Asteroid masses are determined by analyzing an asteroid’s gravitational interaction with another object, such as a spacecraft, Mars, a companion in the case of binary asteroids, or another asteroid during a close encounter. Perturbations caused by the masses of larger asteroids during asteroid-asteroid close encounters can be detected in the post-encounter orbits of the smaller test asteroid involved in such an encounter. This can be described as an inverse problem where the aim is to fit six orbital elements corresponding to a given epoch for each asteroid in addition to masses for the perturbing asteroids.
To solve this inverse problem, which is traditionally done with least-squares methods, we have implemented a Markov-chain Monte Carlo (MCMC) based solution and recently (Siltala & Granvik 2020) reported, among other asteroids, significantly lower than expected masses and densities for the asteroid (16) Psyche in particular. Psyche is an interesting, and topical, object as it is the target of NASA’s eponymous Psyche mission and is commonly thought to be of metallic or stony-iron composition, which our previous density estimates disagreed with. In our previous work our two separate mass estimates for Psyche were based on modeling encounters with two separate test asteroids in both cases. Since then we have further refined our mass estimate for Psyche by simultaneously using eight separate test asteroids for this object thus significantly increasing the amount of observational data included on the model which, in turn, will narrow down the uncertainties of our results at the cost of additional model complexity. Here we report and discuss our latest results for the mass of Psyche based on this case and compute corresponding densities based on existing literature values for the volume. We obtain a mass of (0.972 ± 0.148) × 10-11 solar masses for Psyche corresponding to a bulk density of (3.37 ± 0.58) g/cm³ which is higher than our previous results while still remaining consistent with them. It also remains lower than other previous literature values. We compare our results to these previous literature values and briefly discuss possible physical implications of these results.
In addition, we have computed mass estimates for Ceres and Vesta, both of which already have well known masses from the Dawn mission. As such, these two asteroids are not of direct scientific interest but they serve as an useful benchmark to verify that our algorithm provides realistic results as we have “ground truth” values to compare our results to. We find that, for both cases, our results are in line with those of Dawn.