Complete determination of the orbital parameters of a system with N+1 bodies using a simple Fourier analysis of the data

TL;DR

This paper presents a straightforward Fourier analysis method to determine the orbital parameters of a star with multiple companions, improving initial estimates for further refinement.

Contribution

It introduces a simple Fourier-based approach to accurately derive orbital parameters in multi-body systems from radial velocity data.

Findings

Effective for systems with many observational points

Provides good initial estimates for traditional minimization algorithms

Applicable to systems with planets, brown dwarfs, or other stars

Abstract

Here we show how to determine the orbital parameters of a system composed of a star and N companions (that can be planets, brown-dwarfs or other stars), using a simple Fourier analysis of the radial velocity data of the star. This method supposes that all objects in the system follow keplerian orbits around the star and gives better results for a large number of observational points. The orbital parameters may present some errors, but they are an excellent starting point for the traditional minimization methods such as the Levenberg-Marquardt algorithms.