matrix. This paper proves that the homotopy
method is effective to find periodic orbits in the gravity field of the cube, which provides a new thought of searching for
periodic orbits around non-spherical celestial bodies. The investigation of orbits around the cube could be considered as
the first step of the complicated cases, and helps to understand the dynamics of orbits around bodies with complicated shapes.
The work is an extension of the previous research work about the dynamics of orbits around some simple shaped bodies, including
a straight segment, a circular ring, an annulus disk, and simple planar plates. 相似文献
4.
Egemen Kolemen N. Jeremy Kasdin Pini Gurfil 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):47-74
A new fully numerical method is presented which employs multiple Poincaré sections to find quasiperiodic orbits of the Restricted
Three-Body Problem (RTBP). The main advantages of this method are the small overhead cost of programming and very fast execution
times, robust behavior near chaotic regions that leads to full convergence for given family of quasiperiodic orbits and the
minimal memory required to store these orbits. This method reduces the calculations required for searching two-dimensional
invariant tori to a search for closed orbits, which are the intersection of the invariant tori with the Poincaré sections.
Truncated Fourier series are employed to represent these closed orbits. The flow of the differential equation on the invariant
tori is reduced to maps between the consecutive Poincaré maps. A Newton iteration scheme utilizes the invariance of the circles
of the maps on these Poincaré sections in order to find the Fourier coefficients that define the circles to any given accuracy.
A continuation procedure that uses the incremental behavior of the Fourier coefficients between close quasiperiodic orbits
is utilized to extend the results from a single orbit to a family of orbits. Quasi-halo and Lissajous families of the Sun–Earth
RTBP around the L2 libration point are obtained via this method. Results are compared with the existing literature. A numerical
method to transform these orbits from the RTBP model to the real ephemeris model of the Solar System is introduced and applied. 相似文献
5.
We develop a new and fast method to estimate perturbations by a planet on cometary orbits. This method allows us to identify accurately the cases of large perturbations in a set of fictitious orbits. Hence, it can be used in constructing perturbation samples for Monte Carlo simulations in order to maximize the amount of information. Furthermore, the estimated perturbations are found to yield a good approximation to the real perturbation sample. This is shown by a comparison of the perturbations obtained by the new estimator with the results of numerical integration of regularized equations of motion for the same orbits in the same dynamical model: the three-dimensional elliptic restricted three-body problem (Sun-Jupiter-comet). 相似文献
6.
V. S. Kalantonis E. A. Perdios A. E. Perdiou M. N. Vrahatis 《Celestial Mechanics and Dynamical Astronomy》2001,80(2):81-96
The accurate computation of families of periodic orbits is very important in the analysis of various celestial mechanics systems. The main difficulty for the computation of a family of periodic orbits of a given period is the determination within a given region of an individual member of this family which corresponds to a periodic orbit. To compute with certainty accurate individual members of a specific family we apply an efficient method using the Poincaré map on a surface of section of the considered problem. This method converges rapidly, within relatively large regions of the initial conditions. It is also independent of the local dynamics near periodic orbits which is especially useful in the case of conservative dynamical systems that possess many periodic orbits, often of the same period, close to each other in phase space. The only computable information required by this method is the signs of various function evaluations carried out during the integration of the equations of motion. This method can be applied to any system of celestial mechanics. In this contribution we apply it to the photogravitational problem. 相似文献
7.
The equilibria and periodic orbits around a dumbbell-shaped body 总被引：1，自引：0，他引：1
This paper investigates the equilibria, their stability, and the periodic orbits in the vicinity of a rotating dumbbell-shaped body. First, the geometrical model of dumbbell-shaped body is established. The gravitational potential fields are obtained by the polyhedral method for several dumbbell-shaped bodies with various length–diameter ratios. Subsequently, the equilibrium points of these dumbbell-shaped bodies are computed and their stabilities are analyzed. Periodic orbits around equilibrium points are determined by the differential correction method. Finally, in order to understand further motion characteristic of dumbbell-shaped body, the effect of the rotating angular velocity of the dumbbell-shaped bodies is investigated. This study extends the research work of the orbital dynamics from simple shaped bodies to complex shaped bodies and the results can be applied to the dynamics of orbits around some asteroids. 相似文献
8.
Richard Scuflaire 《Celestial Mechanics and Dynamical Astronomy》1998,71(3):203-228
We study the regular families of periodic orbits in an analytical planar galactic potential, using the method of Lindstedt.
We obtain analytical expressions describing these orbits, validity of which is not limited to small amplitudes. We can delimit,
in the space of the parameters, the domain of existence of each family of orbits.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
V. V. Markellos 《Celestial Mechanics and Dynamical Astronomy》1981,25(1):3-31
We study the generation of three-dimensional periodic orbits of the general three-body problem from special generating plane orbits, the vertical-critical orbits. The bifurcation process is examined analytically and geometrically. A method of obtaining numerically continuous sets of vertical-critical orbits is outlined, and applied for the determination of 16 monoparametric sets including all possible types of such orbits corresponding to all possible types of symmetry of the bifurcating three-dimensional orbits. The stability of all bifurcation orbits is assessed. Examples of three-dimensional periodic orbits generated from the bifurcation orbits are given. 相似文献
10.
Ireneusz Wlodarczyk 《Solar System Research》2012,46(4):301-312
We show how to calculate the impact orbits of dangerous asteroids using the freely available the OrbFit software, and compare our results with impact orbits calculated using Sitarski??s independent software (Sitarski, 1999; 2000; 2006). The new method is tested on asteroid 2009 FJ. Using the OrbFit package to integrate alternate orbits along the line of variation (Milani et al., 2002; 2005a; 2005b), we identify impact orbits and can plot paths of risk for the Earth or any other body in the Solar System. We present the orbital elements of asteroid 2009 FJ and its ephemerides, along with uncertainties, for the next 100 years. This paper continues a long-term research program on impact solutions for asteroids (Wlodarczyk, 2007; 2008; 2009). 相似文献
11.
A method for determining the main families of isolated periodic orbits and their characteristic exponents in planar potentials
which are separated by a point transformation is proposed. Since these orbits are continued analytically with the same stability,
these results are persistent under small perturbations. The method is applied to the two fixed centers problem, the Paul trap
and the dipole expansion of an electrostatic potential.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
M.J. Valtonen J.Q. Zheng S. Mikkola P. Nurmi H. Rickman 《Celestial Mechanics and Dynamical Astronomy》1997,69(1-2):89-102
There is a very large number of small bodies in the Solar System and their orbits are varied and complicated. Some types of
orbits and events are so rare that they occur in numerical simulations only when millions or billions of orbits have been
calculated. In order to study these orbits or events an efficient Monte Carlo simulation is useful. Here we describe a new
Monte Carlo simulation method and test it against some existing simulations of orbits of small bodies which have been obtained
by different methods. We find good agreement with many earlier calculations, and study briefly the possibility of the Oort
Cloud capture origin of short period comets.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
Hongsheng Zhao 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):187-194
Tremendous progress has been made recently in modelling the morphology and kinematics of centers of galaxies. Increasingly
realistic models are built for central bar, bulge, nucleus and black hole of galaxies, including our own. The newly revived
Schwarzschild method has played a central role in these theoretical modellings. Here I will highlights some recent work at
Leiden on extending the Schwarzschild method in a few directions. After a brief discussion of (i) an analytical approach to
include stochastic orbits (Zhao 1996), and (ii) the "pendulum effect" of loop and boxlet orbits (Zhao, Carollo, de Zeeuw 1999),
I will concentrate on the very promising (iii) spectral dynamics method, with which not only can one obtain semi-analytically
the actions of individual orbits as previously known, but also many other physical quantities, such as the density in configuration
space and the line-of-sight velocity distribution of a superposition of orbits (Copin, Zhao & de Zeeuw 1999). The latter method
also represents a drastic reduction of storage space for the orbit library and an increase in accuracy over the grid-based
Schwarzschild method.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
Sándor Molnár 《Celestial Mechanics and Dynamical Astronomy》1981,25(1):81-88
It is shown, that the potential obtained from Joukovsky's formula, corresponding to a given family of orbits is a general solution of Szebehely's equation. Then it is shown how a general solution of Szebehely's equation can be obtained from its particular solution. This method is applied to several examples. Potentials generating families of concentric elliptic orbits and families of orbits of conic sections are determined. Finally, the inverse Keplerian problem is solved using Szebehely's equation in polar coordinates. 相似文献
15.
In our work, the method that can help to predict the existence of distant objects in the Solar system is demonstrated. This
method is connected with statistical properties of a heliocentric orbital complex of meteoroids with high eccentricities.
Heliocentric meteoroid orbits with high eccentricities are escape routes for dust material from distant parental objects with
near-circular orbits to Earth-crossing orbits. Ground-based meteor observations yield trajectory information from which we
can derive their place of possible origin: comets, asteroids, and other objects (e.g. Kuiper Objects) in the Solar system
or even interstellar space. Statistical distributions of radius vectors of nodes, and other parameters of orbits of meteoroids
contain key information about position of greater bodies. We analyze meteor orbits with high eccentricities that were registered
in 1975–1976 in Kharkiv (Ukraine). The orbital data of the Kharkiv electronic catalogue are received from observations of
radiometeors with masses 10−6−10−3 g. 相似文献
16.
V. A. Shefer 《Celestial Mechanics and Dynamical Astronomy》2002,82(1):19-59
A method of construction of intermediate orbits for approximating the real motion of celestial bodies in the initial part of trajectory is proposed. The method is based on introducing a fictitious attracting centre with a time-variable gravitational parameter. The variation of thisparameter is assumed to obey the Eddington–Jeans mass-variationlaw. New classes of orbits having first-, second-, and third-order tangency to the perturbed trajectory at the initial instant of time are constructed. For planar motion, the tangency increases by one or two orders. The constructed intermediate orbits approximate the perturbed motion better than the osculating Keplerian orbit and analogous orbits of otherauthors. The applications of the orbits constructed in Encke's methodfor special perturbations and in the procedure for predicting themotion in which the perturbed trajectory is represented by a sequenceof short arcs of the intermediate orbits are suggested.The use of the constructed orbits is especially advantageous in the investigation of motion under the action of large perturbations. 相似文献
17.
The importance of the stability characteristics of the planar elliptic restricted three-body problem is that they offer insight
about the general dynamical mechanisms causing instability in celestial mechanics. To analyze these concerns, elliptic–elliptic
and hyperbolic–elliptic resonance orbits (periodic solutions with lower period) are numerically discovered by use of Newton's
differential correction method. We find indications of stability for the elliptic–elliptic resonance orbits because slightly
perturbed orbits define a corresponding two-dimensional invariant manifold on the Poincaré surface-section. For the resonance
orbit of the hyperbolic–elliptic type, we show numerically that its stable and unstable manifolds intersect transversally
in phase-space to induce instability. Then, we find indications that there are orbits which jump from one resonance zone to
the next before escaping to infinity. This phenomenon is related to the so-called Arnold diffusion.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
18.
The properties of chaos in 2D self-consistent models of barred galaxies are investigated using Kolmogorov-Sinai entropy hKS. These models are constructed with Schwarzschild's method which combines orbits as elementary building blocks.
Most models are dominated by chaos near the 2/3 of the length of the bar and close to corotation. These locations correspond
to regions where star forming HII regions are observed because gas clouds could shock, shrink and fragment such that star
formation could be ignited.
The model the most similar to N-body models shows a peak of hKS between the corners of the rectangular-like x1 orbits and the maximum extension points of the Lagrangian orbits. This emphasizes the role of Lagrangian orbits in the morphology
of bars. Most models essentially contain 'semi-chaotic' orbits confined inside the corotation.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
P. G. Kazantzis 《Astrophysics and Space Science》1978,57(2):499-509
The orbits of a family of three-dimensional periodic orbits in the restricted problem of three bodies form a surface. In this paper we determine the equation of this surface in the case of the orbits of double symmetry of the family which emanates from the equilibrium pointL
1. This equation is obtained numerically by a least squares approximation method. 相似文献
20.
Yu. D. Medvedev 《Solar System Research》2011,45(5):386-391
Observations at the first opposition are used to determine the orbits of 16 near-Earth asteroids with two or more observed
oppositions. The orbits are improved by the differential method. This paper considers two modifications of the improvement
technique, which are compared to the classical method based on the principle of the least square method (LSM). The first modification
uses the principle of least absolute deviations (LAD). In the second modification, the differences O - C (between the observed and calculated positions) are transformed to fit into a new coordinate system whereby the axes go parallel
and perpendicular to the asteroid’s apparent path (the modified differential method (MDM)). The orbits determined from one
opposition by the classical LSM, LAD, and MDM are compared to a more accurate orbit calculated by the LSM from all the available
oppositions. The calculations show that in 13 cases out of 16, the asteroid orbits calculated by LAD are more accurate than
those calculated by the classical LSM. The improvement by the modified differential method, which includes the O - C transformation, does not produce any perceptible increase in accuracy when compared to the orbits calculated by the classical
method. 相似文献