Chi-squared test for planetary orbits after the impact of a single flyby and multiple stellar flybys

¹ Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
² Yatsukaho Research Center, Kanazawa Institute of Technology, Hakusan, Ishikawa 924-0838, Japan
e-mail: JuanJzTorres@gmail.com

Received: 16 May 2021
Accepted: 4 August 2021

Abstract

Aims. In this work, I present the cumulative effects of passing stars on planetary disks and I explore the orbital modification of their components as a consequence of multiple stellar encounters. I analyze the effects of masses of the passing stars and look for differences between the effects of four encounters with low masses of 0.1 M_⊙, as well as a single 0.4 M_⊙ stellar encounter on a 100 a.u. planetary disk.

Methods. I applied the chi-squared (χ²) test to estimate the correlation between the resulting parameters of orbits after single and multiple impacts. I found that the χ² value is equal to 0.666 and the probability index is equal to 0.955.

Results. This first approach suggests that three or four low-mass multiple encounters can produce comparable orbits of planets as produced by a single massive encounter.