Systematic simulations of FFP scattering by a star–planet pair

  • Vassiliki DoultsinouEmail author
  • B. Loibnegger
  • H. Varvoglis
  • R. Dvorak
Original Article


The increasing number of free-floating planets discovered in recent years confirms earlier theoretical predictions and leads us to believe that the possibility of such an object intruding an existing planetary system is not negligible, especially in dense clusters. We present a theoretical dynamical study on the interaction of a free-floating planet (hereafter FFP) with an initially bound star–planet pair consisting of a Jupiter-sized planet (hereafter BP) orbiting a Sun-like star. Our results could serve as a base for analytical, or semi-analytical, studies on the three-dimensional three-body scattering problem. In our three-dimensional models, thousands of different trajectories for an incoming FFP with initially parabolic velocity are integrated, in order to investigate the interaction between the objects. The study is based on two independent approaches, in order to corroborate the significance of the results. In the first approach, the FFP interacts with a Solar-like system (hereafter SlS) consisting of the Sun and Jupiter at \(5.2\,\mathrm{AU}\). In the second, we compute the trajectories of a FFP interacting with a closely bound exoplanetary system (hereafter ES) with the Jupiter-sized planet at an orbit of \(1\,\mathrm{AU}\) around its host, Sun-like star. For both approaches, the simulations have five free parameters, namely the initial phase of the BP, \(\phi _{BP}\), the mass, \(m_{FFP}\), the initial inclination, \(i_{FFP}\), the orientation of the velocity vector of the FFP and the impact parameter \(d_{FFP}=d\). We focus on three possible final states, namely “flyby,” “capture” and “exchange.” One can observe that the overall picture does not change between the two models used. We present a statistical analysis of the data and the probabilities for the different outcomes for both. Capture and flyby are dominant, in almost equal parts, while the probability for an exchange is rather low. A close look of the orbital elements in case of a capture of the FFP provides more information on the dynamical behavior of the two models, allowing us to draw more precise conclusions, when it comes to the similarities and differences between them. Different mass, as well as different orientation of the velocity vector of the incoming planet, does affect the final outcome quantitatively and qualitatively, in both cases.


Free-floating planets Gravitational scattering Three-body problem 



B. Loibnegger acknowledges support by the Austrian Science Fund (FWF) through grant S11603-N16. V. Doultsinou would like to thank the HellasGRID AUTh team for the extra sources and technical support.

Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Supplementary material


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of ThessalonikiThessalonikiGreece
  2. 2.Department of AstrophysicsUniversity of ViennaViennaAustria

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