# Asteroid mass estimation using Markov-chain Monte Carlo

## TL;DR

This paper introduces three algorithms, including a Markov-chain Monte Carlo method, for estimating asteroid masses from gravitational perturbations, highlighting the advantages of MCMC over traditional linearized approaches.

## Contribution

The paper presents a novel MCMC-based algorithm for asteroid mass estimation, improving accuracy over existing linearized methods and providing a comprehensive comparison with other algorithms.

## Key findings

- MCMC estimates align with published masses but suggest uncertainties may be underestimated.
- The 'marching' approximation simplifies the problem but is less accurate.
- The Nelder-Mead method offers a middle ground in complexity and accuracy.

## Abstract

Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to an inverse problem in at least 13 dimensions where the aim is to derive the mass of the perturbing asteroid(s) and six orbital elements for both the perturbing asteroid(s) and the test asteroid(s) based on astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations: the very rough 'marching' approximation, in which the asteroids' orbital elements are not fitted, thereby reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-chain Monte Carlo (MCMC) approach. We describe each of these algorithms with particular focus on the MCMC algorithm, and present example results using both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans.