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1.
In a previous paper, a semi-analytical solution for the long-term motion of Pluto was presented. The present paper contains: (1) a comparison of the present solution with the solution by Williams and Benson; (2) a discussion of the effect of the near resonance between Pluto and Uranus; and, (3) a calculation of the librational period of the eccentricity, inclination and perihelion.The semi-analytical solution is shown to agree very closely with the long-term solution for Pluto obtained by Williams and Benson using numerical integration of the averaged equations of motion. A small difference between the two solutions is attributed to neglecting the eccentricity and inclination of Neptune in the semi-analytical solution. 相似文献
2.
1992年以来，在海王星外的太阳系发现了近千个小天体，称为Kuiper带天体(KBO)或Edgeworth—Kuiper带天体，其中有一部分偏心率和倾角较大的小天体与海王星之间存在3：2平运动共振，轨道特征类似冥王星，命名为类冥王星，自KBO发现以来，天文学家们进行了多次小天区的搜索，发现了几个质量较大的KBO，通过数值计算，在轨道参数空间发现了两个和冥王星一样同时具有3种共振的区域，在这两个区域里的小天体既避免了海王星的强摄动又不会与冥王星密切交会，轨道非常稳定，因此有可能在其中发现质量较大的类冥王星。 相似文献
3.
Kuiper带天体的轨道动力学 总被引：1，自引：0，他引：1
主要评述太阳系动力学研究的一个新方向——Kuiper带的轨道动力学。早期的研究是为了探讨短周期彗星的起源。在发现第一颗Kuiper带小天体之后，人们开始将注意力转到Kuiper带共振区的相空间结构上，Morbidelli和Malhotra分别采用不同的模型研究了这些共振区的大小。其中主要研究对象是3:2共振区。冥王星也处在这一共振区中。从冥王星的轨道特性来看，冥王星应是一颗较大的Kuiper带天体，它还拥有另外两种共振——Kozai共振和1：1超级共振。正是由于这些共振的存在，冥王星的运动才得以长期保持稳定。观测表明许多Kuiper带天体也处的海王星的平运动共振中。早期的理论认为这些平运动共振起源于灾难性事件，如碰撞。然而这都是一些小概率事件，无法对共振的形成进行合理的解释。Malhotra通过行星迁移成功地解释了冥王星被共振俘获的机制。这一机制的概率非常大，同样可以用来解释Kuiper带天体共振的形成。 相似文献
4.
R. R. Allan 《Planetary and Space Science》1967,15(12):1829-1845
For a satellite in a nominally circular orbit at arbitrary inclination whose mean motion is commensurable with the Earth's rotation, the dependence of gravity on longitude leads to a resonant variation in eccentricity as well as the long-period oscillation in longitude. Provided forces capable of processing perigee are present, it is shown that the change in eccentricity for a satellite captured in librational resonance is not secular but periodic.
There are corresponding resonance effects for a satellite in a nominally equatorial but eccentric orbit. Here the commensurability condition is that the longitudes of the apses shall be nearly repetitive relative to the rotating Earth. There will be a long-period oscillation in longitude which can take the form of either a libration (trapped) or a circulation (free), and there will also be an oscillation of the orbital plane having the same period as the precession of perigee relative to inertial space. 相似文献
5.
Paul Nacozy 《Celestial Mechanics and Dynamical Astronomy》1980,22(1):19-23
A review is given of the determination of the long-term motion of Pluto. In particular, the discovery of the librational character of the two critical arguments is discussed. The stability of the motion of Pluto is shown to have been established when allknown gravitational forces are considered.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978. 相似文献
6.
Gp. Horedt 《Icarus》1974,23(3):459-464
The equations of the plane circular restricted three-body problem are integrated in the case of an exponential mass variation of the small primary m for a particle librating around the tringular point and for a satellite of m. For a mass variation by a factor of 20, the librational amplitude of the particle shows no appreciable variation. The satellite escapes towards the regions inside the orbit of m, provided that the mass loss rate is sufficiently slow. Extrapolating these results to the real solar system, it seems unlikely that Jupiter's Trojans are former Jovian sattelites which escaped because of mass loss of proto-Jupiter. It also seems improbable that Pluto escaped from Neptune due to a proto-Neptunian mass loss. 相似文献
7.
David Parry Rubincam 《Celestial Mechanics and Dynamical Astronomy》1977,15(1):21-33
The motion of a satellite with negligible mass in the Schwarzschild metric is treated as a problem in Newtonian physics. The relativistic equations of motion are formally identical with those of the Newtonian case of a particle moving in the ordinary inverse-square law field acted upon by a disturbing function which varies asr ?3. Accordingly, the relativistic motion is treated with the methods of celestial mechanics. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted into Lagrange's planetary equations. Integration of the equations shows that a typical Earth satellite with small orbital eccentricity is displaced by about 17 cm from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. Application of the equations to the planet Mercury gives the advance of the perihelion and a total displacement of about 85 km after one orbit, with a maximum periodic displacement of about 13 km. 相似文献
8.
Three resonances, the 3:2 exterior mean motion resonance with Neptune, Kozai resonance and 1:1 super resonance, are known to govern concurrently the stability of the motion of Pluto. We explore numerically the resonance zones in which the three resonance coexist. There might exist plutinos with relatively large masses in these zones. Considering that Pluto's perturbation is important to the long-term evolution of plutinos, the resonance zone is mainly explored in the mirror region of Pluto, which is a mirror image of the region around Pluto with respect to the invariant plane of the solar system. We find six resonance zones in the mirror region. The orbit elements at the centers of the six zones and the corresponding heliocentric distances, longitudes and latitudes on July 1, 2003 have been computed and listed for the reference of observation. 相似文献
9.
P. J. Message 《Celestial Mechanics and Dynamical Astronomy》1973,8(2):217-217
Saturn's satellite Hyperion experiences large perturbations by Titan, the largest of Saturn's satellites, because of the closeness of Hyperion's orbital period to three-quarters of that of Titan.The motion of Hyperion is a superposition of periodic fluctuations (both free and forced) onto a motion which is periodic in a suitable uniformly rotating frame of reference, and in which Hyperion would be at a maximum distance from Saturn at each conjunction with Titan.Successive attempts to determine the mass of Titan from observed perturbations of Hyperion have suffered from omissions in the theory of terms subsequently found to be significant.An attempt is in progress which, it is believed, comprises all long-period changes in the osculating elements which are of second degree in the mass of Titan, and of third degree in the eccentricity of its orbit. Results so far obtained indicate that the period of the free motion of the orbit plane of Hyperion is better determined by Woltjer's reduction of the observations than by his theoretical calculations.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972. 相似文献
10.
Winston L. Sweatman 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):37-65
We locate members of an important category of periodic orbits in the Newtonian four-body problem. These systems perform an interplay motion similar to that of the periodic three-body orbit discovered by Schubart. Such orbits, when stable, have been shown to be a key feature and influence on the dynamics of few-body systems. We consider the restricted case where the masses are collinear and are distributed symmetrically about their centre of mass. A family of orbits is generated from the known (three-dimensionally) unstable equal masses case by varying the mass ratio, whilst maintaining the symmetry. The stability of these orbits to perturbation is studied using linear stability analysis, analytical approximation of limiting cases and nonlinear simulation. We answer the natural question: are there any stable periodic orbits of this kind? Three ranges of the mass ratio are found to have stable orbits and three ranges have unstable orbits for three-dimensional motion. The systems closely resemble their three-body counterparts. Here the family of interplay orbits is simpler requiring just one parameter to characterise the mass ratio. Our results provide a further insight into three-body orbits studied previously. 相似文献
11.
E. I. Timoshkova 《Solar System Research》2008,42(1):28-34
The orbital evolution of the near-Earth asteroid (NEA) 30825 1990 TG1 has been studied by numerical integration of the equations of its motion over the 100 000-year time interval with allowance for perturbations from eight major planets and Pluto, and the variations in its osculating orbit over this time interval were determined. The numerical integrations were performed using two methods: the Bulirsch-Stoer method and the Everhart method. The comparative analysis of the two resulting orbital evolutions of motion is presented for the time interval examined. The evolution of the asteroid motion is qualitatively the same for both variants, but the rate of evolution of the orbital elements is different. Our research confirms the known fact that the application of different integrators to the study of the long-term evolution of the NEA orbit may lead to different evolution tracks. 相似文献
12.
S. Alan Stern 《Celestial Mechanics and Dynamical Astronomy》1989,47(3):267-273
We investigate the potential importance of molecular cloud and stellar perturbations on the orbits of Pluto and more distant (hypothetical) planets up to 500 AU from the Sun. It is found that stellar and molecular cloud-core perturbations are of roughly equal importance. It also is found that the likelihood of substantial perturbations on Pluto is not insignificant, and that numerous substantial stellar and molecular cloud perturbations are likely to have influenced the orbits of any planets beyond 200 AU. These perturbations may contribute to a prevalence of moderate eccentricities and inclinations for planets beyond the orbit of Neptune, and may be a characteristic of distant planetary orbits in other solar systems. Given the recent discovery of chaotic behavior in Pluto's orbit (Sussman and Wisdom 1988), the effects of external perturbations on the long-term stability of Pluto's orbit warrant continued study. 相似文献
13.
J.G. Williams 《Icarus》1984,57(1):1-13
The orbit of Mars is perturbed more than 5 m, a value compatible with the accuracy of the Viking lander ranging data, by about three dozen asteroids. In addition to larger asteroids throughout the belt, significant perturbations of long period are generated by smaller objects near commensurabilities with Mars. The largest periodic terms induced by 1 Ceres and 2 Pallas have amplitudes of 0.8 and 0.2 km, respectively, both with 10-year periods. Due to a near commensurability, 4 Vesta causes a 5-km, 52-year term. While the Viking ranges will yield significant mass determinations for the largest three asteroids, and some of the smaller bodies should be detectable, it will be difficult to seperate the smaller bodies with useful accuracies. Accurate discrimination must await range data from future missions to Mars or other bodies in the neighborhood of the asteroid belt. The Viking ranges can also yield improved masses for the outer planets (except Pluto), an application which is being exploited by groups analyzing these data. Uncertainties in the asteroid masses limit the ultimate accuracy of the Viking determinations of both the long time scale motion of the system the inner four planets with respect to an inertial frame and the rate of change of the gravitational constant. 相似文献
14.
Vladimir Pletser 《Earth, Moon, and Planets》1989,46(3):285-295
The comparison of masses and sizes of the Neptunian satellites and of Pluto and Charon to the secondaries of the planetary, Jovian, Saturnian and Uranian systems support the hypotheses, first, that an initial Neptune's satellite system may have been disrupted, second, that Triton may have been the system perturber and, third, that Pluto (or a parent body of Pluto and Charon) was initially a giant satellite of Neptune. Based on recent theoretical works on perturbed proto-planetary nebula and noting the similarity of some characteristics of Neptune and Uranus, a theoretical mean distance ratio of primeval gaseous rings around Neptune is tentatively deduced to be about 1.475, close to the value of the Uranian system. An exponential distance relation gives possible ranges of distances at which small satellites and/or ring structures could be found by Voyager 2, close to Neptune. 相似文献
15.
Marco Giancotti Mauro Pontani Paolo Teofilatto 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):55-76
Analysis and design of low-energy transfers to the Moon has been a subject of great interest for many decades. This paper is concerned with a topological study of such transfers, with emphasis to trajectories that allow performing lunar capture and those that exhibit homoclinic connections, in the context of the circular restricted three-body problem. A fundamental theorem stated by Conley locates capture trajectories in the phase space and can be condensed in a sentence: “if a crossing asymptotic orbit exists then near any such there is a capture orbit”. In this work this fundamental theoretical assertion is used together with an original cylindrical isomorphic mapping of the phase space associated with the third body dynamics. For a given energy level, the stable and unstable invariant manifolds of the periodic Lyapunov orbit around the collinear interior Lagrange point are computed and represented in cylindrical coordinates as tubes that emanate from the transformed periodic orbit. These tubes exhibit complex geometrical features. Their intersections correspond to homoclinic orbits and determine the topological separation of long-term lunar capture orbits from short-duration capture trajectories. The isomorphic mapping is proven to allow a deep insight on the chaotic motion that characterizes the dynamics of the circular restricted three-body, and suggests an interesting interpretation, and together corroboration, of Conley’s assertion on the topological location of lunar capture orbits. Moreover, an alternative three-dimensional representation of the phase space is profitably employed to identify convenient lunar periodic orbits that can be entered with modest propellant consumption, starting from the Lyapunov orbit. 相似文献
16.
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
17.
18.
P. Delibaltas 《Astrophysics and Space Science》1976,45(1):207-233
Several families of planar planetary-type periodic orbits in the general three-body problem, in a rotating frame of reference, for the Sun-Jupiter-Saturn mass-ratio are found and their stability is studied. It is found that the configuration in which the orbit of the smaller planet is inside the orbit of the larger planet is, in general, more stable.We also develop a method to study the stability of a planar periodic motion with respect to vertical perturbations. Planetary periodic orbits with the orbits of the two planets not close to each other are found to be vertically stable. There are several periodic orbits that are stable in the plane but vertically unstable and vice versa. It is also shown that a vertical critical orbit in the plane can generate a monoparametric family of three-dimensional periodic orbits. 相似文献
19.
The volume average of the strain tensor in a body moving in an inverse-square force field is evaluated. The calculation is carried out assuming the satellite to be an isotropic elastic body whose center of mass moves in a planar orbit. An approximate expression, in terms of its volume and elastic properties, is presented for the strain energy in the satellite. Using this expression the equation of planar librational motion is written explicity. This equation is discussed for both circular and elliptic orbits and is modified to include the effects of energy dissipation in the body. It is shown that the concept of Adiabatic Invariants allows one to analyze the influence of slow changes in the material volume and elasticity.This work was supported by NASA Grant No. NGR 05-010-020. 相似文献
20.
Giacomo Giampieri 《Icarus》2004,167(1):228-230
A planetary body moving on an eccentric orbit around the primary is subject to a periodic perturbing potential, affecting its internal mass distribution. In a previous paper (Rappaport et al., 1997, Icarus 126, 313), we have calculated the periodic modulation of the gravity coefficients of degree 2, for a body on a synchronous orbit. Here, the previous analysis is extended by considering also non-synchronous orbits, and by properly accounting for the apparent motion of the primary due to the non uniform motion along the elliptical orbit. The cases of Titan and Mercury are briefly discussed. 相似文献