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1.
Cosmogonical theories as well as recent observations allow us to expect the existence of numerous exo-planets, including in binaries. Then arises the dynamical problem of stability for planetary orbits in double star systems. Modern computations have shown that many such stable orbits do exist, among which we consider orbits around one component of the binary (called S-type orbits). Within the framework of the elliptic plane restricted three-body problem, the phase space of initial conditions for fictitious S-type planetary orbits is systematically explored, and limits for stability had been previously established for four nearby binaries which components are nearly of solar type. Among stable orbits, found up to distance of their sun of the order of half the binarys periastron distance, nearly-circular ones exist for the three binaries (among the four) having a not too high orbital eccentricity. In the first part of the present paper, we compare these previous results with orbits around a 16 Cyg B-like binarys component with varied eccentricities, and we confirm the existence of stable nearly-circular S-type planetary orbits but for very high binarys eccentricity. It is well-known that chaos may destroy this stability after a very long time (several millions years or more). In a first paper, we had shown that a stable planetary orbit, although chaotic, could keep its stability for more than a billion years (confined chaos). Then, in the second part of the present paper, we investigate the chaotic behaviour of two sets of planetary orbits among the stable ones found around 16 Cyg B-like components in the first part, one set of strongly stable orbits and the other near the limit of stability. Our results show that the stability of the first set is not destroyed when the binarys eccentricity increases even to very high values (0.95), but that the stability of the second set is destroyed as soon as the eccentricity reaches the value 0.8. 相似文献
2.
The results obtained by numerical integration of the equations of motion of fictitious comets, in the restricted circular three-dimensional three-body problem, are compared with those obtained with Öpik's theory of close encounters, for an experimental set-up similar to that used by Froeschlé and Rickman (1980, 1981) to model both the infeed of comets from the trans-jovian region into the Jupiter family and their subsequent orbital evolution within the family. The distributions of perturbations in orbital energy E, eccentricity e and inclination i are well reproduced by Öpik's theory, as long as the comparison is made on the outcomes of encounters only up to a certain unperturbed distance bmax; several values of the latter are experimented with and it is found that, surprisingly, Öpik's theory seems to be still working reasonably well for values of bmax in excess of several times the Hill's radius of the planet. 相似文献
3.
The orbital stochasticity of comets P/Ciffréo (1985 XVI) and P/Maury (1985 VI), at the present time near the 5/3 and 4/3 resonances with Jupiter, is investigated using Lyapunov Characteristic Indicators. First results indicate a strong stochastic behaviour for the two comets, mainly induced by encounters with Jupiter, which looks roughly like the behaviour of the group of comets in 1/1 resonance with Jupiter. 相似文献
4.
Sequences of the oscillations of solar lines up to 2 hours 20 min long have been recorded at the same point on the sun. The power spectra show several peaks separated by 0.85 × 10–3 cps on average from each other. A sharp main peak at 3.3 × 10–3 cps (300 sec period) is almost always present.These results suggest that the lifetime of the phase of the oscillation is much longer than that of the amplitude and is likely to exceed one hour. We actually observe the modulation of a wave in smaller wave trains about 11 min long and 20 min apart (average values).Observations with low spatial resolution also suggest that the area of coherence is much greater for the phase than for the amplitude.Kitt Peak National Observatory Contribution No. 425.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation. 相似文献
5.
O. Groussin G. Hahn P. L. Lamy R. Gonczi G. B. Valsecchi 《Monthly notices of the Royal Astronomical Society》2007,376(3):1399-1406
We present a new method to study the long-term evolution of cometary nuclei in order to estimate their original size, and we consider the case of comets 46P/Wirtanen (hereafter 46P) and 67P/Churyumov–Gerasimenko (hereafter 67P). We calculate the past evolution of the orbital elements of both comets over 100 000 yr using a Bulirsch–Stoer integrator and over 450 000 yr using a Radau integrator, and we incorporate a realistic model of the erosion of their nucleus. Their long-term orbital evolution is prominently chaotic, resulting from several close encounters with planets, and this result is independent of the choice of the integrator and of the presence or not of non-gravitational forces. The dynamical lifetime of comet 46P is estimated at ∼133 000 yr and that of comet 67P at ∼105 000 yr. Our erosion model assumes a spherical nucleus composed of a macroscopic mixture of two thermally decoupled components, dust and pure water ice. Erosion strongly depends upon the active fraction and the density of the nucleus. It mainly takes place at heliocentric distances <4 au and lasts for only ∼7 per cent of the lifetime. Assuming a density of 300 kg m−3 and an average active fraction over time of 10 per cent, we find an initial radius of ∼1.3 km for 46P and ∼2.8 km for 67P. Upper limit are obtained assuming a density of 100 kg m−3 and an active fraction of 100 per cent, and amounts to 21 km for 46P and 25 km for 67P. Erosion acts as a rejuvenating process of the surface so that exposed materials on the surface may only contain very little quantities of primordial materials. However, materials located just under it (a few centimetres to metres) may still be much less evolved. We will apply this method to several other comets in the future. 相似文献
6.
Paolo Farinella Christiane Froeschlé Robert Gonczi 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):287-305
We have numerically integrated the orbits of 18 fictitious fragments ejected from the asteroid 6 Hebe, an S-type object about 200km across which is located very close to theg=g
6 (orv
6) secular resonance at a semimajor axis of 2.425AU and a (proper) inclination of 15° .0. A realistic ejection velocity distribution, with most fragments escaping at relative speeds of a few hundredsm/s, has been assumed. In four cases we have found that the resonance pumps up the orbital eccentricity of the fragments to values >0.6, which result into Earth-crossing, within a time span of 1Myr; subsequent close encounters with the Earth cause strongly chaotic orbital evolution. The closest Earth and Mars encounters recorded in our integration occur at miss distances of a few thousandths ofAU, implying collision lifetimes <109
yr. Some other fragments affected by the secular resonance become Mars-crossers but not Earth-crossers over the integration time span. Two bodies are injected into the 3 : 1 mean motion resonance with Jupiter, and also display macroscopically chaotic behaviour leading to Earth-crossing. 6 Hebe is the first asteroid for which a realistic collisional/dynamical evolutionroute to generate meteorites has been fully demonstrated. It may be the parent body of one of the ordinary chondrite classes. 相似文献
7.
G. Contopoulos N. Voglis C. Efthymiopoulos C. Froeschlé R. Gonczi E. Lega R. Dvorak E. Lohinger 《Celestial Mechanics and Dynamical Astronomy》1997,67(4):293-317
The spectra of ‘stretching numbers’ (or ‘local Lyapunov characteristic numbers’) are different in the ordered and in the chaotic
domain. We follow the variation of the spectrum as we move from the centre of an island outwards until we reach the chaotic
domain. As we move outwards the number of abrupt maxima in the spectrum increases. These maxima correspond to maxima or minima
in the curve a(θ), where a is the stretching number, and θ the azimuthal angle. We explain the appearance of new maxima in
the spectra of ordered orbits. The orbits just outside the last KAM curve are confined close to this curve for a long time
(stickiness time) because of the existence of cantori surrounding the island, but eventually escape to the large chaotic domain
further outside. The spectra of sticky orbits resemble those of the ordered orbits just inside the last KAM curve, but later
these spectra tend to the invariant spectrum of the chaotic domain. The sticky spectra are invariant during the stickiness
time. The stickiness time increases exponentially as we approach an island of stability, but very close to an island the increase
is super exponential. The stickiness time varies substantially for nearby orbits; thus we define a probability of escape Pn(x) at time n for every point x. Only the average escape time in a not very small interval Δx around each x is reliable. Then
we study the convergence of the spectra to the final, invariant spectrum. We define the number of iterations, N, needed to
approach the final spectrum within a given accuracy. In the regular domain N is small, while in the chaotic domain it is large.
In some ordered cases the convergence is anomalously slow. In these cases the maximum value of ak in the continued fraction expansion of the rotation number a = [a0,a1,... ak,...] is large. The ordered domain contains small higher order chaotic domains and higher order islands. These can be located
by calculating orbits starting at various points along a line parallel to the q-axis. A monotonic variation of the sup {q}as
a function of the initial condition q0 indicates ordered motions, a jump indicates the crossing of a localized chaotic domain, and a V-shaped structure indicates
the crossing of an island. But sometimes the V-shaped structure disappears if the orbit is calculated over longer times. This
is due to a near resonance of the rotation number, that is not followed by stable islands.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
Using mainly Lyapunov characteristic numbers the stochasticity of Halley like cometary orbits has been investigated in the framework of different models of the restricted three body problem. 相似文献
9.
Cosmogonical theories as well as recent observations allow us to expect the existence of planets around many stars other than the Sun. On an other hand, double and multiple star systems are established to be more numerous than single stars (such as the Sun), at least in the solar neighborhood. We are then faced to the following dynamical problem: assuming that planets can form in a binary early environment (I do not deal here with), does long-term stability for planetary orbits exist in double star systems.Although preliminary studies were rather pessimistic about the possibility of existence of stable planetary orbits in double or multiple star systems, modern computation have shown that many such stable orbits do exist (but possible chaotic behavior), either around the binary as a whole (P-type) or around one component of the binary (S-type), this latter being explored here.The dynamical model is the elliptic plane restricted three-body problem; the phase space of initial conditions is systematically explored, and limits for stability have been established. Stable S-type planetary orbits are found up to distance of their "sun" of the order of half the periastron distance of the binary; moreover, among these stable orbits, nearly-circular ones exist up to distance of their "sun" of the order of one quarter the periastron distance of the binary; finally, among the nearly-circular stable orbits, several stay inside the "habitable zone", at least for two nearby binaries which components are nearly of solar type.Nevertheless, we know that chaos may destroy this stability after a long time (sometimes several millions years). It is therefore important to compute indicators of chaos for these stable planetary orbits to investigate their actual very long-term stability. Here we give an example of such a computation for more than a billion years. 相似文献
10.
R. Gonczi Ch. Froeschlé Cl. Froeschlé 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):117-124
This paper is devoted to study the stochastic behaviour of some Hamiltonian systems with closed velocity curves. We investigate Hamiltonians already studied by Ali and Somorjai (1). These authors, by discussing Poincaré's surfaces of section for several energy values, gave a qualitative evaluation of the stochasticity of the systems.Here we present a quantitative study of this stochastic behaviour. For each energy we compute the Lyapunov characteristic exponents of fifty orbits chosen at random, in order to calculate the Kolmogorov entropy by Pesin's formula. Our results are in agreement with those of Ali and Somorjai: the disorder does not increase monotonically with increasing energy. However, we find that the largest entropy does not necessarily correspond to the maximum of the stochastic volume. The Kolmogorov entropy thus appears to be a good measure of the degree of disorder of dynamical systems. 相似文献