首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 31 毫秒
1.
The area of stable motion for fictitious Trojan asteroids around Uranus’ equilateral equilibrium points is investigated with respect to the inclination of the asteroid’s orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L 4 and L 5, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 × 109 years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 ≤ a ≤ 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids’ orbit was varied in the range 0° < i < 60° and the semimajor axes were fixed. It turned out that only four ‘windows’ of stable orbits survive: these are the orbits for the initial inclinations 0° < i < 7°, 9° < i < 13°, 31° < i < 36° and 38° < i < 50°. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.  相似文献   

2.
We investigated the stable area for fictive Trojan asteroids around Neptune’s Lagrangean equilibrium points with respect to their semimajor axis and inclination. To get a first impression of the stability region we derived a symplectic mapping for the circular and the elliptic planar restricted three body problem. The dynamical model for the numerical integrations was the outer Solar system with the Sun and the planets Jupiter, Saturn, Uranus and Neptune. To understand the dynamics of the region around L 4 and L 5 for the Neptune Trojans we also used eight different dynamical models (from the elliptic problem to the full outer Solar system model with all giant planets) and compared the results with respect to the largeness and shape of the stable region. Their dependence on the initial inclinations (0° < i < 70°) of the Trojans’ orbits could be established for all the eight models and showed the primary influence of Uranus. In addition we could show that an asymmetry of the regions around L 4 and L 5 is just an artifact of the different initial conditions.  相似文献   

3.
The orbits of real asteroids around the Lagrangian points L4 and L 5of Jupiter with large inclinations (i > 20°) were integrated for 50 Myrs. We investigated the stability with the aid of the Lyapunov characteristic exponents (LCE) but tested also two other methods: on one hand we integrated four neighbouring orbits for each asteroid and computed the maximum distance in every group, on the other hand we checked the variation of the Delaunay element H of the asteroid. In a second simulation – for a grid of initial eccentricity versus initial inclination – we examined the stability of the orbits around both Lagrangian points for 20° < i < 55° and 0.0 < e < 0.20. For the initial semimajor axes we have chosen the one ofJupiter(a = 5.202 AU). We determined the stability with the aid of the LCEs and also the maximum eccentricity of the orbits during the whole integration time. The region around L4 turned out to be unstable for large inclinations and eccentricities (i > 55° and e > 0.12). The stable region shrinks for orbits around L5: we found that they become unstable already for i > 45° and e > 0.10. We interpret it as a first hint why we observe more Trojans around the leading Lagrangian point. The results confirm the stability behaviour of the real Trojans which we computed in the first part of the paper.  相似文献   

4.
Trojan asteroids undergo very large perturbations because of their resonance with Jupiter. Fortunately the secular evolution of quasi circular orbits remains simple—if we neglect the small short period perturbations. That study is done in the approximation of the three dimensional circular restricted three-body problem, with a small mass ratio μ—that is about 0.001 in the Sun Jupiter case. The Trojan asteroids can be defined as celestial bodies that have a “mean longitude”, M + ω + Ω, always different from that of Jupiter. In the vicinity of any circular Trojan orbit exists a set of “quasi-circular orbits” with the following properties: (A) Orbits of that set remain in that set with an eccentricity that remains of the order of the mass ratio μ. (B) The relative variations of the semi-major axis and the inclination remain of the order of ${\sqrt{\mu}}$ . (C) There exist corresponding “quasi integrals” the main terms of which have long-term relative variations of the order of μ only. For instance the product c(1 – cos i) where c is the modulus of the angular momentum and i the inclination. (D) The large perturbations affect essentially the difference “mean longitude of the Trojan asteroid minus mean longitude of Jupiter”. That difference can have very large perturbations that are characteristics of the “horseshoes orbit”. For small inclinations it is well known that this difference has two stable points near ±60° (Lagange equilibrium points L4 and L5) and an unstable point at 180° (L3). The stable longitude differences are function of the inclination and reach 180° for an inclination of 145°41′. Beyond that inclination only one equilibrium remains: a stable difference at 180°.  相似文献   

5.
A number of Jupiter family comets such as Otermaand Gehrels 3make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L 1and L 2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L 1and L 2is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L 1and the other around L 2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold tubes associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.  相似文献   

6.
H. Scholl  F. Marzari 《Icarus》2005,175(2):397-408
In this paper we explore the dynamical stability of the Mars Trojan region applying mainly Laskar's Frequency Map Analysis. This method yields the chaotic diffusion rate of orbits and allows to determine the most stable regions. It also gives the frequencies which are responsible for the instability of orbits. The most stable regions are found for inclinations between about 15° and 30°. For inclinations smaller than 15°, we confirm, by applying a synthetic secular theory, that the secular resonances ν3, ν4, ν13, ν14 rapidly excite asteroid orbits within a few Myrs, or even faster. The asteroids are removed from the Trojan region after a close encounter with Mars. For large inclinations, the secular resonance ν5 clears a small region around 30° while the Kozai resonance rapidly removes bodies for inclinations larger than 35°. The dynamical lifetimes of the three L5 Trojans, (5261) Eureka, 1998 VF31, 2001 DH47, and the only L4 Trojan 1999 UJ7 are determined by numerically integrating clouds of corresponding clones over the age of the Solar System. All four Trojans reside in the most stable region with smallest diffusion coefficients. Their dynamical half-lifetime is of the order of the age of the Solar System. The Yarkovsky force has little effect on the known Trojans but for bodies smaller than about 1-5 m the drag is strong enough to destabilize Trojans on a timescale shorter than 4.5 Gyr.  相似文献   

7.
Due to various perturbations, the collinear libration points of the real Earth–Moon system are not equilibrium points anymore. Under the assumption that the Moon’s motion is quasi-periodic, special quasi-periodic orbits called dynamical substitutes exist. These dynamical substitutes replace the geometrical collinear libration points as time-varying equilibrium points. In the paper, the dynamical substitutes of the three collinear libration points in the real Earth–Moon system are computed. For the points L 1 and L 2, linearized motions around the dynamical substitutes are described, and the variational equations of the dynamical substitutes are reduced to a form with a near constant coefficient matrix. Then higher order analytical formulae of the central manifolds are constructed. Using these analytical solutions as initial seeds, Lissajous orbits and halo orbits are computed with numerical algorithms.  相似文献   

8.
In the restricted circular three-body problem, two massive bodies travel on circular orbits about their mutual center of mass and gravitationally perturb the motion of a massless particle. The triangular Lagrange points, L4 and L5, form equilateral triangles with the two massive bodies and lie in their orbital plane. Provided the primary is at least 27 times as massive as the secondary, orbits near L4 and L5 can remain close to these locations indefinitely. More than 2200 cataloged asteroids librate about the L4 and L5 points of the Sun-Jupiter system, and five bodies have been discovered around the L4 point of the Sun-Neptune system. Small satellites have also been found librating about the L4 and L5 points of two of Saturn's moons. However, no objects have been discovered around the Earth-Moon L4 and L5 points. Using numerical integrations, we show that orbits near the Earth-Moon L4 and L5 points can survive for over a billion years even when solar perturbations are included, but the further addition of the far smaller perturbations from other planets destabilize these orbits within several million years. Thus, the lack of observed objects in these regions cannot be used as a constraint on Solar System formation, nor on the tidal evolution of the Moon's orbit.  相似文献   

9.
We studied systematically cases of the families of non-symmetric periodic orbits in the planar restricted three-body problem. We took interesting information about the evolution, stability and termination of bifurcating families of various multiplicities. We found that the main families of simple non-symmetric periodic orbits present a similar dynamical structure and bifurcation pattern. As the Jacobi constant changes each branch of the characteristic of a main family spirals around a focal point-terminating point in x- at which the Jacobi constant is C ∞ = 3 and their periodic orbits terminate at the corotation (at the Lagrangian point L4 or L5). As the family approaches asymptotically its termination point infinite changes of stability to instability and vice versa occur along its characteristic. Thus, infinite bifurcation points appear and each one of them produces infinite inverse Feigenbaum sequences. That is, every bifurcating family of a Feigenbaum sequence produces the same phenomenon and so on. Therefore, infinite spiral characteristics appear and each one of them generates infinite new inner spirals and so on. Each member of these infinite sets of the spirals reproduces a basic bifurcation pattern. Therefore, we have in general large unstable regions that generate large chaotic regions near the corotation points L4, L5, which are unstable. As C varies along the spiral characteristic of every bifurcating family, which approaches its focal point, infinite loops, one inside the other, surrounding the unstable triangular points L4 or L5 are formed on their orbits. So, each terminating point corresponds to an asymptotic non-symmetric periodic orbit that spirals into the corotation points L4, L5 with infinite period. This is a new mechanism that produces very large degree of stochasticity. These conclusions help us to comprehend better the motions around the points L4 and L5 of Lagrange.  相似文献   

10.
We have numerically investigated the stability of retrograde orbits/trajectories around Jupiter and the smaller of the primaries in binary systems RW-Monocerotis (RW-Mon) and Krüger-60 in the presence of radiation. A trajectory is considered as stable if it remains around the smaller mass for at least few hundred binary periods. In case of circular binary orbit, we find that the third order resonance provides the basis for reduction of stability region of retrograde motion of particle in RW-Mon and Sun-Jupiter system both in the presence and absence of radiation. Considering finite ellipticity in Sun-Jupiter system we find that for distant retrograde orbits, radiation from the Sun increases the width of the stable region and covers a significant portion of the region obtained in the absence of solar radiation. Further, due to solar radiation pressure, the stable region in the neighborhood of Jupiter has been found to shift much below the characteristic asymptotic line for the periodic retrograde orbits. In case of Krüger-60 we observe the distant retrograde orbits around the smaller of the primaries get affected considerably with increase in radiation parameter β1. Further the range of velocities for which stable motion may persist narrows down for distant retrograde orbits in this system.  相似文献   

11.
Orbital resonances tend to force bodies into noncircular orbits. If a body is also under the influence of an eccentricity-reducing medium, it will experience a secular change in semimajor axis which may be positive or negative depending on whether its orbit is exterior or interior to that of the perturbing body. Thus a dissipative medium can promote either a loss or a gain in orbital energy. This process may explain the resonant structure of the asteroid belt and of Saturn's rings. For reasonable early solar system parameters, it would clear a gap near the 2:1 resonance with Jupiter on a time scale of a few thousand years; the gap width would be comparable to the Kirkwood gap presently at the location in the asteroid belt. Similarly, a gap comparable in width to Cassini's division would be cleared in Saturn's rings at the 2:1 resonance with Mimas in ～106 yr. Most of the material from the gap would be deposited at the outer edge of ring B. The process would also affect the radial distribution of preplanetary material. Moreover, it provides an explanation for the large amplitude of the Titan-Hyperion libration. Consideration of the effects of dissipation on orbits near the stable L4 and L5 points of the restricted three-body problem indicates that energy loss causes particles to move away from these points. This results explains the large amplitude of Trojan asteroids about these points and the possible capture of Trojan into orbit about Jupiter.  相似文献   

12.
By using Birkhoff's regularizing transformation, we study the evolution of some of the infinite j-k type families of collision periodic orbits with respect to the mass ratio μ as well as their stability and dynamical structure, in the planar restricted three-body problem. The μ-C characteristic curves of these families extend to the left of the μ-C diagram, to smaller values of μ and most of them go downwards, although some of them end by spiralling around the constant point S* (μ=0.47549, C=3) of the Bozis diagram (1970). Thus we know now the continuation of the families which go through collision periodic orbits of the Sun-Jupiter and Earth-Moon systems. We found new μ-C and x-C characteristic curves. Along each μ-C characteristic curve changes of stability to instability and vice versa and successive very small stable and very large unstable segments appear. Thus we found different types of bifurcations of families of collision periodic orbits. We found cases of infinite period doubling Feigenbaum bifurcations as well as bifurcations of new families of symmetric and non-symmetric collision periodic orbits of the same period. In general, all the families of collision periodic orbits are strongly unstable. Also, we found new x-C characteristic curves of j-type classes of symmetric periodic orbits generated from collision periodic orbits, for some given values of μ. As C varies along the μ-C or the x-C spiral characteristics, which approach their focal-terminating-point, infinite loops, one inside the other, surrounding the triangular points L4 and L5 are formed in their orbits. So, each terminating point corresponds to a collision asymptotic symmetric periodic orbit for the case of the μ-C curve or a non-collision asymptotic symmetric periodic orbit for the case of the x-C curve, that spiral into the points L4 and L5, with infinite period. All these are changes in the topology of the phase space and so in the dynamical properties of the restricted three-body problem.  相似文献   

13.
The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T J = T S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β1 ≈ 0.8403504° (Saturn) and β2 ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.  相似文献   

14.
In a previous paper (Hou et al. in Celest Mech Dyn Astron 119:119–142, 2014a), the problem of dynamical symmetry between two Jupiter triangular libration points (TLPs) with Saturn’s perturbation in the present configuration of the two planets was studied. A small short-time scale spatial asymmetry exists but gradually disappears with the time going, so the planar stable regions around the two Jupiter TLPs should be dynamically symmetric from a longtime perspective. In this paper, the symmetry problem is studied when the two planets are in migration. Several mechanisms that can cause asymmetries are discussed. Studies show that three important ones are the large short-time scale spatial asymmetry when Jupiter and Saturn are in resonance, the changing orbits of Jupiter and Saturn in the planet migration process, and the chaotic nature of Trojan orbits during the planet migration process. Their joint effects can cause an observable difference to the two Jupiter Trojan swarms. The thermal Yarkovsky effect is also found to be able to cause dynamical differences to the two TLPs, but generally they are too small to be practically observed.  相似文献   

15.
The character of orbital evolution for bodies moving near the if 1 : 3 commensurability with Jupiter was studied by model calculations for the time interval of ～500 years. A comparison of oscillations of the orbital elements a, e, q and q′ is made for ensembles of bodies along three starting orbits in the vicinity of the sharp commensurability with Jupiter. These orbits are eccentric ones of low inclinations having perihelia near the Earth's orbit. Examples of a deceleration of the rate of orbital evolution near the sharp commensurability are revealed. The existence of a group of asteroids connected with the Kirkwood gap, i.e., being in a resonant motion with Jupiter, is suggested. A connection of asteroids 887 Alinda and 1915 Quetzalcoatl with this gap is confirmed.  相似文献   

16.
Of the three collinear libration points of the Sun–Earth Circular Restricted Three-Body Problem (CR3BP), L3 is that located opposite to the Earth with respect to the Sun and approximately at the same heliocentric distance. Whereas several space missions have been launched to the other two collinear equilibrium points, i.e., L1 and L2, taking advantage of their dynamical and geometrical characteristics, the region around L3 is so far unexploited. This is essentially due to the severe communication limitations caused by the distant and permanent opposition to the Earth, and by the gravitational perturbations mainly induced by Jupiter and the close passages of Venus, whose effects are more important than those due to the Earth. However, the adoption of a suitable periodic orbit around L3 to ensure the necessary communication links with the Earth, or the connection with one or more relay satellites located at L4 or L5, and the simultaneous design of an appropriate station keeping-strategy, would make it possible to perform valuable fundamental physics and astrophysics investigations from this location. Such an opportunity leads to the need of studying the ways to transfer a spacecraft (s/c) from the Earth’s vicinity to L3. In this contribution, we investigate several trajectory design methods to accomplish such a transfer, i.e., various types of two-burn impulsive trajectories in a Sun-s/c two-body model, a patched conics strategy exploiting the gravity assist of the nearby planets, an approach based on traveling on invariant manifolds of periodic orbits in the Sun–Earth CR3BP, and finally a low-thrust transfer. We examine advantages and drawbacks, and we estimate the propellant budget and time of flight requirements of each.  相似文献   

17.
The regions of quasi-periodic motion around non-symmetric periodic orbits in the vicinity of the triangular equilibrium points are studied numerically. First, for a value of the mass parameter less than Routh's critical value, the stability regions determined by quasi-periodic motion are examined around the existing families of short (Ls 4) and long (Ll 4) period solutions. Then, for two values of μ greater than the Routh value, the unified family Lsl 4, to which, in these cases, Ls 4 and Ll 4 merge, is considered. It is found that such regions surround in general the linearly stable segments of the corresponding families and become smaller as the mass ratio increases. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

18.
  相似文献   

19.
The third-order parametric expansions given by Buck in 1920 for the three-dimensional periodic solutions about the triangular equilibrium points of the restricted Problem are improved by fourthorder terms. The corresponding family of periodic orbits, which are symmetrical w.r.t. the (x, y) plane, is computed numerically for =0.00095. It is found that the family emanating from L4 terminates at the other triangular point L5 while it bifurcates with the family of three-dimensional periodic orbits originating at the collinear equilibrium point L3. This family consists of stable and unstable members. A second family of nonsymmetric three-dimensional periodic orbits is found to bifurcate from the previous one. It is also determined numerically until a collision orbit is encountered with the computations.  相似文献   

20.
To identify temporal variations of the characteristics of Jupiter’s cloud layer, we take into account the geometric modulation caused by the rotation of the planet and planetary orbital motion. Inclination of the rotation axis to the orbital plane of Jupiter is 3.13°, and the angle between the magnetic axis and the rotation axis is β ≈ 10°. Therefore, over a Jovian year, the jovicentric magnetic declination of the Earth φ m varies from–13.13° to +13.13°, and the subsolar point on Jupiter’s magnetosphere is shifted by 26.26° per orbital period. In this connection, variations of the Earth’s jovimagnetic latitude on Jupiter will have a prevailing influence in the solar-driven changes of reflective properties of the cloud cover and overcloud haze on Jupiter. Because of the orbit eccentricity (e = 0.048450), the northern hemisphere receives 21% greater solar energy inflow to the atmosphere, because Jupiter is at perihelion near the time of the summer solstice. The results of our studies have shown that the brightness ratio A j of northern to southern tropical and temperate regions is an evident factor of photometric activity of Jupiter’s atmospheric processes. The analysis of observational data for the period from 1962 to 2015 reveals the existence of cyclic variations of the activity factor A j of the planetary hemispheres with a period of 11.86 years, which allows us to talk about the seasonal rearrangement of Jupiter’s atmosphere.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号