The full set of published radial velocity data (52 measurements from Keck + 58 ones from ELODIE + 17 ones from CORALIE) for the star HD37124 is analysed. Two families of dynamically stable high-eccentricity orbital solutions for the planetary system are found. In the first one, the outer planets c and d are trapped in the 2/1 mean-motion resonance. The second family of solutions corresponds to the 5/2 mean-motion resonance between these planets. In both families, the planets are locked in (or close to) an apsidal corotation resonance. In the case of the 2/1 MMR, it is an asymmetric apsidal corotation (with the difference between the longitudes of periastra $Δω\sim 60^\circ$), whereas in the case of the 5/2 MMR it is a symmetric antialigned one ($Δω= 180^\circ$).
It remains also possible that the two outer planets are not trapped in an orbital resonance. Then their orbital eccentricities should be relatively small (less than, say, 0.15) and the ratio of their orbital periods is unlikely to exceed $2.3-2.5$.
The spatial distribution of Kuiper belt objects (KBOs) in 2:1 exterior resonance with Neptune constrains that planet's migration history. Numerical simulations demonstrate that fast planetary migration generates a larger population of KBOs trailing rather than leading Neptune in orbital longitude. This asymmetry corresponds to a greater proportion of objects caught into asymmetric resonance such that their resonance angles librate about values > pi (trailing) as opposed to < pi (leading). We provide, for the first time, an explanation of this phenomenon, using physical, analytic, and semi-anal…
The resonance perturbation of planetary ring by distant satellite is considered. The gravity interaction between rings particles is taken into account. The gravitation interaction between particles in rings can change shape of non-circular rings, so it is differ from keplerian ellipse. The shift between simple mean motion resonances and parametric resonance zones is detected. This shift depends on ring properties.
We investigate the secular resonances for massless small bodies and Earth-like planets in several planetary systems. We further compare the results with those of Solar System. For example, in the GJ 876 planetary system, we show that the secular resonances $ν_1$ and $ν_2$ (respectively, resulting from the inner and outer giant planets) can excite the eccentricities of the Earth-like planets with orbits 0.21 AU $\leq a <$ 0.50 AU and eject them out of the system in a short timescale. However, in a dynamical sense, the potential zones for the existence of Earth-like planets are in the area 0.50 …
Following the general numerical analysis of Melita and Woolfson (1996), I showed in a recent paper that a restricted, planar, circular planetary system consisting of Sun, Jupiter and Saturn would be captured in a near (2:1) resonance when one would allow for frictional dissipation due to interplanetary medium (Haghighipour, 1998). In order to analytically explain this resonance phenomenon, the method of partial averaging near a resonance was utilized and the dynamics of the first-order partially averaged system at resonance was studied. Although in this manner, the finding that resonance lock …
We analyze the possible relationship between the current orbital elements fits of known exoplanets in the 2/1 mean-motion resonance and the expected orbital configuration due to migration. It is found that, as long as the orbital decay was sufficiently slow to be approximated by an adiabatic process, all captured planets should be in apsidal corotations. In other words, they should show a simultaneous libration of both the resonant angle and the difference in longitudes of pericenter. We present a complete set of corotational solutions for the 2/1 commensurability, including previously known s…
With the help of the Laplace-Lagrange solution of the secular perturbation theory in a double-planet system, we study the occurrence and the stability of apsidal secular resonance between the two planets. The explicit criteria to predict whether two planets are in apsidal resonance is derived. The pobability of two planets falling in apsidal resonance is given in the initial element space. We verify the criteria with numerical integrations for the HD12661 system, and find they give good predictions except at the boundary of the criteria or when the planet eccentricities are too large. The nonl…
(Abridged) A diversity of 2:1 resonance configurations can be expected in extrasolar planetary systems, and their geometry can provide information about the origin of the resonances. Assembly during planet formation by the differential migration of planets due to planet-disk interaction is one scenario for the origin of mean-motion resonances in extrasolar planetary systems. The stable 2:1 resonance configurations that can be reached by differential migration of planets with constant masses and initially coplanar and nearly circular orbits are (1) anti-symmetric configurations with the mean-mo…
Multi-planet systems detected until now are in most cases characterized by hot-Jupiters close to their central star as well as high eccentricities. As a consequence, from a dynamical point of view, compact multi-planetary systems form a variety of the general N-body problem (with N >= 3), whose solutions are not necessarily known. Extrasolar planets are up to now found in prograde (i.e. direct) orbital motions about their host star and often in mean-motion resonances (MMR). In the present paper, we investigate a theoretical alternative suitable for the stability of compact multi-planetary syst…
The recent radial velocity Keck data for GJ876 in Laughlin et al. (2005) is shown to be in good agreement, apart from a 6 m/s scatter, with a theoretical calculation (Nauenberg, 2002) based on orbital parameters from a fit to the earlier Keck data. The time variation of the periods of the inner and outer planets, which are locked in a near 2:1 resonance, are evaluated, and their mean values, Pi and Po, are shown to satisfy closely the relation Po/Pi=2+Po/P, where P is the period for the retrograde precesion of the common mean periastron of these planets.
The formation of resonant planets pairs in exoplanetary systems involves planetary migration inside the protoplanetary disc : an inwards migrating outer planet captures in Mean Motion Resonance an inner planet. During the migration of the resonant pair of planets, the eccentricities are expected to rise excessively, if no damping mechanism is applied on the inner planet. We express the required damping action to match the observations, and we show that the inner disk can play this role. This result applies for instance to the system GJ 876 : we reproduce the observed orbital elements through a…
In this paper we present a new method that can be used for analysis of time of arrival of a pulsar pulses (TOAs). It is designated especially to detect quasi-periodic variations of TOAs. We apply our method to timing observations of PSR B1257+12 and demonstrate that using it it is possible to detect not only first harmonics of a periodic variations, but also the presence of a resonance effect. The resonance effect detected, independently of its physical origin, can appear only when there is a non-linear interaction between two periodic modes. The explanation of TOAs variations as an effect of …
A restricted planar circular three-body system, consisting of the Sun and two planets, is studied as a simple model for a planetary system. The mass of the inner planet is considered to be larger and the system is assumed to be moving in a uniform interplanetary medium with constant density. Numerical integrations of this system indicate a resonance capture when the dynamical friction of the interplanetary medium is taken into account. As a result of this resonance trapping, the ratio of orbital periods of the two planets becomes nearly commensurate and the eccentricity and semimajor axis of t…
This paper considers the effects of turbulence on mean motion resonances in extrasolar planetary systems and predicts that systems rarely survive in a resonant configuration. A growing number of systems are reported to be in resonance, which is thought to arise from the planet migration process. If planets are brought together and moved inward through torques produced by circumstellar disks, then disk turbulence can act to prevent planets from staying in a resonant configuration. This paper studies this process through numerical simulations and via analytic model equations, where both approach…
We integrate the orbital solutions of the planets orbiting 55 Cnc. In the simulations, we find that not only three resonant arguments $θ_{1}=λ_{1}-3λ_{2}+2\tildeω_{1}$, $θ_{2}=λ_{1}-3λ_{2}+2\tildeω_{2}$ and $θ_{3}=λ_{1}-3λ_{2}+(\tildeω_{1}+\tildeω_{2})$ librate respectively, but the relative apsidal longitudes $Δω$ also librates about $250^{\circ}$ for millions of years. The results imply the existence of the 3:1 resonance and the apsidal resonance for the studied system. We emphasize that the mean motion resonance and apsidal locking can act as two important mechanisms of stabilizing the syst…
This paper continues previous work on the effects of turbulence on mean motion resonances in extrasolar planetary systems. Turbulence is expected to arise in the disks that form planets, and these fluctuations act to compromise resonant configurations. This paper extends previous work by considering how interactions between the planets and possible damping effects imposed by the disk affect the outcomes. These physical processes are studied using three approaches: numerical integrations of the 3-body problem with additional forcing due to turbulence, model equations that reduce the problem to …
We study the time evolution of two protoplanets still embedded in a protoplanetary disk. The results of two different numerical approaches are presented and compared. In the first approach, the motion of the disk material is computed with viscous hydrodynamical simulations, and the planetary motion is determined by N-body calculations including exactly the gravitational forces exerted by the disk material. In the second approach, only the N-body integration is performed but with additional dissipative forces included such as to mimic the effect of the disk torques acting on the disk. This type…
We study the effect of poloidal magnetic field on type I planetary migration by linear perturbation analysis in the shearing-sheet approximation and the analytic results are compared with numerical calculations. In contrast to the unmagnetized case, the basic equations that describe the wake due to the planet in the disk allow magnetic resonances at which density perturbation diverges. In order to simplify the problem, we consider the case without magneto-rotational instability. We perform two sets of analyses: two-dimensional and three-dimensional. In two-dimensional analysis, we find the gen…
The orbits in the HD 160691 planetary system at first appeared highly unstable, but using the MEGNO and FLI techniques of global dynamics analysis in the orbital parameter space we have found a stabilizing mechanism that could be the key to its existence. In order to be dynamically stable, the HD 160691 planetary system has to satisfy the following conditions: (1) a 2:1 mean motion resonance, combined with (2) an apsidal secular resonance in (3) a configuration $P_{c}(ap) - S - P_{b}(ap)$ where the two apsidal lines are anti-aligned, and (4) specific conditions on the respective sizes of the e…
In a previous paper, we have found that the resonance structure of the present Jupiter Trojan swarms could be split up into four different families of resonances. Here, in a first step, we generalize these families in order to describe the resonances occurring in Trojan swarms embedded in a generic planetary system. The location of these families changes under a modification of the fundamental frequencies of the planets and we show how the resonant structure would evolve during a planetary migration. We present a general method, based on the knowledge of the fundamental frequencies of the plan…
We revisit the "dynamical shakeup" model of Solar System terrestrial planet formation, wherein the whole process is driven by the sweeping of Jupiter's secular resonance as the gas disk is removed. Using a large number of 0.5 Gyr-long N-body simulations, we investigate the different outcomes produced by such a scenario. We confirm that in contrast to existing models, secular resonance sweeping combined with tidal damping by the disk gas can reproduce the low eccentricities and inclinations, and high radial mass concentration, of the Solar System terrestrial planets. At the same time, this also…
We present an updated analysis of the GJ 876 planetary system based on an augmented data set that incorporates 65 new high-precision radial velocities obtained with the Keck telescope from 2001 to 2004. These new radial velocities permit a more accurate characterization of the planet-planet interactions exhibited by the system. Self-consistent three-body orbital fits (which incorporate both the estimated instrumental uncertainties and 6 m/s Gaussian stellar jitter) continue to show that GJ 876 b and GJ 876 c are participating in a stable and symmetric 2:1 resonance condition in which the lowes…
The nonlinear stability domain of Lagrange's celebrated 1772 solution of a three-body problem is obtained numerically as a function of the masses of the bodies and the common eccentricity of their Keplerian orbits. This domain shows that this solution may be realized in extra-solar planetary systems similar to those that have been discovered recently with two Jupiter-size planets orbiting a solar-size star. For an exact 1:1 resonance, the Doppler shift variation in the emitted light would be the same as for stars which have only a single planetary companion. But it is more likely that in actua…
The orbits of the outer two known planets orbiting Upsilon Andromedae are remarkably eccentric. Planet C possesses an orbital eccentricity of e1 = 0.253. For the more distant planet D, e2 = 0.308. Previous dynamical analyses strongly suggest that the two orbits are nearly co-planar and are trapped in an apsidal resonance in which the difference between their longitudes of periastron undergoes a bounded oscillation about 0 degrees. Here we elucidate the origin of these large eccentricities and of the apsidal alignment. Resonant interactions between a remnant circumstellar disk of gas lying exte…
Most multi-planetary systems are characterized by hot-Jupiters close to their central star, moving on eccentric orbits. From a dynamical point of view, compact multi-planetary systems form a specific class of the general N-body problem (where N>=3). Moreover, extrasolar planets are found in prograde orbits about their host star, and often in mean motion resonances (MMR). In a first step, we study theoretically a new stabilizing mechanism suitable for compact two-planet systems. This mechanism involves counter-revolving orbits forming a retrograde MMR. In a second step, we investigate the feasi…
A significant number of the known multiple exoplanetary systems are containing a pair of giant planets engaged in a low order mean motion resonance. Such a resonant condition protects the dynamics of these planets resulting in very stable orbits. According to recent studies the capture into a resonance is the result of a planetary migration process induced by the interaction of the planets with a protoplanetary disk. If the migration is slow enough (adiabatic) next to a mean motion resonance, the two planets will also be in apsidal corotation. The recently refined orbital parameters of the sys…
We present results of numerical simulations which examine the dynamical stability of known planetary systems, a star with two or more planets. First we vary the initial conditions of each system based on observational data. We then determine regions of phase space which produce stable planetary configurations. For each system we perform 1000 ~1 million year integrations. We examine upsilon And, HD83443, GJ876, HD82943, 47UMa, HD168443, and the solar system (SS). We find that the resonant systems, 2 planets in a first order mean motion resonance, (HD82943 and GJ876) have very narrow zones of st…
In this paper, we present preliminary results on the stability of massless particles in two and three-planet systems. The results of our study may be used to address questions concerning the stability of terrestrial planets in these systems and also the trapping of particles in resonances with the planets. The possibility of the existence of islands of stability and/or instability at different regions in multi-body systems and their probable correspondence to certain resonances are also discussed.
Among the many new irregular satellites that have been discovered in the last five years, at least six are in the so-called Kozai resonance. Due to solar perturbations, the argument of pericenter of a satellite usually precesses from 0 to 360 degrees. However, at inclinations higher than 39.3 degrees and lower than 140.7 degrees a new kind of behavior occurs for which the argument of pericenter oscillates around +/-90 degrees. In this work we will concentrate on the orbital history of the saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance Kiviuq…
The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.
(Abridged) We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly concentrate on the study of the HD 82943 system by employing two sets of the orbital parameters (Mayor et al. 2004). We find that all stable orbits are related to the 2:1 commensurability for $10^{7}$ yr, and the apsidal phase-locking between two orbits can further enhance the stability for this system. For HD 82943, there exist three possible stable configurations:(1) Type I, only $θ_{1} \approx 0^{\circ}$,(2) Type II, $θ_{1}\approxθ_{2}\…
We calculate the linear torque exerted by a planet on a circular orbit on a disc containing a toroidal magnetic field. All fluid perturbations are singular at the so--called magnetic resonances, where the Doppler shifted frequency of the perturbation matches that of a slow MHD wave propagating along the field line. These lie on both sides of the corotation radius. Waves propagate outside the Lindblad resonances, and also in a restricted region around the magnetic resonances. The magnetic resonances contribute to a significant global torque which, like the Lindblad torque, is negative (positive…
We present an analysis of the HD 82943 planetary system based on a radial velocity data set that combines new measurements obtained with the Keck telescope and the CORALIE measurements published in graphical form. We examine simultaneously the goodness of fit and the dynamical properties of the best-fit double-Keplerian model as a function of the poorly constrained eccentricity and argument of periapse of the outer planet's orbit. The fit with the minimum chi_{nu}^2 is dynamically unstable if the orbits are assumed to be coplanar. However, the minimum is relatively shallow, and there is a wide…
The migration of a planet through a gaseous disc causes the locations of their resonant interactions to drift and can alter the torques exerted between the planet and the disc. We analyse the time-dependent dynamics of a non-coorbital corotation resonance under these circumstances. The ratio of the resonant torque in a steady state to the value given by Goldreich & Tremaine (1979) depends essentially on two dimensionless quantities: a dimensionless turbulent diffusion time-scale and a dimensionless radial drift speed. When the drift speed is comparable to the libration speed and the viscosity …
The two planets about the star GJ 876 appear to have undergone extensive migration from their point of origin in the protoplanetary disk -- both because of their close proximity to the star (30 and 60 day orbital periods) and because of their occupying three stable orbital resonances at the 2:1 mean-motion commensurability. The resonances were most likely established by converging differential migration of the planets leading to capture into the resonances. A problem with this scenario is that continued migration of the system while it is trapped in the resonances leads to orbital eccentriciti…
We report in this paper the numerical simulations of the capture into the 3:1 mean-motion resonance between the planet b and c in the 55 Cancri system. The results show that this resonance can be obtained by a differential planetary migration. The moderate initial eccentricities, relatively slower migration and suitable eccentricity damping rate increase significantly the probability of being trapped in this resonance. Otherwise, the system crosses the 3:1 commensurability avoiding resonance capture, to be eventually captured into a 2:1 resonance or some other higher-order resonances. After th…
In this work we perform a global analysis of the radial velocity curve of the HD 12661 system. Orbital fits that are obtained by the genetic and gradient algorithms of minimization reveal the proximity of the system to the 6:1 mean motion resonance. The orbits are locked in the secular resonance with apsidal axes librating about 180 deg with the full amplitude $\simeq (90,180) deg$. Our solution incorporates the mutual interaction between the companions. The stability analysis with the MEGNO fast indicator shows that the system is located in an extended stable zone of quasi-periodic motions. T…
The mass and period ratios of the two planets orbiting 47 UMa suggest a possible kinship to the Jupiter-Saturn pair in our solar system. We explore the current dynamical state of the 47 UMa system with numerical integrations, and compare the results with analytic secular theory. We find that the planets in the system are likely participating in a secular resonance in which the difference in the longitudes of pericenter librates around zero. Alternately, it is possible that the system is participating in the 7:3 mean motion resonance. We show that stability considerations restrict the mutual in…
We report on a possible correlation between the mass ratio and period ratio of pairs of adjacent planets in extra-solar planetary systems. Monte-Carlo simulations show that the effect is significant to level of 0.7%, as long as we exclude two pairs of planets whose periods are at the 1:2 resonance. Only the next few multiple systems can tell if the correlation is real.
Using numerical methods we thoroughly investigate the dynamical stability in the region between the two planets found in HD 74156. The two planets with minimum masses 1.56 M_JUP (HD 74156b) and 7.5 M_JUP (HD 74156c), semimajor axes 0.276 AU and 3.47 AU move on quite eccentric orbits (e=0.649 and 0.395). There is a region between 0.7 and 1.4 AU which may host additional planets which we checked via numerical integrations using different dynamical models. Besides the orbital evolution of several thousands of massless regarded planets in a three-dimensional restricted 4-body problem (host star, t…
We have used the SHARC II camera at Caltech Submillimeter Observatory to make 350 and 450 micron images of the Vega dust disk at spatial resolutions (FWHM) of 9.7" and 11.1", respectively. The images show a ring-like morphology (radius \~ 100 AU) with inhomogeneous structure that is qualitatively different from that previously reported at 850 microns and longer wavelengths. We attribute the 350/450 micron emission to a grain population whose characteristic size (~ 1 mm) is intermediate between that of the cm-sized grains responsible for emission longward of 850 microns and the much smaller gra…
We show that interaction with a gas disk may produce young planetary systems with closely-spaced orbits, stabilized by mean-motion resonances between neighbors. On longer timescales, after the gas is gone, interaction with a remnant planetesimal disk tends to pull these configurations apart, eventually inducing dynamical instability. We show that this can lead to a variety of outcomes; some cases resemble the Solar System, while others end up with high-eccentricity orbits reminiscent of the observed exoplanets. A similar mechanism has been previously suggested as the cause of the lunar Late He…
The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while Lagrange stability also requires all planets to remain bound to the central star. The Hill stability boundary is defined analytically, but no equations exist to define the Lagrange boundary, so we perform numerical experiments to estimate the location of this boundary. To explore the effect of resonances, we consider orbital element space near the conditions in the…
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 analog of the Solar system. Our work is inspired by work of Malhotra and Minton (2008). 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 sub-system of Jupiters may be found in dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular…
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in geometrical pictures allowing us to investigate a large domain of the phase space of this problem without time-expensive numerical integrations of the equations of motion and without any restriction on the magnitude of the planetary eccentricities, inclinations and mutual distance. Several regimes of motion of the system are observed. With respect to the secul…
The formation of resonant pairs of planets in exoplanetary systems involves planetary migration in the protoplanetary disc. After a resonant capture, the subsequent migration in this configuration leads to a large increase of planetary eccentricities if no damping mechanism is applied. This has led to the conclusion that the migration of resonant planetary systems cannot occur over large radial distances and has to be terminated sufficiently rapidly through disc dissipation. In this study, we investigate whether the presence of an inner disc might supply an eccentricity damping of the inner pl…
We carry out numerical simulations to explore the dynamical evolution of the HD 82943 and HD 37124 planetary systems,which both have two Jupiter-like planets. By simulating various planetary configurations in the neighborhood of the fitting orbits, we find three mechanisms to maintain the stability of these systems: For HD 82943,we find that the 2:1 mean motion resonance can act as the first mechanism for all the stable orbits. The second mechanism is the alignment of the periastron of the two planets of HD 82943 system. In the paper,we show one case is simultaneously maintained by the two mec…
A migrating planet can capture planetesimals into mean motion resonances. However, resonant trapping can be prevented when the drift or migration rate is sufficiently high. Using a simple Hamiltonian system for first and second order resonances, we explore how the capture probability depends on the order of the resonance, drift rate and initial particle eccentricity. We present scaling factors as a function of the planet mass and resonance strength to estimate the planetary migration rate above which the capture probability drops to less than 1/2. Applying our framework to multiple extra solar…
During orbital migration of a giant extrasolar planet via ejection of planetesimals (Murray et al.~1998), inner mean motion resonances can be strong enough to cause planetesimals to graze or impact the star. We integrate numerically the motions of particles which pass through the 3:1 or 4:1 mean motion resonances of a migrating Jupiter mass planet. We find that many particles can be trapped in the 3:1 or 4:1 resonances and pumped to high enough eccentricities that they impact the star. This implies that for a planet migrating a substantial fraction of its semi major axis, a significant fractio…
A residual planetesimal disk of mass 10-100 Earth masses remained in the outer solar system following the birth of the giant planets, as implied by the existence of the Oort cloud, coagulation requirements for Pluto, and inefficiencies in planet formation. Upon gravitationally scattering planetesimal debris, planets migrate. Orbital migration can lead to resonance capture, as evidenced here in the Kuiper and asteroid belts, and abroad in extra-solar systems. Finite sizes of planetesimals render migration stochastic ("noisy"). At fixed disk mass, larger (fewer) planetesimals generate more noise…
In recent years several pairs of extrasolar planets have been discovered in the vicinity of mean-motion commensurabilities. In some cases, such as the Gliese 876 system, the planets seem to be trapped in a stationary solution, the system exhibiting a simultaneous libration of the resonant angle theta_1 = 2 lambda_2 - lambda_1 - varpi_1 and of the relative position of the pericenters. In this paper we analyze the existence and location of these stable solutions, for the 2/1 and 3/1 resonances, as function of the masses and orbital elements of both planets. This is undertaken via an analytical m…
The possible existence of additional long-period planetary-mass objects in the extrasolar planetary systems 47 UMa and 14 Her is investigated. We combine all available radial-velocity data on these stars, spanning up to 18 years. For the 47 UMa system, we show that while a second planet improves the fit to all available data, there is still substantial ambiguity as to the orbital parameters of the proposed planetary companion 47 UMa c. We also present new observations which clearly support a long-period companion in the 14 Her system. With a period of 6906+/-70 days, 14 Her c may be in a 4:1 r…
Based on radial velocity measurements it has been found recently that the two giant planets detected around the star HD 73526 are in 2:1 resonance. However, as our numerical integration shows, the derived orbital data for this system result in chaotic behavior of the giant planets, which is uncommon among the resonant extrasolar planetary systems. We intend to present regular (non-chaotic) orbital solutions for the giant planets in the system HD 73526 and offer formation scenarios based on combining planetary migration and sudden perturbative effects such as planet-planet scattering or rapid d…
(Abridged)We numerically investigated the dynamical architecture of 47 UMa with the planetary configuration of the best-fit orbital solutions by Fischer et al. We systematically studied the existence of Earth-like planets in the region 0.05 AU $\leq a \leq 2.0$ AU for 47 UMa with numerical simulations, and we also explored the packed planetary geometry and Trojan planets in the system. In the simulations, we found that "hot Earths" at 0.05 AU $\leq a < $ 0.4 AU can dynamically survive at least for 1 Myr. The Earth-like planets can eventually remain in the system for 10 Myr in areas involved in…
