Optimisation of the 3-body dynamics applied to extra-solar planetary systems

TL;DR

This paper introduces a novel method combining gravitational dynamics simulation and optimization to model and fit radial velocity data for extra-solar planetary systems, emphasizing three-body interactions.

Contribution

The paper presents the Planetary Orbit Fitting Process (POFP), integrating a three-body gravitational solver with an optimization scheme for improved modeling of exoplanetary systems.

Findings

POFP effectively fits radial velocity data with realistic three-body dynamics.

The method highlights the importance of dynamical stability in model validation.

The approach demonstrates general applicability to physics and mathematics problems.

Abstract

The body of work presented here revolves around the investigation of the existence and nature of extra-solar planetary systems. The fitting of stellar radial velocity time series data is attempted by constructing a model to quantify the orbital properties of a star-planetary system. This is achieved with the Planetary Orbit Fitting Process (POFP). Though specific to the investigated problem, the POFP is founded on two separate, more general ideas. One is a Solver producing the gravitational dynamics of a Three-Body system by integrating its Newtonian equations of motion. The other is an independent optimisation scheme. Both have been devised using MATLAB. Applying the optimisation to the Solver results in a realistic Three-Body dynamics that best describes the radial velocity data under the model-specific orbital-observational constraints. Combining these aspects also allows for the study of dynamical instability derived from interaction, which is reaffirmed as a necessary criterion for evaluating the fit. The validity of POFP solutions with respect to the observations and other models is discussed in this context. The underlying generality and fundamental principles demonstrate a larger frame of operation where problems in Physics and Mathematics can be solved with a multitude of techniques.