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1.
We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the simulations, we show that this sys-tem can be stable for at least 108 yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790 AU ≤ a ≤ 5.900 AU to examine the existence of potential asteroid structure and Habitable Zones (HZs). We show that there are unstable regions for orbits about 4:1, 3:1 and 5:2 mean motion resonances (MMRs) of the outermost planet in the system, and sev-eral stable orbits can remain at 3:2 and 1:1 MMRs, which resembles the asteroid belt in the solar system. From a dynamical viewpoint, proper HZ candidates for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU with relatively low eccentricities.  相似文献   

2.
The stability of the motion of a hypothetical planet in the binary system ?? Cen A?CB has been investigated. The analysis has been performed within the framework of a planar (restricted and full) three-body problem for the case of prograde orbits. Based on a representative set of initial data, we have obtained the Lyapunov spectra of the motion of a triple system with a single planet. Chaotic domains have been identified in the pericenter distance-eccentricity plane of initial conditions for the planet through a statistical analysis of the data obtained. We have studied the correspondence of these chaotic domains to the domains of initial conditions that lead to the planet??s encounter with one of the binary??s stars or to the escape of the planet from the system. We show that the stability criterion based on the maximum Lyapunov exponent gives a more clear-cut boundary of the instability domains than does the encounterescape criterion at the same integration time. The typical Lyapunov time of chaotic motion is ??500 yr for unstable outer orbits and ??60 yr for unstable inner ones. The domain of chaos expands significantly as the initial orbital eccentricity of the planet increases. The chaos-order boundary has a fractal structure due to the presence of orbital resonances.  相似文献   

3.
We study systems of close orbiting planets evolving under the influence of tidal circularization. It is supposed that a commensurability forms through the action of disk induced migration and orbital circularization. After the system enters an inner cavity or the disk disperses the evolution continues under the influence of tides due to the central star which induce orbital circularization. We derive approximate analytic models that describe the evolution away from a general first order resonance that results from tidal circularization in a two planet system and which can be shown to be a direct consequence of the conservation of energy and angular momentum. We consider the situation when the system is initially very close to resonance and also when the system is between resonances. We also perform numerical simulations which confirm these models and then apply them to two and four planet systems chosen to have parameters related to the GJ 581 and HD 10180 systems. We also estimate the tidal dissipation rates through effective quality factors that could result in evolution to observed period ratios within the lifetimes of the systems. Thus the survival of, or degree of departure from, close commensurabilities in observed systems may be indicative of the effectiveness of tidal disipation, a feature which in turn may be related to the internal structure of the planets involved.  相似文献   

4.
We present an analysis of the significantly expanded HARPS 2011 radial velocity data set for GJ 581 that was presented by Forveille et al. (2011). Our analysis reaches substantially different conclusions regarding the evidence for a Super‐Earth‐mass planet in the star's Habitable Zone. We were able to reproduce their reported χ2ν and RMS values only after removing some outliers from their models and refitting the trimmed down RV set. A suite of 4000 N‐body simulations of their Keplerian model all resulted in unstable systems and revealed that their reported 3.6σ detection of e = 0.32 for the eccentricity of GJ 581e is manifestly incompatible with the system's dynamical stability. Furthermore, their Keplerian model, when integrated only over the time baseline of the observations, significantly increases the χ2ν and demonstrates the need for including non‐Keplerian orbital precession when modeling this system. We find that a four‐planet model with all of the planets on circular or nearly circular orbits provides both an excellent self‐consistent fit to their RV data and also results in a very stable configuration. The periodogram of the residuals to a 4‐planet all‐circular‐orbit model reveals significant peaks that suggest one or more additional planets in this system. We conclude that the present 240‐point HARPS data set, when analyzed in its entirety, and modeled with fully self‐consistent stable orbits, by and of itself does offer significant support for a fifth signal in the data with a period near 32 days. This signal has a false alarm probability of <4% and is consistent with a planet of minimum mass 2.2 M⊕, orbiting squarely in the star's habitable zone at 0.13 AU, where liquid water on planetary surfaces is a distinct possibility (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

5.
Since the first extrasolar planet was discovered about 10 years ago, a major point of dynamical investigations was the determination of stable regions in extrasolar planetary systems where additional planets may exist. Using numerical methods, we investigate the dynamical stability in known multiple planetary systems (HD74156, HD38529, HD168443, HD169830) with special interest on the region between the two known planets and on the mean motion resonances inside this region. As a dynamical model we take the restricted 4-body problem containing the host star, the two planets and massless test-planets. For our numerical integrations, we used the Lie-integrator and additionally the Fast Lyapunov Indicators as a tool for detecting chaotic motion. We also investigated the inner resonances with the outer planet and the outer resonances with the inner planet with test-planets located inside the resonances.  相似文献   

6.
We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analogue of the Solar system. Our work is inspired by the work of Malhotra & Minton. Using the linear Laplace–Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the subsystem of Jupiters may be found in a dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semimajor axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance.  相似文献   

7.
In long-term stability studies of terrestrial planets moving in the habitable zone (HZ) of a sun-like star, we distinguish four different configurations: (i) planets moving in binary star systems, (ii) the inner type (where the gas giant moves outside the HZ), (iii) the outer type (where the gas giant is closer to the star, than the HZ) and (iv) the Trojan type (where the gas giant moves in the HZ). Since earlier calculations indicated, that the stability of the motion in the HZ also depends on the inclination of the terrestrial planet orbits, we present a detailed numerical investigation to show correlations between the eccentricity, the mass and the distance of the giant planet for various inclinations of the terrestrial planets. The orbital stability of the HZ was examined for all four configurations stated above. While we could find hardly any stable orbits for the first three types for inclinations higher than 40°, the Trojan planets can be stable up to an inclination of 60°. Additionally, we could also find some stabilizing effects of the inclination for the first three types. As dynamical model we used the elliptic restricted three-body problem, which consists of two massive and one mass-less body. This allows an application to all detected and future extrasolar single planet systems.  相似文献   

8.
Prior to the detection of its outermost Uranus-mass object, it had been suggested that GJ 876 could host an Earth-sized planet in a 15-day orbit. Observation, however, did not support this idea, but instead revealed evidence for the existence of a larger body in a ~125-day orbit, near a three-body resonance with the two giant planets of this system. In this paper, we present a detailed analysis of the dynamics of the four-planet system of GJ 876, and examine the possibility of the existence of other planetary objects interior to its outermost body. We have developed a numerical scheme that enables us to search the orbital parameter-space very effectively and, in a short time, identify regions where an object may be stable. We present details of this integration method and discuss its application to the GJ 876 four-planet system. The results of our initial analysis suggested possible stable orbits at regions exterior to the orbit of the outermost planet and also indicated that an island of stability may exist in and around the 15-day orbit. However, examining the long-term stability of an object in that region by direct integration revealed that the 15-day orbit becomes unstable and that the system of GJ 876 is most likely dynamically full. We present the results of our study and discuss their implications for the formation and final orbital architecture of this system.  相似文献   

9.
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10.
The development of principles, systems, and instruments enable the detection of exoplanets with 6–8 Earth masses or less. The launches of specialized satellites, such as CoRoT (2006) and Kepler (2009), into orbits around the Earth have enabled the discovery of new exoplanetary systems. These missions are searching for relatively low-mass planets by observing their transits over the disks of their parent stars. At the same time, supporting studies of exoplanets using ground-based facilities (that measure Keplerian components of radial velocities) are in progress. The properties of at least two objects discovered by different methods, Kepler-22 and GJ 1214b, suggested that there was another class of celestial bodies among the known types of extrasolar planets: planetans, or oceanic planets. The structure of Kepler-22 and GJ 1214b suggest that they can be these oceanic planets. In this paper, we consider to what extent this statement is valid. The consideration of exoplanet Gl 581g as an oceanic planet is more feasible. Some specific features of the physical nature of these unusual planets are presented.  相似文献   

11.
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12.
The discovered exoplanetary systems have highly diverse dynamic properties, which differ from those of the Solar System. A single model including planet migration effects and their gravitational interaction is used to investigate the features of dynamic processes that lead to the formation of giant-planet systems with different orbital characteristics. It is shown for a system of four giant planets similar to the Solar System how Type I migration could lead to all the planets being captured into resonant configurations. The resonant motion can continue for a long period of time after the transition to Type II migration and after the dissipation of the gas-and-dust disk. The three-planet system of GJ 876 is used to investigate the migration of the planets inward the orbit of the most massive planet and their capture into low-order resonant configurations under the conditions of Type II migration. A system similar to the exoplanetary system of HD 102272 is used to study the capture into high-order resonances followed by an increase in the orbit’s eccentricity.  相似文献   

13.
Asteroid families are believed to originate by catastrophic disruptions of large asteroids. They are nowadays identified as clusters in the proper orbital elements space. The proper elements are analytically defined as constants of motion of a suitably simplified dynamical system. Indeed, they are generally nearly constant on a 107-108-year time scale. Over longer time intervals, however, they may significantly change, reflecting the accumulation of the tiny nonperiodic evolutions provided by chaos and nonconservative forces. The most important effects leading to a change of the proper orbital elements are (i) the chaotic diffusion in narrow mean motion resonances, (ii) the Yarkovsky nongravitational force, and (iii) the gravitational impulses received at close approaches with large asteroids. A natural question then arises: How are the size and shape of an asteroid family modified due to evolution of the proper orbital elements of its members over the family age? In this paper, we concentrate on the dynamical dispersion of the proper eccentricity and inclination, which occurs due to (i), but with the help of (ii) and (iii). We choose the Flora family as a model case because it is unusually dispersed in eccentricity and inclination and, being located in the inner main belt, is intersected by a large number of effective mean motion resonances with Mars and Jupiter. Our results suggest that the Flora family dynamically disperses on a few 108-year time scale and that its age may be significantly less than 109 years. We discuss the possibility that the parent bodies of the Flora family and of the ordinary L chondrite meteorites are the same object. In a broader sense, this work suggests that the common belief that the present asteroid families are simple images of their primordial dynamical structure should be revised.  相似文献   

14.
Precision radial velocity measurements of the Sun-like dwarf 14 Herculis published by Naef et al., Butler et al. and Wittenmyer, Endl & Cochran reveal a Jovian planet in a 1760-d orbit and a trend indicating the second distant object. On the grounds of dynamical considerations, we test a hypothesis that the trend can be explained by the presence of an additional giant planet. We derive dynamical limits to the orbital parameters of the putative outer Jovian companion in an orbit within ∼13 au. In this case, the mutual interactions between the Jovian planets are important for the long-term stability of the system. The best self-consistent and stable Newtonian fit to an edge-on configuration of Jovian planets has the outer planet in 9-au orbit with a moderate eccentricity of ∼0.2 and confined to a zone spanned by the low-order mean motion resonances 5:1 and 6:1. This solution lies in a shallow minimum of (χ2ν)1/2 and persists over a wide range of the system inclination. Other stable configurations within 1σ confidence interval of the best fit are possible for the semimajor axis of the outer planet in the range of (6,13) au and the eccentricity in the range of (0, 0.3). The orbital inclination cannot yet be determined but when it decreases, both planetary masses approach ∼10 m J and for i ∼ 30° the hierarchy of the masses is reversed.  相似文献   

15.
This article is devoted to studying the dynamical evolution and orbital stability of compact extrasolar three-planetary system GJ 3138.In this system,all semima...  相似文献   

16.
The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at κ E ∈ (4, 6), where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different ‘Solar Systems’ clarified that including only Jupiter and Saturn with their actual masses together with a more ‘massive’ Earth (4 < κ E < 6) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace‐Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

17.
We use full available array of radial velocity data, including recently published HARPS and Keck observatory sets, to characterize the orbital configuration of the planetary system orbiting GJ876. First, we propose and describe in detail a fast method to fit perturbed orbital configuration, based on the integration of the sensitivity equations inferred by the equations of the original N-body problem. Further, we find that it is unsatisfactory to treat the available radial velocity data for GJ876 in the traditional white noise model, because the actual noise appears autocorrelated (and demonstrates non-white frequency spectrum). The time scale of this correlation is about a few days, and the contribution of the correlated noise is about 2 m/s (i.e., similar to the level of internal errors in the Keck data). We propose a variation of the maximum-likelihood algorithm to estimate the orbital configuration of the system, taking into account the red noise effects. We show, in particular, that the non-zero orbital eccentricity of the innermost planet d, obtained in previous studies, is likely a result of misinterpreted red noise in the data. In addition to offsets in some orbital parameters, the red noise also makes the fit uncertainties systematically underestimated (while they are treated in the traditional white noise model). Also, we show that the orbital eccentricity of the outermost planet is actually ill-determined, although bounded by ~0.2. Finally, we investigate possible orbital non-coplanarity of the system, and limit the mutual inclination between the planets b and c orbits by 5°?C15°, depending on the angular position of the mutual orbital nodes.  相似文献   

18.
Keiko Atobe  Shigeru Ida 《Icarus》2004,168(2):223-236
We have investigated obliquity variations of possible terrestrial planets in habitable zones (HZs) perturbed by a giant planet(s) in extrasolar planetary systems. All the extrasolar planets so far discovered are inferred to be jovian-type gas giants. However, terrestrial planets could also exist in extrasolar planetary systems. In order for life, in particular for land-based life, to evolve and survive on a possible terrestrial planet in an HZ, small obliquity variations of the planet may be required in addition to its orbital stability, because large obliquity variations would cause significant climate change. It is known that large obliquity variations are caused by spin-orbit resonances where the precession frequency of the planet's spin nearly coincides with one of the precession frequencies of the ascending node of the planet's orbit. Using analytical expressions, we evaluated the obliquity variations of terrestrial planets with prograde spins in HZs. We found that the obliquity of terrestrial planets suffers large variations when the giant planet's orbit is separated by several Hill radii from an edge of the HZ, in which the orbits of the terrestrial planets in the HZ are marginally stable. Applying these results to the known extrasolar planetary systems, we found that about half of these systems can have terrestrial planets with small obliquity variations (smaller than 10°) over their entire HZs. However, the systems with both small obliquity variations and stable orbits in their HZs are only 1/5 of known systems. Most such systems are comprised of short-period giant planets. If additional planets are found in the known planetary systems, they generally tend to enhance the obliquity variations. On the other hand, if a large/close satellite exists, it significantly enhances the precession rate of the spin axis of a terrestrial planet and is likely to reduce the obliquity variations of the planet. Moreover, if a terrestrial planet is in a retrograde spin state, the spin-orbit resonance does not occur. Retrograde spin, or a large/close satellite might be essential for land-based life to survive on a terrestrial planet in an HZ.  相似文献   

19.
We have carried out an extensive study of the possibility of the detection of Earth-mass and super-Earth Trojan planets using transit timing variation method with the Kepler space telescope. We have considered a system consisting of a transiting Jovian-type planet in a short period orbit, and determined the induced variations in its transit timing due to an Earth-mass/super-Earth Trojan planet. We mapped a large section of the phase space around the 1:1 mean-motion resonance and identified regions corresponding to several other mean-motion resonances where the orbit of the planet would be stable. We calculated transit timing variations (TTVs) for different values of the mass and orbital elements of the transiting and perturbing bodies as well as the mass of central star, and identified orbital configurations of these objects (ranges of their orbital elements and masses) for which the resulted TTVs would be within the range of the variations of the transit timing of Kepler’s planetary candidates. Results of our study indicate that in general, the amplitudes of the TTVs fall within the detectable range of timing precision obtained from the Kepler’s long-cadence data, and depending on the parameters of the system, their magnitudes may become as large as a few hours. The probability of detection is higher for super-Earth Trojans with slightly eccentric orbits around short-period Jovian-type planets with masses slightly smaller than Jupiter. We present the details of our study and discuss the implications of its results.  相似文献   

20.
Richard Greenberg 《Icarus》1975,24(3):325-332
Current knowledge of the dynamics of Uranus' satellites is reviewed in support of preliminary planning for a mission to that planet. The determination of past and present orbital and rotational behavior is discussed. Improved understanding in this area is important not only for its own sake, but also for the implications with regard to the structure of the planet and to the general dynamical history of the solar system. A program of Earth-based observations over the next few years would permit most effective use of a Uranus probe.  相似文献   

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