Stability of outer planetary systems

Szebehely, V.; McKenzie, R.

doi:10.1007/bf01228541

Cited by 50 publications

(24 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Dvorak et al (1989) also considered P-type planetary orbits. They compared their results with the results from two other papers, Henon & Guyot (1970) and Szebehely & McKenzie (1981) in tabular form for mass ratios of 0.1 to 0.5, defined in the same way as by Kubala et al (1993). While these authors defined only a single stability boundary, Dvorak et al (1989) defined an upper and lower critical orbit.…”

Section: Stability Of P-type Orbitsmentioning

confidence: 90%

“…2). An extensive body of literature is devoted to the stability of the P and S-type orbits in binary systems (e.g., Henon & Guyot 1970;Szebehely & McKenzie 1981;Dvorak 1984Dvorak , 1986Dvorak et al 1989;Benest 1988Benest , 1989Benest , 1993Benest , 1996Kubala et al 1993;Holman & Wiegert 1999). Specifically, in the work of Holman and Wiegert, binaries with different eccentricities and mass ratios were considered and regions of stability of both S-type and P-type orbits were identified.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability of planetary orbits in binary systems

Musielak

Cuntz

Marshall

et al. 2005

A&A

View full text Add to dashboard Cite

Abstract. Stability of S-type and P-type planetary orbits in binary systems of different mass and separation ratios is investigated. Criteria for stable, marginally stable and unstable planetary orbits are specified. These criteria are used to determine regions of stability of planetary orbits in different binary systems with Jupiter-type planets. The obtained results show that the regions of stability for S-type orbits depend on the distance ratio between the star and planet, and the stellar companions, in the range of 0.22 and 0.46, depending on the mass ratio. For P-type orbits, the regions of stability also depend on that distance ratio, in the range of 1.75 and 2.45, again depending on the the mass ratio. Applications of these results to three observed binary systems with giant planets, namely, τ Boo, HD 195019 and GJ 86, show that the orbits of the giant planets in those systems can be classified as stable, as expected.

show abstract

Section: Stability Of P-type Orbitsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Stability of planetary orbits in binary systems

Musielak

Cuntz

Marshall

et al. 2005

A&A

View full text Add to dashboard Cite

show abstract

“…All of them are giant planets moving in high eccentric orbits, except HD 28185 which has an eccentricity of only 0.06 but more than 5 Jupitermasses. However, recently Marcy et al (2002) discovered the first giant planet moving at about 5.5 AU (which can be On the other hand there are general stability studies of P-and S-type motions 2 using the elliptic restricted three body problem 3 like the ones by Harrington (1977), Szebehely (1980), Szebehely & McKenzie (1981), Dvorak (1984Dvorak ( , 1986 Rabl & Dvorak (1988), and Dvorak et al (1989). More recently these studies have been continued by Holman & Wiegert (1999), Pilat-Lohinger (2000a,b) and Pilat-Lohinger & Dvorak (2002).…”

Section: Introductionmentioning

confidence: 99%

Stability limits in double stars

Pilat-Lohinger

Funk

Dvořák

2003

A&A

View full text Add to dashboard Cite

Abstract.We treat the problem of the stability of planetary orbits in double stars with the aid of numerical studies in the model of the elliptic restricted three-body problem. Many investigations exist for the limits of the stability of the S-type planetary motion (i.e. the motion around one component of the binary). In this paper we present a numerical investigation of the so-called P-type orbits which are defined as orbits of the planet around both primary masses. The growing interest of such stability studies is due to the discovery of the numerous extra-solar planets, where five of them move in double star systems. Two different methods are used; in a first study the stability was investigated systematically for different initial conditions of the planet, which is regarded to be massless. We vary the initial starting distance from the barycenter (always with velocities corresponding to circular orbits at the beginning), the angle to the connecting line of the binary and the starting position of the primaries (peri-astron and apo-astron); the primaries' masses are considered to be equal. The numerical stability criterion is set to the condition that during the whole integration time (50 000 periods of the primaries) the planet should not suffer from a close encounter to one of the primaries. The binary's eccentricity (e) is increased form 0 to 0.5 with ∆e = 0.05, and the initial distance (A) to the barycenter is taken of the range from 1.8 to 3.5 AU (for e ≤ 0.15) or to 4.5 AU (for e ≥ 0.2) with ∆A = 0.05 AU. For the first time, we study inclined P-type orbits (0 • ≤ i ≤ 50 • with a step of ∆i = 2.5 • ) for which we analyse the border line of the stable zone. Additionally we also record the escape times for all orbits. In the second part of our study we apply the Fast Lyapunov Indicator (FLI) to distinguish between the differnt types of motion, taking the same initial conditions, only the grid for the initial distance to the barycenter was finer (∆A = 0.01 AU). Since the FLI is known to be a fast chaos indicator we reduced the integration time to 10 4 periods of the primaries. A comparison of the results of the two studies show that they are in good agreement. It turned out that the inclination does not influence the stability significantly. The stability limit itself varies between A = 2.1 AU (for e = 0 and i = 42, 5 • ) and A = 3.85 AU (for e = 0.5 and i = 50 • ).

show abstract

“…For instance, the notion of stability as introduced by Harrington (1977) implied no secular changes in the semimajor axis and orbital eccentricity of a planet during the time of integration. Szebehely (1980) and Szebehely & McKenzie (1981), on the other hand, used the integrals of motion and curves of zero velocity to establish orbital stability. These authors considered a restricted, planar, and circular three-body system with a small planet (with negligible mass) orbiting either of the stars, or the entire binary system.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Stability and Habitability of the γ Cephei Binary‐Planetary System

Haghighipour

2006

ApJ

View full text Add to dashboard Cite

It has been suggested that the long-lived residual radial velocity variations observed in the precision radial velocity measurements of the primary of Cephei ( HR 8974, HD 222404, HIP 116727) are likely due to a Jupiterlike planet orbiting this star. In this paper, the dynamics of this planet is studied, and the possibility of the existence of a terrestrial planet around its central star is discussed. Simulations, which have been carried out for different values of the eccentricity and semimajor axis of the binary, as well as the orbital inclination of its Jupiter-like planet, expand on previous studies of this system and indicate that, for the values of the binary eccentricity smaller than 0.5, and for all values of the orbital inclination of the Jupiter-like planet ranging from 0 to 40 , the orbit of this planet is stable. For larger values of the binary eccentricity, the system becomes gradually unstable. Integrations also indicate that, within this range of orbital parameters, a terrestrial planet, such as an Earth-like object, can have a long-term stable orbit only at distances of 0.3-0.8 AU from the primary star. The habitable zone of the primary, at a range of approximately 3.05-3.7 AU, is, however, unstable.

show abstract

Stability of outer planetary systems

Cited by 50 publications

References 1 publication

Stability of planetary orbits in binary systems

Stability of planetary orbits in binary systems

Stability limits in double stars

Dynamical Stability and Habitability of the γ Cephei Binary‐Planetary System

Contact Info

Product

Resources

About