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1.
Abstract— A large body of evidence, including the presence of a dynamical family associated with 4 Vesta, suggests that this asteroid might be the ultimate source of both the V-type near-Earth asteroids (NEAs) and howardite, eucrite and diogenite (HED) meteorites. Dynamical routes from Vesta to the inner regions of the solar system are provided by both the 3:1 mean-motion resonance with Jupiter and the V6, secular resonance. For this reason, numerical integrations of the orbits of fictitious Vesta fragments injected in both of these resonances have been performed. At the same time, the orbital evolution of the known V-type NEAs has been investigated. The results indicate that the dynamical half lifetimes of Vesta fragments injected in both the 3:1 and the V6, resonances are rather short ('2 Ma). The present location of the seven known V-type NEAs is better explained by orbital evolutions starting from the v6 secular resonance. The most important result of the present investigation, however, is that we now face what we call the “Vesta paradox.” Roughly speaking, the paradox consists of the fact that the present V-type NEAs appear to be too dynamically young to have originated in the event that produced the family, but they are too big to be plausible second-generation fragments from the family members. The cosmic-ray exposure (CRE) age distribution of HED meteorites also raises a puzzle, since we would expect an overabundance of meteorites with short CRE ages. We propose different scenarios to explain these paradoxes.  相似文献   

2.
Using a gravitational field truncated at the 4th degree and order, the 1:1 ground-track resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non-spherical terms higher than degree and order 2 introduces new phenomena. For a further study about this resonance, a 2-DOF model which includes a main resonance term (the 1-DOF system) and a perturbing resonance term is studied. With the aid of Poincaré sections, the generation of chaos in the phase space is studied in detail by addressing the overlap process of these two resonances with arbitrary combinations of eccentricity (e) and inclination (i). Retrograde orbits, near circular orbits and near polar orbits are found to have better stability against the perturbation of the second resonance. The situations of complete chaos are estimated in the \(e-i\) plane. By applying the maximum Lyapunov Characteristic Exponent (LCE), chaos is characterized quantitatively and similar conclusions can be achieved. This study is applied to three asteroids 1996 HW1, Vesta and Betulia, but the conclusions are not restricted to them.  相似文献   

3.
Dawn is the first NASA mission to operate in the vicinity of the two most massive asteroids in the main belt, Ceres and Vesta. This double-rendezvous mission is enabled by the use of low-thrust solar electric propulsion. Dawn will arrive at Vesta in 2011 and will operate in its vicinity for approximately one year. Vesta's mass and non-spherical shape, coupled with its rotational period, presents very interesting challenges to a spacecraft that depends principally upon low-thrust propulsion for trajectory-changing maneuvers. The details of Vesta's high-order gravitational terms will not be determined until after Dawn's arrival at Vesta, but it is clear that their effect on Dawn operations creates the most complex operational environment for a NASA mission to date. Gravitational perturbations give rise to oscillations in Dawn's orbital radius, and it is found that trapping of the spacecraft is possible near the 1:1 resonance between Dawn's orbital period and Vesta's rotational period, located approximately between 520 and 580 km orbital radius. This resonant trapping can be escaped by thrusting at the appropriate orbital phase. Having passed through the 1:1 resonance, gravitational perturbations ultimately limit the minimum radius for low-altitude operations to about 400 km, in order to safely prevent surface impact. The lowest practical orbit is desirable in order to maximize signal-to-noise and spatial resolution of the Gamma-Ray and Neutron Detector and to provide the highest spatial resolution observations by Dawn's Framing Camera and Visible InfraRed mapping spectrometer. Dawn dynamical behavior is modeled in the context of a wide range of Vesta gravity models. Many of these models are distinguishable during Dawn's High Altitude Mapping Orbit and the remainder are resolved during Dawn's Low Altitude Mapping Orbit, providing insight into Vesta's interior structure. Ultimately, the dynamics of Dawn at Vesta identifies issues to be explored in the planning of future EP missions operating in close proximity to larger asteroids.  相似文献   

4.
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   

5.
Nonlinear dynamical analysis and the control problem for a displaced orbit above a planet are discussed. It is indicated that there are two equilibria for the system, one hyperbolic (saddle) and one elliptic (center), except for the degenerate h z max, a saddle-node bifurcation point. Motions near the equilibria for the nonresonance case are investigated by means of the Birkhoff normal form and dynamical system techniques. The Kolmogorov–Arnold–Moser (KAM) torus filled with quasiperiodic trajectories is measured in the τ 1 and τ 2 directions, and a rough algorithm for calculating τ 1 and τ 2 is proposed. A general iterative algorithm to generate periodic Lyapunov orbits is also presented. Transitions in the neck region are demonstrated, respectively, in the nonresonance, resonance, and degradation cases. One of the important contributions of the paper is to derive necessary and sufficiency conditions for stability of the motion near the equilibria. Another contribution is to demonstrate numerically that the critical KAM torus of nontransition is filled with the (1,1)-homoclinic orbits of the Lyapunov orbit.  相似文献   

6.
The dynamics of space debris with very high A/m near the geostationary orbit is dominated by the gravitational coefficient C 22 and the solar radiation pressure. An analysis of the stability of the orbits by the chaos indicator MEGNO and frequency analysis map FAM shows chaotic layers around the separatrix and reveals a web of sub-structures associated to resonances with the annual period of the Sun. This succession of stable thin islands and chaotic layers can be reproduced and explained by a quite simple toy model, based on a pendulum approach, perturbed, through the eccentricity, by the external (Sun) frequency. The use of suitable action-angle variables in the circulation and libration regions of the pendulum allows to point out new resonances between the geostationary libration angle and the Sun’s longitude. They correspond very well (positions, shape, width) to the structures visible on the FAM representations.  相似文献   

7.
We explore the effect of oblateness of Saturn (more massive primary) on the periodic orbits and the regions of quasi-periodic motion around both the primaries in the Saturn-Titan system in the framework of planar circular restricted three-body problem. First order interior and exterior mean motion resonances are located. The effect of oblateness is studied on the location, nature and size of periodic and quasi-periodic orbits, using the numerical technique of Poincare surface of sections. Some of the periodic orbits change to quasi-periodic orbits due to the effect of oblateness and vice-versa. The stability of the orbits around Saturn, Titan and both varies with the inclusion of oblateness. The centers of the periodic orbits around Titan move towards Saturn, whereas those around Saturn move towards Titan. For the orbit around Titan at C=2.9992, x=0.959494, the apocenter becomes pericenter. By incorporating oblateness effect, the orbit around Titan at C=2.99345, x=0.924938 is captured by Saturn, remains in various trajectories around Saturn, and as time progresses it spirals away around both the primaries.  相似文献   

8.
We calculate the position of dust trails from comet 8P/Tuttle, in an effort to explain unusual Ursid meteor shower outbursts that were seen when the comet was near aphelion. Comet 8P/Tuttle is a Halley-type comet in a 13.6-year orbit, passing just outside of Earth's orbit. We find that the meteoroids tend to be trapped in the 12:14 mean motion resonance with Jupiter, while the comet librates in a slightly shorter period orbit around the 13:15 resonance. It takes 6 centuries to decrease the perihelion of the meteoroid orbits enough to intersect Earth's orbit, during which time the meteoroids and comet separate in mean anomaly by 6 years, thus explaining the 6-year lag between the comet's return and Ursid outbursts. The resonances also prevent dispersion along the comet orbit and limit viewing to only one year in each return. We identified past dust trail encounters with dust trails from 1392 (Dec. 1945) and 1378 (Dec. 1986) and predicted another outburst on 2000 December 22 at around 7:29 and 8:35 UT, respectively, from dust trails dating to the 1405 and 1392 returns. This event was observed from California using video and photographic techniques. At the same time, five Global-MS-Net stations in Finland, Japan, and Belgium counted meteors using forward meteor scatter. The outburst peaked at 8:06±07 UT, December 22, at zenith hourly rate ∼90 per hour, and the Ursid rates were above half peak intensity during 4.2 h. We find that most Ursid orbits do scatter around the anticipated positions, confirming the link with comet 8P/Tuttle and the epoch of ejection. The 1405 and 1392 dust trails appear to have contributed similar amounts to the activity profile. Some orbits provide a hint of much older debris being present as well. This work is the strongest evidence yet for the relevance of mean motion resonances in Halley-type comet dust trail evolution.  相似文献   

9.
We present a global view of the resonant structure of the phase space of a planetary system with two planets, moving in the same plane, as obtained from the set of the families of periodic orbits. An important tool to understand the topology of the phase space is to determine the position and the stability character of the families of periodic orbits. The region of the phase space close to a stable periodic orbit corresponds to stable, quasi periodic librations. In these regions it is possible for an extrasolar planetary system to exist, or to be trapped following a migration process due to dissipative forces. The mean motion resonances are associated with periodic orbits in a rotating frame, which means that the relative configuration is repeated in space. We start the study with the family of symmetric periodic orbits with nearly circular orbits of the two planets. Along this family the ratio of the periods of the two planets varies, and passes through rational values, which correspond to resonances. At these resonant points we have bifurcations of families of resonant elliptic periodic orbits. There are three topologically different resonances: (1) the resonances (n + 1):n, (2:1, 3:2, ...), (2) the resonances (2n + 1):(2n-1), (3:1, 5:3, ...) and (3) all other resonances. The topology at each one of the above three types of resonances is studied, for different values of the sum and of the ratio of the planetary masses. Both symmetric and asymmetric resonant elliptic periodic orbits exist. In general, the symmetric elliptic families bifurcate from the circular family, and the asymmetric elliptic families bifurcate from the symmetric elliptic families. The results are compared with the position of some observed extrasolar planetary systems. In some cases (e.g., Gliese 876) the observed system lies, with a very good accuracy, on the stable part of a family of resonant periodic orbits.  相似文献   

10.
The behaviour of ‘resonances’ in the spin-orbit coupling in celestial mechanics is investigated in a conservative setting. We consider a Hamiltonian nearly-integrable model describing an approximation of the spin-orbit interaction. The continuous system is reduced to a mapping by integrating the equations of motion through a symplectic algorithm. We study numerically the stability of periodic orbits associated to the above mapping by looking at the eigenvalues of the matrix of the linearized map over the full cycle of the periodic orbit. In particular, the value of the trace of the matrix is related to the stability character of the periodic orbit. We denote by ε* (p/q) the value of the perturbing parameter at which a given elliptic periodic orbit with frequency p/q becomes unstable. A plot of the critical function ε* (p/q) versus the frequency at different orbital eccentricities shows significant peaks at the synchronous resonance (for low eccentricities) and at the synchronous and 3:2 resonances (at higher eccentricities) in good agreement with astronomical observations. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

11.
F. MarzariH. Scholl 《Icarus》2002,159(2):328-338
We have numerically explored the mechanisms that destabilize Jupiter's Trojan orbits outside the stability region defined by Levison et al. (1997, Nature385, 42-44). Different models have been exploited to test various possible sources of instability on timescales on the order of ∼108 years.In the restricted three-body model, only a few Trojan orbits become unstable within 108 years. This intrinsic instability contributes only marginally to the overall instability found by Levison et al.In a model where the orbital parameters of both Jupiter and Saturn are fixed, we have investigated the role of Saturn and its gravitational influence. We find that a large fraction of Trojan orbits become unstable because of the direct nonresonant perturbations by Saturn. By shifting its semimajor axis at constant intervals around its present value we find that the near 5:2 mean motion resonance between the two giant planets (the Great Inequality) is not responsible for the gross instability of Jupiter's Trojans since short-term perturbations by Saturn destabilize Trojans, even when the two planets are far out of the resonance.Secular resonances are an additional source of instability. In the full six-body model with the four major planets included in the numerical integration, we have analyzed the effects of secular resonances with the node of the planets. Trojan asteroids have relevant inclinations, and nodal secular resonances play an important role. When a Trojan orbit becomes unstable, in most cases the libration amplitude of the critical argument of the 1:1 mean motion resonance grows until the asteroid encounters the planet. Libration amplitude, eccentricity, and nodal rate are linked for Trojan orbits by an algebraic relation so that when one of the three parameters is perturbed, the other two are affected as well. There are numerous secular resonances with the nodal rate of Jupiter that fall inside the region of instability and contribute to destabilize Trojans, in particular the ν16. Indeed, in the full model the escape rate over 50 Myr is higher compared to the fixed model.Some secular resonances even cross the stability region delimited by Levison et al. and cause instability. This is the case of the 3:2 and 1:2 nodal resonances with Jupiter. In particular the 1:2 is responsible for the instability of some clones of the L4 Trojan (3540) Protesilaos.  相似文献   

12.
In the gravity field of an asteroid with the second order and degree harmonics C 20 and C 22, the attitude stability of a spacecraft with two flexible solar arrays on a stationary orbit subjected to the fourth-order gravity gradient torque is investigated in this paper. The sufficient conditions of attitude stability of the spacecraft are obtained, the effect of the direction of the flexible solar arrays and some special cases are discussed. Taking the asteroids 4769 Castalia, 25143 Itokawa and the imaginary asteroids as examples, the attitude stability domains, determined by the sufficient conditions, of the spacecrafts moving on stationary orbits around them are presented. It is found that the attitude stability domains of the spacecraft with two flexible solar arrays are evidently different when the solar arrays are installed in different directions; the effect of the harmonics C 20 and C 22 of the asteroids has the significant influence on the attitude stability domains of the spacecrafts with flexible appendages moving on stationary orbits; in the certain case, the effect of the harmonics C 20 and C 22 of the asteroids has no influence on the attitude stability domains of the rigid spacecrafts moving on stationary orbits, but in the other cases, the effect of the harmonics C 20 and C 22 of the asteroids has also the significant influence on the attitude stability domains of the rigid spacecrafts moving on stationary orbits; whether the harmonics C 20 and C 22 of the asteroids are considered or not, the effect of flexible appendages decreases the attitude stability domains.  相似文献   

13.
We study the orbit of a particle in the plane of symmetry of two equal mass primaries in rectilinear keplerian motion. Using the surfaces of section we look for periodic orbits, examine their stability and search for quasi-periodic orbits and regions of escape. For large values of the angular momentumC, we verify the validity of the approximation of two fixed centers. However, we also find irregular families of orbits and resonance zones.For small values ofC, the approximation is no longer valid, but we find invariant curves whose interpretation might be interesting.  相似文献   

14.
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   

15.
Ariel 1, the first international satellite, was launched on 26 April 1962, into an orbit inclined at 53.85° to the equator, with an initial perigee height near 390 km. On 8 May 1973 the orbit passed through 15th-order resonance and has been determined, with the RAE orbit refinement program PROP, at eight epochs between February and August 1973 using 500 observations.The orbital inclinations during the time of 15th-order resonance, as given by these eight orbits and 31 U.S. Navy orbits, were fitted with a theoretical curve using the THROE computer program, the best fit giving 109C?15 = ?370 ± 14 and 109S15 = ?114 ± 31.The values of eccentricity were also successfully fitted using THROE, and the results are discussed.  相似文献   

16.
Here, we construct a comprehensive howardite, eucrite, and diogenite (HED) bulk chemistry data set to compare with Dawn data. Using the bulk chemistry data set, we determine four gamma‐ray/neutron parameters in the HEDs (1) relative fast neutron counts (fast counts), (2) macroscopic thermal neutron absorption cross section (absorption), (3) a high‐energy gamma‐ray compositional parameter (Cp), and (4) Fe abundance. These correspond to the four measurements of Vesta made by Dawn's Gamma Ray and Neutron Detector (GRaND) that can be used to discern HED lithologic variability on the Vestan surface. We investigate covariance between fast counts and average atomic mass (<A>) in the meteorite data set, where a strong correlation (r2 = 0.99) is observed, and we demonstrate that systematic offsets from the fast count/<A> trend are linked to changes in Fe and Ni concentrations. To compare the meteorite and GRaND data, we investigate and report covariance among fast counts, absorption, Cp, and Fe abundance in the HED meteorite data set. We identify several GRaND measurement spaces where the Yamato type B diogenites are distinct from all other HED lithologies, including polymict mixtures. The type B's are diogenites that are enriched in Fe + pigeonite + diopside ± plagioclase, relative to typical, orthopyroxenitic diogenites. We then compare these results to GRaND data and demonstrate that regions north of ~70°N latitude on Vesta (including the north pole) are consistent with type B diogenites. We propose two models to explain type B diogenite compositions in the north (1) deposition as Rheasilvia ejecta, or (2) type B plutons that were emplaced at shallow depths in the north polar region and sampled by local impacts. Lastly, using principal component (PC) analysis, we identify unique PC spaces for all HED lithologies, indicating that the corresponding GRaND measurables may be used to produce comprehensive lithologic maps for Vesta.  相似文献   

17.
We have accumulated thousands of orbits of test particles in the Solar System from the asteroid belt to beyond the orbit of Neptune. We find that the time for an orbit to make a close encounter with a perturbing planet, T c ,is a function of the Lyapunov time, T ty .The relation is log (T c /T o )= a + b log (T ly T o )where T o is a fiducial period which we have taken as the period of the principal perturber or the period of the asteroid. There are exceptions to this rule interior to the 2/3 resonance with Jupiter. There, at least in the restricted problem, for sufficiently small Jupiter mass, orbits may have a positive Lyapunov exponent and still be blocked from having a close approach to Jupiter by a zero velocity curve. Of more serious concern is whether the relation holds for purely secular resonances, and if it does, how to choose T o .This is the case of interest for the planets in the solar system.  相似文献   

18.
In a previous publication (Tsiganis et al. 2000, Icarus146, 240-252), we argued that the occurrence of stable chaos in the 12/7 mean motion resonance with Jupiter is related to the fact that there do not exist families of periodic orbits in the planar elliptic restricted problem and in the 3-D circular problem corresponding to this resonance. In the present paper we show that nonexistence of resonant periodic orbits, both for the planar and for the 3-D problem, also occurs in other jovian resonances—namely the 11/4, 22/9, 13/6, and 18/7—where cases of real asteroids on stable-chaotic orbits have been identified. This property may provide a “protection mechanism”, leading to semiconfinement of chaotic orbits and extremely slow migration in the space of proper elements, so that diffusion is practically unrelated to the value of the Lyapunov time, TL, of chaotic orbits. However, we show that, in more complicated dynamical models, the long-term evolution of chaotic orbits initiated in the vicinity of these resonances may also be governed by secular resonances. Finally, we find that stable-chaotic orbits have a characteristic spectrum of autocorrelation times: for the action conjugate to the critical argument the autocorrelation time is of the order of the Lyapunov time, while for the eccentricity- and inclination-related actions the autocorrelation time may be longer than 103TL. This behavior is consistent with the trajectory being sticky around a manifold of lower-than-full dimensionality in phase space (e.g., a 4-D submanifold of the 5-D energy manifold in a three-degrees-of-freedom autonomus Hamiltonian system) and reflects the inability of these “flawed” resonances to modify secular motion significantly, at least for times of the order of 200 Myr.  相似文献   

19.
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   

20.
The orbits of 12 Trojan asteroids, which have Lyapunov times T L105 years and were previously classified as ASCs(=asteroids in stable chaos), are integrated for 50 Myrs, along with a group of neighbouring initial conditions for each nominal orbit. About 40% of the orbits present strong instabilities in the inclination, which may be attributed primarily to the action of the 16 secular resonance; two escapes are also recorded. Higher-order secular resonances, involving the nodes of the outer planets, are also found to be responsible for chaotic motion. Orbital stability depends critically on the choice of initial conditions and, thus, these objects can be regarded as being on the edge of strong chaos.  相似文献   

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