Stability of fictitious Trojan planets in extrasolar systems (original) (raw)
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Survey of the stability region of hypothetical habitable Trojan planets
Astronomy and Astrophysics, 2007
Aims. In this work we study the dynamical possibility in extrasolar planetary systems that a terrestrial planet can exist in 1:1 mean motion resonance with a Jovian-like planet. We compiled a catalogue of hypothetical habitable Trojan planets, to be able to make a stability forecast for further extrasolar planetary systems discovered in the future. When speaking of habitability we also took the influence of the spectral type of the central star into account. Methods. We integrated some 10 6 orbits of fictitious Trojans around the Lagrangian points for up to 10 7 orbital periods of the primary bodies and checked the stability of the orbital elements and their chaoticity with the aid of the Lyapunov characteristic indicator and maximum eccentricity. The computations were carried out using the dynamical model of the elliptic, restricted three-body problem that consists of a central star, a gas giant moving in the habitable zone, and a hypothetical (massless) terrestrial planet. Results. Our investigations have shown that 7 exoplanetary systems can harbour habitable Trojan planets with stable orbits (
On the dynamics of Trojan planets in extrasolar planetary systems
Proceedings of the International Astronomical Union, 2007
In this article we examine the motion of fictitious Trojan planets close to the equilateral Lagrangean equilibrium points in extrasolar planetary systems. Whether there exist stable motion in this area or not depends on the massratio of the primariy bodies in the restricted three body problem, namely the host star and the gasgiant. Taking into account also the eccentricity of the primaries we show via results of extensive numerical integrations that Trojan planets may survive only fore< 0.25. We also show first results of a mapping in the 1:1 resonance with a gas giant on an eccentric orbit which is applied to the extrasolar planetary systems HD 17051. We furthermore study the influence of an additional outer planet which perturbs the motion of the gasgiant as well as the Trojan cloud around itsL4Lagrangean point.
Dynamics of possible Trojan planets in binary systems
Monthly Notices of the Royal Astronomical Society, 2009
This paper is devoted to the dynamical stability of possible Trojan planets in binaries and in binary systems where one of the substellar companions is not larger than a brown dwarf. Using numerical integrations, we investigated how the size of the stable region around the Lagrangian point L 4 depends on the mass parameter and the eccentricity of the secondary star. An additional goal of this work was to create a catalogue of all possible candidates, which could be useful for future observations to detect such objects.
Extrasolar Trojan planets close to habitable zones
Astronomy and Astrophysics, 2004
We investigate the stability regions of hypothetical terrestrial planets around the Lagrangian equilibrium points L4 and L5 in some specific extrasolar planetary systems. The problem of their stability can be treated in the framework of the restricted three body problem where the host star and a massive Jupiter-like planet are the primary bodies and the terrestrial planet is regarded as being massless. From these theoretical investigations one cannot determine the extension of the stable zones around the equilibrium points. Using numerical experiments we determined their largeness for three test systems chosen from the table of the know extrasolar planets, where a giant planet is moving close to the so-called habitable zone around the host star in low eccentric orbits. The results show the dependence of the size and structure of this region, which shrinks significantly with the eccentricity of the known gas giant.
Dynamics of possible Trojan planets in binary systems-the 3 dimensional case
This paper is devoted to the stability of possible, inclined Trojan planets in double star systems. We investigated the size of the stable region around the Lagrangian point L4 by using numerical integrations, depending on the mass ratio and the eccentricity of the secondary star. The dynamical model we used was the spatial elliptic restricted three body problem. We created a catalogue of initial conditions where a Trojan planet can be stable. These results could be useful for future observations and help to detect such objects.
Monthly Notices of the Royal Astronomical Society, 2012
This paper is devoted to the study of the stability of the Lagrangian point L 4 in the spatial restricted three-body problem and to the possibility of inclined Trojan-like objects in exoplanetary systems (single and binary star systems). The stability is investigated by numerical methods, computing stability maps in different parameter planes. In the case of circular motion of the primary bodies, it is shown that there are stable orbits up to an inclination i = 61 • of the test particle. At moderate inclinations (∼10 • to ∼50 •), we find that the stability limit in the mass ratio of the primaries extends well beyond the linear stability value of 0.0385-with stable orbits existing even for extreme mass ratios of 0.048. In the case of elliptic motion of the primaries, the stable region in the mass ratio-eccentricity plane shrinks as the inclination increases, with no stable orbits being found for inclinations in excess of i = 61 •. Both in the circular and elliptic cases, the structure of the stability regions is closely connected with secondary resonances between the librational frequencies. As an application, the results are applied to 35 known exoplanetary systems showing which of them may possess Trojan-like objects in inclined orbits.
Dynamics and stability of telluric planets within the habitable zone of extrasolar planetary systems
2008
Aims. We study gravitational perturbation effects of observed giant extrasolar planets on hypothetical Earth-like planets in the context of the three-body problem. This paper considers a large parameter survey of different orbital configuration of two extrasolar giant planets (HD 70642b and HD 4208b) and compares their dynamical effect on Earth-mass planetary orbits initially located within the respective habitable terrestrial region. We are interested in determining giant-planet orbit (and mass) parameters that favor the condition to render an Earth-mass planet to remain on a stable and bounded orbit within the continuous habitable zone. Methods. We applied symplectic numerical integration techniques to studying the short and long term time evolution of hypothetical Earth-mass planets that are treated as particles. In addition, we adopt the MEGNO technique to obtain a complete dynamical picture of the terrestrial phase space environment. Both multi-particle and single-particle simulations were performed to follow an Earth-mass planet in the habitable region and its subsequent long term evolution. Results. Our numerical simulations show that giant planets should be on circular orbits to minimize the perturbative effect on terrestrial orbits. The orbit eccentricity (and hence proximity) is the most important orbital parameter of dynamical significance. The most promising candidate for maintaining an Earth-mass planet on a stable and bounded orbit well-confined to the continuous habitable zone is HD 70642b. Even the large planetary mass of HD 70642b renders an Earth-mass planet habitable during the complete lifetime of the host star. The results allow us to extrapolate similar observed systems and points the necessity further constraining the uncertainty range in giant planet orbital eccentricity by future follow-up observations.
A dynamical stability study of Kepler Circumbinary planetary systems with one planet
Monthly Notices of the Royal Astronomical Society, 2014
To date, 17 circumbinary planets have been discovered. In this paper, we focus our attention on the stability of the Kepler circumbinary planetary systems with only one planet, i.e. . In addition to their intrinsic interest, the study of such systems is an opportunity to test our understanding of planetary system formation and evolution around binaries. The investigation is done by means of numerical simulations. We perform numerical integrations of the full equations of motion of each system with the aim of checking the stability of the planetary orbit. The investigation of the stability of the above systems consists of three numerical experiments. In the first one, we perform a long-term (1 Gyr) numerical integration of the nominal solution of the six Kepler systems under investigation. In the second experiment, we look for the critical semimajor axis of the six planetary orbits, and finally, in the third experiment, we construct two-dimensional stability maps on the eccentricity-pericentre distance plane. Additionally, using numerical integrations of the nominal solutions we checked if these solutions were close to the exact resonance.
The Observed Trojans and the Global Dynamics Around The Lagrangian Points of the Sun–Jupiter System
Celestial Mechanics and Dynamical Astronomy, 2005
In this paper, we make a systematic study of the global dynamical structure of the Sun-Jupiter L 4 tadpole region. The results are based on long-time simulations of the Trojans in the Sun, Jupiter, Saturn system and on the frequency analysis of these orbits. We give some initial results in the description of the resonant structure that guides the long-term dynamics of this region. Moreover, we are able to connect this global view of the phase space with the observed Trojans and identify resonances in which some of the real bodies are located.
Regular motions in extra-solar planetary systems
Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems, 2000
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes oscillates around a constant value. It introduces the Hamiltonian equations of the N -planet problem and Poincaré's reduction of them to 3N degrees of freedom with a detailed discussion of the non-osculating "canonical" heliocentric Keplerian elements that should be used with Poincaré relative canonical variables. It also includes Beaugé's approximation to expand the disturbing function in the exoplanetary case where masses and eccentricities are large. The paper is concluded with a discussion of systems captured into resonance and their evolution to symmetric and asymmetric stationary solutions with apsidal corotation.