Analytical determination of orbital elements using Fourier analysis. I. The radial velocity case

TL;DR

This paper introduces an efficient analytical method to determine planetary orbital elements from radial velocity data using Fourier analysis, serving as a fast initial step for more precise numerical algorithms.

Contribution

The paper presents a novel analytical approach for estimating orbital parameters from radial velocity signals, complementing existing numerical methods and enabling iterative multi-planet searches.

Findings

Method provides good approximation of orbital parameters

Accuracy depends on Fourier decomposition quality

Can be used as initial conditions for numerical algorithms

Abstract

We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is mainly limited by the accuracy of the computation of the Fourier decomposition of the signal which is sensitive to sampling and noise. Our method is complementary with more accurate (and more expensive in computer time) numerical algorithms (e.g. Levenberg-Marquardt, Markov chain Monte Carlo, genetic algorithms). Indeed, the analytical approximation can be used as an initial condition to accelerate the convergence of these numerical methods. Our method can be applied iteratively to search for multiple planets in the same system.