共查询到20条相似文献，搜索用时 15 毫秒
1.
The effect of the eccentricity of a planet’s orbit on the stability of the orbits of its satellites is studied. The model
used is the elliptic Hill case of the planar restricted three-body problem. The linear stability of all the known families
of periodic orbits of the problem is computed. No stable orbits are found, the majority of them possessing one or two pairs
of real eigenvalues of the monodromy matrix, while a part of a family with complex instability is found. Two families of periodic
orbits, bifurcating from the Lagrangian points L1, L2 of the corresponding circular case are found analytically. These orbits are very unstable and the determination of their
stability coefficients is not accurate, so we compute the largest Liapunov exponent in their vicinity. In all cases these
exponents are positive, indicating the existence of chaotic motions 相似文献
2.
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
3.
The orbits of fictitious bodies around Jupiter’s stable equilibrium points L 4 and L 5 were integrated for a fine grid of initial conditions up to 100 million years. We checked the validity of three different dynamical models, namely the spatial, restricted three body problem, a model with Sun, Jupiter and Saturn and also the dynamical model with the Outer Solar System (Jupiter to Neptune). We determined the chaoticity of an orbit with the aid of the Lyapunov Characteristic Exponents (=LCE) and used also a method where the maximum eccentricity of an orbit achieved during the dynamical evolution was examined. The goal of this investigation was to determine the size of the regions of motion around the equilibrium points of Jupiter and to find out the dependance on the inclination of the Trojan’s orbit. Whereas for small inclinations (up to i=20°) the stable regions are almost equally large, for moderate inclinations the size shrinks quite rapidly and disappears completely for i>60°. Additionally, we found a difference in the dynamics of orbits around L 4 which – according to the LCE – seem to be more stable than the ones around L 5. 相似文献
4.
M. A. Vashkov’yak 《Astronomy Letters》2001,27(6):404-409
Data on three recently discovered satellites of Uranus are used to determine basic evolutional parameters of their orbits: the extreme eccentricities and inclinations, as well as the circulation periods of the pericenter arguments and of the longitudes of the ascending nodes. The evolution is mainly investigated by analytically solving Hill’s double-averaged problem for the Uranus-Sun-satellite system, in which Uranus’s orbital eccentricity e U and inclination i U to the ecliptic are assumed to be zero. For the real model of Uranus’s evolving orbit with e U≠0 and i U≠0, we refine the evolutional parameters of the satellite orbits by numerically integrating the averaged system. Having analyzed the configuration and dynamics of the orbits of Uranus’s five outer satellites, we have revealed the possibility of their mutual crossings and obtained approximate temporal estimates. 相似文献
5.
The recently discovered coorbital satellites of Saturn, 1980S1 and 1980S3, are shown to be librating in horseshoe orbits. By considering the effects of tangential forces on the semimajor axes of the satellite orbits, we derive an accurate relation between the sum of the satellite masses and (a) their minimum angular separation, (b) the variation of their angular separation with time and (c) the libration period. Observations of (b) and (c) are the most practical methods of determining the satellite masses. The orbits of the coorbital satellites of Dione and Tethys are discussed. We demonstrate the possibility of calculating a new value for the mass of Dione and we show that one of the coorbital satellites of Tethys could be moving in a horseshoe orbit even though another satellite is librating in a tadpole orbit about the leading Lagrangian equilibrium point L4. The origin of coorbital satellites and the stability of their orbits are discussed. 相似文献
6.
J. Henrard 《Celestial Mechanics and Dynamical Astronomy》1983,31(2):115-122
We examine the conjecture made by Brown (1911) that in the restricted three body problem, the long period family of periodic orbits aroundL 4, ends on a homoclinic orbit toL 3. By numerical integration we establish that for the mass ratio Sun-Jupiter such a homoclinic orbit toL 3 does not exist but that there exists a family of homoclinic orbits to periodic orbits aroundL 3. 相似文献
7.
W. S. Koon M. W. Lo J. E. Marsden S. D. Ross 《Celestial Mechanics and Dynamical Astronomy》2001,81(1-2):27-38
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
8.
Up to now, 17 Neptune Trojan asteroids have been detected with their orbits being well determined by continuous observations. This paper analyzes systematically their orbital dynamics. Our results show that except for two temporary members with relatively short lifespans on Trojan orbits, the vast majority of Neptune Trojans located within their orbital uncertainties may survive in the solar system age. The escaping probability of Neptune Trojans, through slow diffusion in the orbital element space in 4.5 billion years, is estimated to be ～50%. The asteroid 2012 UW177 classified as a Centaur asteroid by the IAU Minor Planet Center currently is in fact a Neptune Trojan. Numerical simulations indicate that it is librating on the tadpole-shaped orbit around the Neptune's L4 point. It was captured into the current orbit approximately 0.23 million years ago, and will stay there for at least another 1.3 million years in the future. Its high inclination of i ≈ 54° not only makes it the most inclined Neptune Trojan, but also makes it exhibit the complicated and interesting co-orbital transitions between the leading and trailing Trojans via the quasi-satellite orbit phase. 相似文献
9.
A detailed derivation of the effect of solar radiation pressure on the orbit of a body about a primary orbiting the Sun is
given. The result is a set of secular equations that can be used for long-term predictions of changes in the orbit. Solar
radiation pressure is modeled as a Fourier series in the body’s rotation state, where the coefficients are based on the shape
and radiation properties of the body as parameters. In this work, the assumption is made that the body is in a synchronous
orbit about the primary and rotates at a constant rate. This model is used to write explicit variational equations of the
energy, eccentricity vector, and angular momentum vector for an orbiting body. Given that the effect of the solar radiation
pressure and the orbit are periodic functions, they are readily averaged over an orbit. Furthermore, the equations can be
averaged again over the orbit of the primary about the Sun to give secular equations for long-term prediction. This methodology
is applied to both circular and elliptical orbits, and the full equations for secular changes to the orbit in both cases are
presented. These results can be applied to natural systems, such as the binary asteroid system 1999 KW4, to predict their
evolution due to the Binary YORP effect, or to artificial Earth orbiting, nadir-pointing satellites to enable more precise
models for their orbital evolution. 相似文献
10.
This paper analyses three types of artificial orbits around Mars pushed by continuous low-thrust control: artificial frozen orbits, artificial Sun-Synchronous orbits and artificial Sun-Synchronous frozen orbits. These artificial orbits have similar characteristics to natural frozen orbits and Sun-Synchronous orbits, and their orbital parameters can be selected arbitrarily by using continuous low-thrust control. One control strategy to achieve the artificial frozen orbit is using both the transverse and radial continuous low-thrust control, and another to achieve the artificial Sun-Synchronous orbit is using the normal continuous low-thrust control. These continuous low-thrust control strategies consider J 2, J 3, and J 4 perturbations of Mars. It is proved that both control strategies can minimize characteristic velocity. Relevant formulas are derived, and numerical results are presented. Given the same initial orbital parameters, the control acceleration and characteristic velocity taking into account J 2, J 3, and J 4 perturbations are similar to those taking into account J 2 perturbations for both Mars and the Earth. The control thrust of the orbit around Mars is smaller than that around the Earth. The magnitude of the control acceleration of ASFOM-4 (named as Artificial Sun-Synchronous Frozen Orbit Method 4) is the lowest among these strategies and the characteristic velocity within one orbital period is only 0.5219 m/s for the artificial Sun-Synchronous frozen orbit around Mars. It is evident that the relationship among the control thrusts and the primary orbital parameters of Martian artificial orbits is always similar to that of the Earth. Simulation shows that the control scheme extends the orbital parameters’ selection range of three types of orbits around Mars, compared with the natural frozen orbit and Sun-Synchronous orbit. 相似文献
11.
12.
P.K. Seidelmann R.S. Harrington D. Pascu W.A. Baum D.G. Currie J.A. Westphal G.E. Danielson 《Icarus》1981,47(2):282-287
The ground-based observations of the recently discovered Saturnian satellites, obtained during the 1980 apparition, have been collected from the IAU Circulars and identified with and fit to four orbital groups: (1) the inner pair of coorbital librating satellites, (2) the satellite known as “Dione B” near the L4 point of Dione-Saturn, (3) the satellites associated with the L4 and L5 points of Tethys-Saturn or, alternatively, one satellite unconfortably near the orbit of Tethys, and (4) the F-ring satellites observed by Voyager I. 相似文献
13.
We numerically investigate the stability of systems of 1 \({{\rm M}_{\oplus}}\) planets orbiting a solar-mass star. The systems studied have either 2 or 42 planets per occupied semimajor axis, for a total of 6, 10, 126, or 210 planets, and the planets were started on coplanar, circular orbits with the semimajor axes of the innermost planets at 1 AU. For systems with two planets per occupied orbit, the longitudinal initial locations of planets on a given orbit were separated by either 60° (Trojan planets) or 180°. With 42 planets per semimajor axis, initial longitudes were uniformly spaced. The ratio of the semimajor axes of consecutive coorbital groups in each system was approximately uniform. The instability time for a system was taken to be the first time at which the orbits of two planets with different initial orbital distances crossed. Simulations spanned virtual times of up to 1 × 108, 5 × 105, and 2 × 105 years for the 6- and 10-planet, 126-planet, and 210-planet systems, respectively. Our results show that, for a given class of system (e.g., five pairs of Trojan planets orbiting in the same direction), the relationship between orbit crossing times and planetary spacing is well fit by the functional form log(t c /t 0) = b β + c, where t c is the crossing time, t 0 = 1 year, β is the separation in initial orbital semimajor axis (in terms of the mutual Hill radii of the planets), and b and c are fitting constants. The same functional form was observed in the previous studies of single planets on nested orbits (Smith and Lissauer 2009). Pairs of Trojan planets are more stable than pairs initially separated by 180°. Systems with retrograde planets (i.e., some planets orbiting in the opposite sense from others) can be packed substantially more closely than can systems with all planets orbiting in the same sense. To have the same characteristic lifetime, systems with 2 or 42 planets per orbit typically need to have about 1.5 or 2 times the orbital separation as orbits occupied by single planets, respectively. 相似文献
14.
Antonis D. Pinotsis 《Planetary and Space Science》2009,57(12):1389-1404
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
15.
Secondary explosions of the primary ice fragments ejected in the explosion of the electrolyzed massive ice envelopes of the Galilean satellites are capable of imparting velocities of up to ~5km s–1 to the secondary fragments. As a result, the secondary fragments can enter the orbits of the irregular satellites (Agafonova and Drobyshevski, 1984b) and the Trojan libration orbits. In the latter case a perturbation velocity of V 0.3–2 km s–1 is sufficient.The primary fragments ejected by the gravitational perturbations due to the Galilean satellites sunward from Jupiter's sphere of action move faster relative to the Sun than Jupiter does and therefore reach their first aphelion ahead of Jupiter in the neighborhood of L
4. At the same time the fragments propelled from Jupiter's sphere of action beyond the planet's orbit approach it again in their perihelia behind Jupiter in the region of L
5. The concentration of the fragments and, hence, the frequency of their collisions and explosions at L
4 turn out to be much greater than those at L
5. As a result, the number of the secondary fragments of diameter 15 km captured into libration orbits ahead of Jupiter can be as high as many hundreds and should exceed by more than a factor 3.5 that captured behind Jupiter.Since the icy mix of the fragments contains hydrocarbons and particulate material (silicates and the like), after ice sublimation from the surface layers the Trojans should reveal type C and RD spectra typical for Jupiter's irregular satellites, comet nuclei and other distant ice bodies of similar origin. Among the Trojans there cannot be rocky or metallic objects which are known to exist in the main asteroid belt.It is shown that a velocity perturbation of 150–200 m s–1 resulting from a purely mechanical impact of two bodies may be sufficient to move collision fragments from the orbits of the Trojans to horseshoe-shaped trajectories with a subsequent transfer to the cometary orbits of Jupiter's family. 相似文献
16.
Halo orbits for solar sails at artificial Sun–Earth L1 points are investigated by a third order approximate solution. Two families of halo orbits are explored as defined by the
sail attitude. Case I: the sail normal is directed along the Sun-sail line. Case II: the sail normal is directed along the
Sun–Earth line. In both cases the minimum amplitude of a halo orbit increases as the lightness number of the solar sail increases.
The effect of the z-direction amplitude on x- or y-direction amplitude is also investigated and the results show that the effect is relatively small. In case I, the orbit period
increases as the sail lightness number increases, while in case II, as the lightness number increases, the orbit period increases
first and then decreases after the lightness number exceeds ~0.01. 相似文献
17.
月球卫星轨道力学综述 总被引：5，自引：0，他引：5
月球探测器的运动通常可分为3个阶段，这3个阶段分别对应3种不同类型的轨道：近地停泊轨道、向月飞行的过渡轨道与环月飞行的月球卫星轨道。近地停泊轨道实为一种地球卫星轨道；过渡轨道则涉及不同的过渡方式(大推力或小推力等)；环月飞行的月球卫星轨道则与地球卫星轨道有很多不同之处，它决不是地球卫星轨道的简单克隆。针对这一点，全面阐述月球卫星的轨道力学问题，特别是环月飞行中的一些热点问题，如轨道摄动解的构造、近月点高度的下降及其涉及的卫星轨道寿命、各种特殊卫星(如太阳同步卫星和冻结轨道卫星等)的轨道特征、月球卫星定轨等。 相似文献
18.
G. Bianco R. Devoti M. Fermi V. Luceri P. Rutigliano C. Sciarretta 《Planetary and Space Science》1998,46(11-12)
Geodetic satellites have been providing the low frequency part of the geopotential models used for precise orbit determination purposes (e.g. JGM3, EGM96, …). Nevertheless they can be used to estimate the temporal variation of selected coefficients, helping to clarify the complex interrelations in the earth-ocean-atmosphere system. In this paper we present the two years long analysis of SLR data from the seven available geodetic satellites (Lageos I–II, Stella, Starlette, Ajisai, Etalon I–II) to recover monthly estimates of low degree geopotential coefficients; the results are obtained analysing the satellites separately and in proper combination. An accurate modelling of the satellite orbits is required in order to separate the geopotential coefficients: we assume as a priori geopotential the JGM3 model together with its associated tides and we take care of non-gravitational effects on the satellites by means of proper empirical estimated accelerations. The time series of the estimated coefficients (J2, J3, J4, J5) are inspected to detect the sub-annual perturbations related to seasonal variation of mass distribution. Huge residual seasonal signals in the orbit of Stella indicate a strong model deficiency related to the Sun's influence on the environment. The remaining six satellites are homogeneously modelled and build up a three cycles per year oscillation on J2 and a seasonal oscillation (1 year and six month periods) revealed on the J4. The origin and possible causes of these signals are further discussed in the text. We also present a preliminary
estimate, using twelve years of Lageos-I and Lageos-II observations, that is compared with previous obtained values. 相似文献
19.
We consider the motion of a test particle around a triaxial primary and an oblate companion orbiting each other in elliptic orbits about their common barycenter in the neighborhood of triangular libration points. The positions and stability of these points are influenced by the triaxiality and oblateness of the primary and secondary, and by the semi-major axis and eccentricity of the orbits. The triangular points are stable for 0<μ<μ c ; where μ is the mass ratio (μ≤1/2) and μ c is the critical mass value influenced by the eccentricity, oblateness, semi major axis and triaxiality factors. The size of the region of stability increases with decreasing values of triaxiality and oblateness. An application of the results obtain to double neutron star binaries results show that the positions and stability of the triangular points of PSR J1518+4904, PSR B1534+12, PSR B1914+16 and PSR B2127+11c are affected by the parameters in the systems’ dynamics. 相似文献
20.
运动学定轨是星载GPS特有的定轨方法,该方法不依赖于任何力学模型(地球重力场、大气阻力及太阳辐射压等),尤其适用于受大气阻力影响严重的低轨卫星定轨.基于双频星载GPS数据,研究了运动学定轨原理,讨论了数据预处理方法,建立了一套非差运动学定轨算法.并以GRACE (Gravity Recovery And Climate Experiment)-A、B卫星2008年2月实测数据作为试算验证了本研究方法的有效性和可靠性.GRACE 卫星实测数据计算结果表明:运动学定轨能达到5 cm精度(相对于SLR (Satellite Laser Ranging)),与动力学和简化动力学定轨精度相当. 相似文献