共查询到20条相似文献，搜索用时 140 毫秒
1.
Sławomir Breiter 《Celestial Mechanics and Dynamical Astronomy》2000,77(3):201-214
The resonance C7 is a 1:1 eccentricity (apsidal) resonance between the longitude of a satellite's pericentre and the mean
longitude of the Sun. A previous paper by the author (Breiter, 1999) identified it as the strongest of the lunisolar apsidal
resonances. After the reduction to a single degree of freedom, the problem is studied qualitatively for the prograde orbits
around the Earth and Mars. Pitchfork, saddle-node, and saddle connection bifurcations give rise to a complicated phase flow,
which may involve up to nine critical points.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
Dimitri Veras 《Celestial Mechanics and Dynamical Astronomy》2014,118(4):315-353
Planetary, stellar and galactic physics often rely on the general restricted gravitational $N$ -body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted problem entirely and specifically in terms of the commonly used orbital elements of semimajor axis, eccentricity, inclination, longitude of ascending node, argument of pericentre, and true anomaly, without any assumptions about their magnitudes. I derive the equations of motion in the general, unaveraged case, as well as specific cases, with respect to both a bodycentric and barycentric origin. I then reduce the equations to three-body systems, and present compact singly- and doubly-averaged expressions which can be readily applied to systems of interest. This method recovers classic Lidov–Kozai and Laplace–Lagrange theory in the test particle limit to any order, but with fewer assumptions, and reveals a complete analytic solution for the averaged planetary pericentre precession in coplanar circular circumbinary systems to at least the first three nonzero orders in semimajor axis ratio. Finally, I show how the unaveraged equations may be used to express resonant angle evolution in an explicit manner that is not subject to expansions of eccentricity and inclination about small nor any other values. 相似文献
3.
We report results from long term numerical integrations and analytical studies of particular orbits in the circular restricted three-body problem. These are mostly high-inclination trajectories in 1 : 1 resonance starting at or near the triangular Lagrangian L5 point. In some intervals of inclination these orbits have short Lyapunov times, from 100 to a few hundred periods, yet the osculating semi-major axis shows only relatively small fluctuations and there are no escapes from the 1 : 1 resonance. The eccentricity of these chaotic orbits varies in an erratic manner, some of the orbits becoming temporarily almost rectilinear. Similarly the inclination experiences large variations due to the conservation of the Jacobi constant. We studied such orbits for up to 109 periods in two cases and for 106 periods in all others, for inclinations varying from 0° to 180°. Thus our integrations extend from thousands to 10 million Lyapunov times without escapes of the massless particle. Since there are no zero-velocity curves restricting the motion this opens questions concerning the reason for the persistence of the 1 : 1 resonant motion. In the theory sections we consider the mechanism responsible for the observed behavior. We derive the averaged 1 : 1 resonance disturbing function, to second order in eccentricity, to calculate a critical inclination found in the numerical experiment, and examine motion close to this inclination. The cause of the chaos observed in the numerical experiments appears to be the emergence of saddle points in the averaged disturbing potential. We determine the location of several such saddle points in the (, ) plane, with being the mean longitude difference and the argument of pericentre. Some of the saddle points are illustrated with the aid of contour plots of the disturbing function. Motion close to these saddles is sensitive to initial conditions, thus causing chaos.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
4.
Alan H. Jupp 《Celestial Mechanics and Dynamical Astronomy》1975,11(3):361-378
The behaviour of the argument of the pericentre is investigated for the orbit of an artificial satellite which is moving under the potential when the inclination of the orbit is close to thecritical value tan?1 2. The theory is developed to first order and it is applicable to all values of the eccentricity, with the exception of those in the neighbourhood of zero and unity. Four principal types of behaviour are noted and these are illustrated in appropriate phase-plane diagrams. It is shown that the two types which exhibit double libration in the argument of the pericentre are restricted to a relatively small domain in the (a, e)-plane of possible motions. Moreover, it is demonstrated that for double libration to occur it is necessary, but not sufficient, that \(e > \sqrt 6/13\) . The ranges of values of the inclination for which libration of the pericentre is a possibility are given for the more important cases. The general results are applied to the specific case of artificial Earth satellites whose orbits are inclined to the equator at angles close to the value of the critical inclination. 相似文献
5.
Xiaodong Liu Hexi Baoyin Xingrui Ma 《Celestial Mechanics and Dynamical Astronomy》2011,109(3):303-320
Frozen orbits are always important foci of orbit design because of their valuable characteristics that their eccentricity
and argument of pericentre remain constant on average. This study investigates quasi-circular frozen orbits and examines their
basic nature analytically using two different methods. First, an analytical method based on Lagrangian formulations is applied
to obtain constraint conditions for Martian frozen orbits. Second, Lie transforms are employed to locate these orbits accurately,
and draw the contours of the Hamiltonian to show evolutions of the equilibria. Both methods are verified by numerical integrations
in an 80 × 80 Mars gravity field. The simulations demonstrate that these two analytical methods can provide accurate enough
results. By comparison, the two methods are found well consistent with each other, and both discover four families of Martian
frozen orbits: three families with small eccentricities and one family near the critical inclination. The results also show
some valuable conclusions: for the majority of Martian frozen orbits, argument of pericentre is kept at 270° because J
3 has the same sign as J
2; while for a minority of ones with low altitude and low inclination, argument of pericentre can be kept at 90° because of
the effect of the higher degree odd zonals; for the critical inclination cases, argument of pericentre can also be kept at
90°. It is worthwhile to note that there exist some special frozen orbits with extremely small eccentricity, which could provide
much convenience for reconnaissance. Finally, the stability of Martian frozen orbits is estimated based on the trace of the
monodromy matrix. The analytical investigations can provide good initial conditions for numerical correction methods in the
more complex models. 相似文献
6.
The classical Öpik theory provides an estimate of the collision probability between two bodies on bound, heliocentric or planetocentric orbits under restrictive assumptions of: (i) constant eccentricity and inclination, and (ii) uniform circulation of the longitude of node and argument of pericenter. These assumptions are violated whenever either of the orbits has a large inclination with respect to the local Laplace plane or large eccentricity, and their motion is perturbed by an exterior (tidal) gravitational field of a planet or the Sun. In this situation, known as the Lidov–Kozai regime, the eccentricity and inclination values exhibit large and correlated oscillations. At the same time, the longitude of node and the argument of pericenter may have strongly nonlinear time evolution, with the latter being even bound to a small interval of values. Here we develop a new Öpik-type collision probability theory which is valid even for highly inclined and/or eccentric orbits of the projectile. We assume that the orbit of the target is circular and in the local Laplace plane. Such a generalized setting is necessary, as an example, to correctly estimate the terrestrial impact fluxes of sporadic micrometeoroids on high-inclination orbits (notably those from the toroidal source and the associated helion and anti-helion arcs). 相似文献
7.
G. A. J. Hussain C. Allende Prieto S. H. Saar M. Still 《Monthly notices of the Royal Astronomical Society》2006,367(4):1699-1708
We present surface spot maps of the K2V primary star in the pre-cataclysmic variable binary system, V471 Tau. The spot maps show the presence of large high-latitude spots located at the sub-white dwarf longitude region. By tracking the relative movement of spot groups over the course of four nights (eight rotation cycles), we measure the surface differential rotation rate of the system. Our results reveal that the star is rotating rigidly with a surface shear rate, dΩ= 1.6 ± 6 mrad d−1 . The single active star AB Dor has a similar spectral type, rotation period and activity level as the K star in V471 Tau, but displays much stronger surface shear (46 < dΩ < 58 mrad d−1 ) . Our results suggest that tidal locking may inhibit differential rotation; this reduced shear, however, does not affect the overall magnetic activity levels in active K dwarfs. 相似文献
8.
Fabienne Delhaise Alessandro Morbidelli 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):155-173
The luni-solar effects of a geosynchronous artificial satellite orbiting near the critical inclination is investigated. To tackle this four-degrees-of-freedom problem, a preliminary exploration separately analyzing each harmonic formed by a combination of the satellite longitude of the node and the Moon longitude of the node is opportune. This study demonstrates that the dynamics induced by these harmonics does not show resonance phenomena. In a second approach, the number of degrees of freedom is halved by averaging the total Hamiltonian over the two non-resonant angular variables. A semi-numerical method can now be applied as was done when considering solely the inhomogeneity of the geopotential (see Delhaise et Henrard, 1992). Approximate surfaces of section are constructed in the plane of the inclination and argument of perigee. The main effects of the Sun and Moon attractions compared to the terrestrial attraction alone are a strong increase in the amplitude of libration in inclination (from 0.6° to 3.2°) and a decrease of the corresponding libration period (from the order of 200 years to the order of 20 years).Research Assistant for the Belgian National Fund for Scientific Research 相似文献
9.
We study the effect of eccentricity and inclination on small amplitude librations around the equilibrium points L
4 and L
5 in the circular restricted three-body problem. We show that the effective libration centres can be displaced appreciably
from the equilateral configuration. The secular extrema of the eccentricity as a function of the argument of pericentre are
shifted by ∼25 °
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
J2 Invariant Relative Orbits for Spacecraft Formations 总被引：1，自引：0，他引：1
An analytic method is presented to establish J
2 invariant relative orbits. Working with mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the J2 influence. Two first order conditions are established between the differences in momenta elements (semi-major axis, eccentricity and inclination angle) that guarantee that the drift rates of two neighboring orbits are equal on the average. Differences in the longitude of the ascending node, argument of perigee and initial mean anomaly can be set at will, as long as they are setup in mean element space. For near polar orbits, enforcing both momenta element constraints may result in impractically large relative orbits. It this case it is shown that dropping the equal ascending node rate requirement still avoids considerable relative orbit drift and provides substantial fuel savings.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
11.
An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit. 相似文献
12.
Makoto Yoshikawa 《Celestial Mechanics and Dynamical Astronomy》1992,54(1-3):287-290
Motions of asteroids in mean motion resonances with Jupiter are studied in three-dimensional space. Orbital changes of fictitious asteroids in the Kirkwood gaps are calculated by numerical integrations for 105 – 106 years. The main results are as follows: (1) There are various motions of resonant asteroids, and some of them are very complicated and chaotic and others are regular. (2) The eccentricity of some asteroids becomes very large, and the variation of the inclination is large while the eccentricity is large. (3) In the 3:1 resonance, there is a long periodic change in the variation of the inclination, when (7 : ) is a simple ratio (7: longitude of perihelion, : longitude of node). (4) In the 7:3 resonance, the variation of the inclination of some resonant asteroids is so large that prograde motion becomes retrograde. Some asteroids in the 7:3 resonance can collide with the Sun as well as with the inner planets. 相似文献
13.
We have earlier investigated the surface structures of a late‐type, single, giant FK Com for the years 1994–1998 using Doppler imaging. These surface temperature maps revealed long‐lived active regions at high latitudes. Long‐term photometric observations also show that these active regions tend to occur at two permanent active longitudes which are 180 degrees apart from each other, and that the activity switches the longitude with an average period of about 3 years (the “flip‐flop” phenomenon). In this work we present new Doppler maps of FK Com obtained 1998‐2003 and light‐curve maps obtained 2002–2003. These new maps are investigated together with the earlier temperature maps and light‐curve maps, with an aim of further studying the active longitudes, “flip‐flop” phenomenon and surface differential rotation on FK Com. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
We analyze the interactions between Saturn's coorbital satellites, Janus and Epimetheus, and the outer edge of the A ring, which is presumably maintained by these moons at their 7:6 resonance. Using two distinct but conceptually related methods, we show that ring torques are driving these satellites into a tighter lock. Unless there is a counterbalancing force which we have neglected, their orbital configuration will evolve from the current horseshoe-type lock to one of tadpole orbits around a single Lagrange point in ～20 myr. This finding adds an additional member to the list of short time scale problems associated with the interactions between Saturn's rings and its inner moons 相似文献
15.
Donald H. Eckhardt 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):307-324
The acceleration of the mean lunar longitude has a small effect on the periods of most terms in a Fourier expansion of the longitude. There are several planetary perturbation terms that have small amplitudes, but whose periods are close to the resonant period of the lunar libration in longitude. Some of these terms are moving toward resonance, some are moving away from resonance, and the periods of those terms that do not include the Delaunay variables in their arguments are not moving. Because of its acceleration of longitude, the Moon is receding from the Earth, so the magnitude of the restoring torque that the Earth exerts on the rotating Moon is gradually attenuating; thus resonance itself is moving, but at a much slower rate than the periods of the accelerating planetary perturbations. There are five planetary perturbation terms from the ELP-2000 Ephemeris (with amplitudes of 0.00001 or greater) that have passed through resonance in the past two million years. One of them is of special interest because it appears to be the excitation source of a supposed free libration in longitude that has been detected by the lunar laser ranging experiment. The amplitude of the term is only 0.00021 but it could be the source of the 1 amplitude free libration term if the viscoelastic properties of the Moon are similar to those of the Earth. 相似文献
16.
The binary star 55 Cancri harbors at least five giant planets. The discovery of a possible dust disk around the primary of the system was announced in 1998 although it was later dismissed as an observational artifact induced by the presence of three background galaxies. However, the possible existence of an asteroid belt beyond 6 AU from the primary could not be excluded. The actual properties of a hypothetical outer asteroid belt around 55 Cancri A are likely to be the result of the gravitational influence of the outermost planets and gas drag during the late stages of the formation of the planetary system. Gaseous drag within a protoplanetary disk in a multiplanet context can induce resonant capture of solid material rather easily, triggering the formation of asteroid belts similar to our own transneptunian belt. In this paper we investigate this scenario using numerical simulations within the framework of the planar restricted four-body problem to find possible stable debris locations or additional planets around 55 Cancri A. Our results indicate that, beyond 55 Cancri d, only the 1:2 and 1:3 mean-motion resonances may be possible although the details of gas drag-induced resonant trapping depend strongly on the size of the particles, with larger particles being preferentially trapped farther away from the host star. For a primary of mass 0.94 M and i=53° we find solid particles submitted to confined chaos at 10.14 and 13.22 AU with average eccentricities 0.14 and 0.20, respectively. The argument of pericentre of the trapped particles is found to librate around π/2 with the pericentres of the two resonant structures nearly aligned. The resonance responsible for the inner ring effectively halts the migration of the particles. The outer structure resembles a rosette or separatrix orbit. Our calculations suggest that hypothetical planets or asteroid belts in these locations would be, in principle, dynamically stable. 相似文献
17.
The motion of Pluto is said to be chaotic in the sense that the maximum Lyapunov exponent is positive: the Lyapunov time (the inverse of the Lyapunov exponent) is about 20 million years. So far the longest integration up to now, over 845 million years (42 Lyapunov times), does not show any indication of a gross instability in the motion of Pluto. We carried out the numerical integration of Pluto over the age of the solar system (5.5 billion years ≈ 280 Lyapunov times). This integration also did not give any indication of chaotic evolution of Pluto. The divergences of Keplerian elements of a nearby trajectory at first grow linearly with the time and then start to increase exponentially. The exponential divergences stop at about 420 million years. The divergences in the semi-major axis and the mean anomaly ( equivalently the longitude and the distance) saturate. The divergences of the other four elements, the eccentricity, the inclination, the argument of perihelion, and the longitude of node still grow slowly after the stop of the exponential increase and finally saturate. 相似文献
18.
Assigning to the equivalent gravitational parameter of a two-body dynamic system, a periodic change of a small amplitude B and arbitrary frequency and phase, the behaviour of an elliptic-type orbit is studied. The first order (in B) perturbations of the orbital elements are determined by using Delaunay's canonical variables. According to the value of the ratio between oscillation frequency and dynamic frequency, three cases (non-resonant (NR), quasi-resonant (QR), and resonant (R) ones) are pointed out. The solution of motion equations shows that only in the QR and R cases there are elements (argument of pericentre and mean anomaly) affected by secular perturbations. The solutions are valid over prediction times of order of pericentre and mean anomaly) affected by secular perturbations. The solutions are valid over prediction times of order B−1 in the NR case and B−1/2 in the QR and R cases. 相似文献
19.
E. M. Alessi F. Deleflie A. J. Rosengren A. Rossi G. B. Valsecchi J. Daquin K. Merz 《Celestial Mechanics and Dynamical Astronomy》2016,125(1):71-90
We present the results of an extensive numerical exploration performed on the eccentricity growth in MEO associated with two possible end-of-life disposal strategies for GNSS satellites. The study calls attention to the existence of values of initial inclination, longitude of ascending node, and argument of perigee that are more advantageous in terms of long-term stability of the orbit. The important role of the initial epoch and a corresponding periodicity are also shown. The present investigation is influential in view of recent analytical and numerical developments on the chaotic nature of the region due to lunisolar perturbations, but also for the upcoming Galileo and BeiDou constellations. 相似文献
20.
M. A. Fardal P. Guhathakurta A. Babul A. W. McConnachie 《Monthly notices of the Royal Astronomical Society》2007,380(1):15-32
Published maps of red giant stars in the halo region of M31 exhibit a giant stellar stream to the south of this galaxy, as well as a giant 'shelf' to the northeast of M31's centre. Using these maps, we find that there is a fainter shelf of comparable size on the western side as well. By choosing appropriate structural and orbital parameters for an accreting dwarf satellite within the accurate M31 potential model of Geehan et al., we produce a very similar structure in an N -body simulation. In this scenario, the tidal stream produced at pericentre of the satellite's orbit matches the observed southern stream, while the forward continuation of this tidal stream makes up two orbital loops, broadened into fan-like structures by successive pericentric passages; these loops correspond to the north-eastern and western shelves. The tidal debris from the satellite also reproduces a previously observed 'stream' of counterrotating planetary nebulae and a related stream seen in red giant stars. The debris pattern in our simulation resembles the shell systems detected around many elliptical galaxies, though this is the first identification of a shell system in a spiral galaxy and the first in any galaxy close enough to allow measurements of stellar velocities and relative distances. We discuss the physics of these partial shells, highlighting the role played by spatial and velocity caustics in the observations. We show that kinematic surveys of the tidal debris will provide a sensitive measurement of M31's halo potential, while quantifying the surface density of debris in the shelves will let us reconstruct the original mass and time of disruption of the progenitor satellite. 相似文献