Connection between Hill stability and weak stability in the elliptic restricted three-body problem

Makó, Zoltán

doi:10.1007/s10569-014-9577-0

Cited by 11 publications

(9 citation statements)

References 25 publications

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“…Integrating these equations over those written in rotating frames allows us (1) tracking the authentic number of revolutions, in place of spurious counts, as in Hyeraci and Topputo (2010); (2) computing conveniently the Kepler energy, so avoiding complex derivations as in Makó et al (2010) and Makó (2014); (3) comparing directly the orbits in the three models, with no need of post-processing.…”

Section: Numerical Integrationmentioning

confidence: 99%

“…Capture sets are sets containing orbits that perform ballistic capture, and are defined by manipulation of the stable sets (Hyeraci and Topputo, 2010). This approach can be replicated in models incorporating planets eccentricity (Makó et al, 2010;Makó , 2014), fourth-body perturbations (Romagnoli and Circi, 2009), and full-ephemeris dynamics (Luo et al, 2014). Differences on capture orbits in the circular restricted three-body problem (CRTBP) and elliptic restricted three-body problem (ERTBP) have been observed in Hyeraci and Topputo (2010).…”

Section: Introductionmentioning

confidence: 99%

“…Differences on capture orbits in the circular restricted three-body problem (CRTBP) and elliptic restricted three-body problem (ERTBP) have been observed in Hyeraci and Topputo (2010). The effect of the primaries true anomaly in the ERTBP has been studied in Circi and Teofilatto (2005), Prado and Neto (2006), Hyeraci and Topputo (2013) and Makó (2014). The effect of perturbations has been analyzed in Machuy et al (2007) and Topputo (2013).…”

Section: Introductionmentioning

confidence: 99%

“…(2) Analyses in Circi (2012), Hyeraci and Topputo (2013) and Makó (2014) show that the capture is facilitated when the primaries are about their perihelion. Does this behavior happen in general for any Sun-planet system?…”

Section: Introductionmentioning

confidence: 99%

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Analysis of ballistic capture in Sun–planet models

Luo

Topputo

2015

Advances in Space Research

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Analysis of ballistic capture orbits in Sun–planet systems is conducted in this paper. This mechanism utilizes purely gravitational forces, and may occur in non-Keplerian regimes. Ballistic capture orbits are generated by proper manipulation of sets of initial conditions that satisfy a simple definition of stability. Six Sun–planet systems are considered, including the inner planets, Jupiter, and Saturn. The role of planets orbital eccentricity, their true anomaly, and mass ratios is investigated. Moreover, the influence of the post-capture orbit in terms of inclination and orientation is also assessed. Analyses are performed from qualitative and quantitative perspective. The quality of capture orbits is measured by means of the stability index, whereas the capture ratio gives information on their statistical occurrence. Some underlying principles on the selection of the dynamical model, the initial true anomaly, and inclination are obtained. These provide a reference for practical cases

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Section: Numerical Integrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of ballistic capture in Sun–planet models

Luo

Topputo

2015

Advances in Space Research

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“…At present, the Hill stability criteria in the elliptic restricted three body problem is not well developed due to the timedependent Jacobi integral. Mako (2004Mako ( , 2005Mako ( , 2014, Mako and Szenkovits (2008), Mako et al (2010) have done a lot of work on this topic. A similar criterion to the circular restricted three body problem is given to measure the Hill stability .…”

Section: Introductionmentioning

confidence: 99%

Analytical criteria of Hill stability in the elliptic restricted three body problem

Gong

2015

Astrophys Space Sci

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Due to the time-dependent Jacobi integral in the elliptic restricted three body problem, it is difficult to develop analytical criteria of Hill stability. In this paper, the Hill stability of the orbit around the one primary is concerned. Several analytical criteria are established based on the bifurcation of the extremum of the Jacobi integral. One criterion is used to judge the Hill stability of the orbit with orbit size known. One criterion is used to judge the Hill stability of the orbit with orbital element completely known. These criteria are applied to the judge the Hill stability of Jupiter's moons and planets in three stellar binaries.

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Basic Formulation

Musielak¹,

Quarles²

2017

SpringerBriefs in Astronomy

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Connection between Hill stability and weak stability in the elliptic restricted three-body problem

Cited by 11 publications

References 25 publications

Analysis of ballistic capture in Sun–planet models

Analysis of ballistic capture in Sun–planet models

Analytical criteria of Hill stability in the elliptic restricted three body problem

Basic Formulation

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