Stability of planetary systems with bifurcation theory

Szebehely, V.; McKenzie, R.

doi:10.1086/112011

Cited by 33 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The computation of the stability parameter is described by Szebehely and McKenzie (1977) with additional details.…”

Section: Discussionmentioning

confidence: 99%

Qualitative Dynamics of the Sun-Jupiter-Saturn System

Szebehely

1978

International Astronomical Union Colloquium

Self Cite

View full text Add to dashboard Cite

The stability of the three-body problem formed by the Sun, Jupiter and Saturn is investigated using surfaces of zero velocity. The results obtained with the models of the restricted and general problems of three bodies are compared with numerical integration. The system is found to be stable in the sense that Saturn will neither interrupt the (perturbed) binary orbit of Jupiter around the Sun, nor will it escape from the system. It is shown that the known classical triple stellar systems are “more stable” than the solar system, which in turn is “more stable” than the Earth-Moon system.

show abstract

“…The computation of the stability parameter is described by Szebehely and McKenzie (1977) with additional details.…”

Section: Discussionmentioning

confidence: 99%

Qualitative Dynamics of the Sun-Jupiter-Saturn System

Szebehely

1978

International Astronomical Union Colloquium

Self Cite

View full text Add to dashboard Cite

show abstract

“…We first consider, however, the possibility that the threebody system is Hill stable (Szebehely & McKenzie 1977;Marchal & Bozis 1982;Gladman 1993;Barnes & Greenberg 2006), which is determined analytically, but can only approximate orbital stability. The definition of "Hill stability" is that the ordering of the bodies cannot change.…”

Section: Stability Criteriamentioning

confidence: 99%

Orbital Stability and Secular Dynamics of the Proxima Centauri Planetary System

Livesey,

Barnes,

Deitrick

2024

ApJ

View full text Add to dashboard Cite

The two innermost planets of the Proxima Centauri system are separated by just 0.02 au, inducing strong gravitational interactions between them. We assess this interaction by leveraging fast orbital stability indicators and find that orbital stability is very likely if the initial eccentricities of planets b and d are less than ∼0.2, but cannot confirm stability at larger values. We find that stability is not strongly affected by the true masses of the planets or by the distant planet c. However, mutual inclinations between 95° and 142° often result in unstable motion. We further explore the long-term evolution of the orbits in these stable regions of parameter space and find that circularization can take over 5 Gyr. This tidal evolution could support surface energy fluxes in excess of 1 W m−2 for over 1 Gyr, possibly affecting planet b’s habitability.

show abstract

“…If the necessary dynamical prerequisites are fulfilled, even both stars can harbor planets. Generalized dynamical investigations such as Holman & Wiegert (1999), Pilat-Lohinger & Dvorak (2002), semi-analytical (Pichardo et al 2005) or analytical approaches (Szebehely & McKenzie 1977;Eggleton 1983) can be used to determine regions where a test-planet can remain on a stable orbit on secular dynamical timescales.…”

Section: Dynamical Stability Of Circumstellar Planets In Binary Starsmentioning

confidence: 99%

Circumstellar Habitable Zones of Binary Star Systems in the Solar Neighborhood

Eggl,

Pilat-Lohinger,

Funk

et al. 2012

Preprint

View full text Add to dashboard Cite

Binary and multiple systems constitute more than half of the total stellar population in the Solar neighborhood (Kiseleva-Eggleton & Eggleton 2001). Their frequent occurrence as well as the fact that more than 70 (Schneider et al. 2011) planets have already been discovered in such configurations -most noteably the telluric companion of α Cen B (Dumusque et al. 2012) -make them interesting targets in the search for habitable worlds. Recent studies (Eggl et al. 2012b;Forgan 2012) have shown, that despite the variations in gravitational and radiative environment, there are indeed circumstellar regions where planets can stay within habitable insolation limits on secular dynamical timescales. In this article we provide habitable zones for 19 near S-Type binary systems from the Hipparchos and WDS catalogues with semimajor axes between 1 and 100 AU. Hereby, we accounted for the combined dynamical and radiative influence of the second star on the Earth-like planet. Out of the 19 systems presented, 17 offer dynamically stable habitable zones around at least one component. The 17 potentially habitable systems contain 5 F, 3 G, 7 K and 16 M class stars. As their proximity to the Solar System (d < 31 pc) makes the selected binary stars exquisite targets for observational campaigns, we offer estimates on radial velocity, astrometric and transit signatures produced by habitable Earth-like planets in eccentric circumstellar orbits.

show abstract

Stability of planetary systems with bifurcation theory

Cited by 33 publications

References 0 publications

Qualitative Dynamics of the Sun-Jupiter-Saturn System

Qualitative Dynamics of the Sun-Jupiter-Saturn System

Orbital Stability and Secular Dynamics of the Proxima Centauri Planetary System

Circumstellar Habitable Zones of Binary Star Systems in the Solar Neighborhood

Contact Info

Product

Resources

About