共查询到20条相似文献，搜索用时 31 毫秒
1.
We consider the Laplace's problem pertaining to occurrence probability of elliptical and hyperbolical orbits of comets, assuming various distributions of their velocities and variable initial conditions. Such approach seems to explain contradictory results obtained by different investigators and suggests that predominance of one type over the other type orbits, may result-among other-from assumed maximal velocity range of comets and their velocity distribution. 相似文献
2.
R. A. Serafin 《Celestial Mechanics and Dynamical Astronomy》1985,36(3):273-280
We consider the collision probability for comets with the Sun under the suppositions of different velocity distributions and various initial conditions. We solve the problem applying Laplace's method and using Schiaparelli's hyperboloid of visibility. The probabilities obtained in this manner are given separately for elliptic and hyperbolic orbits. 相似文献
3.
The calculation of collision probability is the foundation of collision detection and avoidance maneuver for space objects. Now an assumption of linear relative motion is usually applied in the calculation of collision probability and then the complex 3-dimensional problem can be reduced to a 2-dimensional integral of probability density function over the area of circle. However, if the relative velocity value is very small, the term of linear relative motion is not valid. So it is necessary to consider the calculation of collision probability for nonlinear relative motions. The method used to calculate collision probability for nonlinear relative motion is studied, and test cases are designed to justify the validity of this method. It is applicable to collision probability problems involving relative velocity and error covariance varying with time. The results indicate that it is necessary to calculate collision probability with this nonlinear method under certain circumstances. For example, for elliptical relative motions in Satellite Formation Flying, when the relative velocity is below 100 m/s, the relative error between the linear method and the nonlinear method exceeds 5%; for the problem of conjunction analysis of two satellites with circular orbits, when the relative velocity is below 10 m/s, the relative error is also larger than 1%. Some significant conclusions are obtained for the collision detection system of our country. 相似文献
4.
Burton B. Lieberman 《Celestial Mechanics and Dynamical Astronomy》1971,3(4):408-426
A rigorous proof is given for the existence of quasi-periodic solutions with only two degrees of freedom to a planar three-body problem. The solution corresponds physically to the small bodies moving on different, nearly elliptical orbits about a large mass located at a focus. The perihelia of the two orbits are locked in such a way that the difference of the two perihelia has mean value zero. 相似文献
5.
Demetrios D. Dionysiou 《Astrophysics and Space Science》1986,125(1):115-125
The average loss of energy over one period of the elliptical motion of the two-body system is given, within the quadrupole approximation, by using the relative motion in the post-Newtonian centre of the mass frame. More explicit formulae are derived for the elliptical orbits and detailed results are presented for the circular orbits assuming small orbital velocities compared to the velocity of light. On the other hand, using the defined Lagrangian we give the integrals of motion. 相似文献
6.
In this paper, the periodic orbits around triangular points in the range of linear stability of the restricted three body problem, when the smaller primary and the test particle have the shape of an oblate spheroid and the larger primary is a radiation emitter with the allowance for the gravitational potential from the belt, is studied. It is observed that the orbits around these points are elliptical and have long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits are found. The study includes some numerical examples in the case of the Sun-Earth and Sun-Jupiter systems. 相似文献
7.
In this paper we have found secular solutions at the triangular equilibrium point in the generalized photogravitational restricted
three body problem. The problem is generalised in the sense that smaller primary is an oblate spheroid and more massive primary
as source of radiation. The triangular point has long or short-period retrograde elliptical orbits. The critical mass parameter
decreases with the increase in oblateness and radiation pressure.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
Leon Blitzer 《Celestial Mechanics and Dynamical Astronomy》1987,42(1-4):215-222
A survey of classes of elliptical orbits outside the usual ones due to the attractive direct power and inverse square force laws reveals some extremely interesting orbits with surprising dynamical characteristics. Particular elliptical orbits of interest in celestial mechanics are discussed. 相似文献
9.
R. Capuzzo-Dolcetta A. Vicari 《Monthly notices of the Royal Astronomical Society》2005,356(3):899-912
The present work extends and deepens previous examinations of the evolution of globular cluster orbits in elliptical galaxies, by means of numerical integrations of a wide set of orbits in five self-consistent triaxial galactic models characterized by a central core and different axial ratios. These models are valid and complete in the representation of regular orbits in elliptical galaxies. Dynamical friction is definitely shown to be an efficient cause of evolution for the globular cluster systems in elliptical galaxies of any mass or axial ratio. Moreover, our statistically significant sample of computed orbits confirms that the globular cluster orbital decay times are, at least for clusters moving on box orbits, much shorter than the age of the galaxies. Consequently, the mass carried into the innermost galactic region in the form of decayed globular clusters may have contributed significantly to feeding and accreting a compact object therein. 相似文献
10.
Maria Gousidou-Koutita 《Earth, Moon, and Planets》1985,32(1):21-45
The present study deals with numerical modeling of the elliptic restricted three-body problem as well as of the perturbed elliptic restricted three-body (Earth-Moon-Satellite) problem by a fourth body (Sun). Two numerical algorithms are established and investigated. The first is based on the method of the series solution of the differential equations and the second is based on a 5th-order Runge-Kutta method. The applications concern the solution of the equations and integrals of motion of the circular and elliptical restricted three-body problem as well as the search for periodic orbits of the natural satellites of the Moon in the Earth-Moon system in both cases in which the Moon describes circular or elliptical orbit around the Earth before the perturbations induced by the Sun. After the introduction of the perturbations in the Earth-Moon-Satellite system the motions of the Moon and the Satellite are studied with the same initial conditions which give periodic orbits for the unperturbed elliptic problem. 相似文献
11.
Mir Abbas Jalali 《Monthly notices of the Royal Astronomical Society》1999,310(1):97-104
The bifurcations of orbit-averaged dynamics are studied in a class of razor-thin discs with central black holes. The model used here consists of a perturbed harmonic oscillator Hamiltonian augmented with a GM r potential. Through a sequence of conformal and canonical transformations, we reduce the phase-space flows of the system to a set of non-linear differential equations on a sphere. Based on the critical points of the averaged system, we classify orbit families and reveal the existence of six types of periodic motions: circular , long - and short-axis elliptical , long - and short-axis radial and inclined radial orbits. Long-axis elliptical orbits and their surrounding tubes have significant features: whilst they keep stars away from the centre, they elongate in the same direction as the density profile. These properties are helpful in the construction of self-consistent equilibria. 相似文献
12.
M. A. Vashkov’yak 《Astronomy Letters》2001,27(7):464-469
We consider the structural peculiarities of Uranus’s satellite system associated with its separation into two groups: inner equatorial satellites moving in nearly circular orbits and distant irregular satellites with retrograde motion in highly elliptical orbits. The intermediate region is free from satellites in a wide range of semimajor axes. By analyzing the evolution of satellite orbits under the combined effect of solar attraction and Uranus’s oblateness, we offer a celestial-mechanical explanation for the absence of equatorial satellites in this region. M.L. Lidov’s studies during 1961–1963 have served as a basis for our analysis. 相似文献
13.
Ram Krishan Sharma 《Astrophysics and Space Science》1987,135(2):271-281
This paper deals with the stationary solutions of the planar restricted three-body problem when the more massive primary is a source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. The collinear equilibria have conditional retrograde elliptical periodic orbits around them in the linear sense, while the triangular points have long- or short-periodic retrograde elliptical orbits for the mass parameter 0 < crit, the critical mass parameter, which decreases with the increase in oblateness and radiation force. Through special choice of initial conditions, retrograde elliptical periodic orbits exist for the case = crit, whose eccentricity increases with oblateness and decreases with radiation force for non-zero oblateness. 相似文献
14.
In a model galaxy composed of a relativistically active nucleus, a main body, and a halo, all three components considered
as homogeneous prolate ellipsoids, we explore the probable association of the internal characteristics of the nucleus and
the observed orbits of the stars near the surface of the main body. Using the authors’ theoretical framework of post-Newtonian
general relativistic galactic dynamics, proposed earlier, we prove that a fast-rotating and possibly expanding or contracting
nucleus affects the distribution of the box-type orbits near the surface of the main body resulting in a flattening of the
main body. The nuclear rotation always results in a flattening, and the contraction contributes less to the flattening than
the expansion. However, the contributions of a rotating and changing nucleus are not additive. The study of the post-Newtonian
effects in the nucleus on the stellar orbits in the main body, and the consequent modifications of the corresponding non-relativistic
results, could in principle provide useful information concerning the kinematical and dynamical characteristics of the nuclei
of the elliptical galaxies. The explanation (of at least the post-Newtonian part) of the flattening of elliptical galaxies
attempted here seems to be the first theoretical one proposed in the literature. 相似文献
15.
A solution to the fixed-time minimum-fuel two-impulse rendezvous problem for the general non-coplanar elliptical orbits is
provided. The optimal transfer orbit is obtained using the constrained multiple-revolution Lambert solution. Constraints consist
of lower bound for perigee altitude and upper bound for apogee altitude. The optimal time-free two-impulse transfer problem
between two fixed endpoints implies finding the roots of an eighth order polynomial, which is done using a numerical iterative
technique. The set of feasible solutions is determined by using the constraints conditions to solve for the short-path and
long-path orbits semimajor axis ranges. Then, by comparing the optimal time-free solution with the feasible solutions, the
optimal semimajor axis for the two fixed-endpoints transfer is identified. Based on the proposed solution procedure for the
optimal two fixed-endpoints transfer, a contour of the minimum cost for different initial and final coasting parameters is
obtained. Finally, a numerical optimization algorithm (e.g., evolutionary algorithm) can be used to solve this global minimization
problem. A numerical example is provided to show how to apply the proposed technique. 相似文献
16.
Solar System Research - Problems on optimizing the noncoplanar flights with low thrust from elliptical to geosynchronous orbits for different control accelerations are solved. Recommendations for... 相似文献
17.
Harry Varvoglis Vasiliki Sgardeli Kleomenis Tsiganis 《Celestial Mechanics and Dynamical Astronomy》2012,113(4):387-402
The recent discovery of free-floating planets and their theoretical interpretation as celestial bodies, either condensed independently or ejected from parent stars in tight clusters, introduced an intriguing possibility. Namely, that some exoplanets are not condensed from the protoplanetary disk of their parent star. In this novel scenario a free-floating planet interacts with an already existing planetary system, created in a tight cluster, and is captured as a new planet. In the present work we study this interaction process by integrating trajectories of planet-sized bodies, which encounter a binary system consisting of a Jupiter-sized planet revolving around a Sun-like star. To simplify the problem we assume coplanar orbits for the bound and the free-floating planet and an initially parabolic orbit for the free-floating planet. By calculating the uncertainty exponent, a quantity that measures the dependence of the final state of the system on small changes of the initial conditions, we show that the interaction process is a fractal classical scattering. The uncertainty exponent is in the range (0.2–0.3) and is a decreasing function of time. In this way we see that the statistical approach we follow to tackle the problem is justified. The possible final outcomes of this interaction are only four, namely flyby, planet exchange, capture or disruption. We give the probability of each outcome as a function of the incoming planet’s mass. We find that the probability of exchange or capture (in prograde as well as retrograde orbits and for very long times) is non-negligible, a fact that might explain the possible future observations of planetary systems with orbits that are either retrograde (see e.g. Queloz et?al. Astron. Astrophys. 417, L1, 2010) or tight and highly eccentric. 相似文献
18.
N. N. Myagkov 《Solar System Research》2012,46(2):144-148
Estimation is made of the possibility of clustering of debris particles in circular and elliptical orbits around the Earth
due to the change in drag, caused by quasi-periodic variations of the atmospheric density in the orbit. The estimations show
that the collective behavior of particles has time to be manifested in highly elliptical orbits, where the relative change
in the atmospheric density along the orbital path is greater and characteristic lifetimes of the particles are longer. However,
in this case the limit distributions of the particles are not realized, because the clusters form and break down several times
during the lifetime of the particles in the orbit. 相似文献
19.
C. S. Arnot C. R. McInnes R. J. McKay M. Macdonald J. Biggs 《Celestial Mechanics and Dynamical Astronomy》2018,130(2):12
This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill–Clohessy–Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The \(\Delta v\) requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology. 相似文献
20.
We formulate a completely three-dimensional nonstationary model of the thermal state and gas production rate of rotating spherical cometary nuclei moving in circular and elliptical orbits around the Sun. We perform a thermophysical analysis of the problem and formulate a system of similarity criteria. The possible thermal regimes of cometary nuclei are analyzed in the space of suggested similarity criteria. Only one criterion dependent on the nucleus spin period is shown to play a dominant role for rotating nuclei at a given heliocentric distance. This simplifies greatly a parametric study of the gas production rate of real cometary nuclei under conditions of uncertainty in their parameters. Based on the developed model, we numerically investigate the thermal state and gas production rate of rotating nuclei. The results of our calculations are in complete agreement with those of the similarity analysis for the problem. We perform a comparative analysis of the currently used simplified thermal models for cometary nuclei and determine the range of their applicability. 相似文献