Main Belt Asteroid Mass Estimation from High-Precision Astrometry

The most massive asteroids in the main belt perturb the trajectories of planets and other asteroids. High-precision astrometric measurements of the positions of the perturbed asteroids can show this deviation, especially with long observation arcs before and after the encounters. The large, perturbing asteroid masses can be included in the orbital fitting process to obtain new asteroid mass estimates [1]. We use all available astrometric observations of perturbed asteroids (referred as test asteroids) to estimate the mass of as many large asteroids (referred as perturbers) as possible. In particular, the Gaia Focused Product Release (FPR) [2] of high-precision astrometry allows more precise estimates of asteroid masses [3], which we attempt in general for large asteroids in the main belt.

Close Approach Search: We select an initial perturber list of N_L=1783 main belt, trojan, centaur and TNO asteroids with an inferred GM > 0.003 km³/s², based on a size estimate from the absolute magnitude and density from taxonomic type [4]. All asteroids in JPL’s Small-Body Database^[1] with well-determined orbits are considered as candidate test asteroids (1.07 million asteroids with MPC condition code = 0 out of the 1.4 million discovered asteroids). Then, we integrate the test asteroid orbits within their data arcs considering the perturbations of all planets (ephemeris model DE441 [5]) and perturber asteroids. We search for encounters with any asteroid in the perturber list. We find that 0.97 million objects have at least one encounter closer than 0.05 au with any of the objects in the perturber list within their respective data arcs.

Mass Estimation Methodology:

Test asteroid orbit determination: We correct astrometry for star catalog biases [6] and set station specific data weights [7], with specific treatment for Gaia FPR astrometry [8]. We fit the orbits of all test asteroids while estimating N_p perturber masses that the test asteroid encountered within its data arc, a subset of N_L. We set an apriori GM uncertainty to a large value, which prevents orbit determination divergence. We identify cases when the post-fit mass uncertainty is significantly smaller, which indicates there is real signal of the mass in the astrometry. We iterate the fitting process from updating the masses and perturber trajectories to the test asteroid orbit determination. After the orbital fit, we have the full (6+ N_p)x(6+ N_p) orbit covariance for each test asteroid, from which we sub-select the (N_pxN_p) perturber mass covariance.

Perturber masses: We compute the final mass estimates as a N-dimensional weighted mean of the individual estimates alongside the corresponding (N_LxN_L) covariance. The weighted mean only includes the test asteroids that had at least 1 perturber estimate with reduced uncertainty, extracted as the square root of the diagonal terms of the covariance. This full-size covariance allows us to identify cases with coupled mass estimates [1], typically due to encounters between those perturbers or encounters occurring shortly after one another.

Results: Out of all the test asteroids, we find ~10% of them are considered for the final perturber weighted mass estimates. The combination yields a total number of 77 mass estimates with SNR>10 (error <10%) and 231 estimates with SNR>3, which represent a significant addition to previous estimates from spacecraft position measurements [9] or other estimates in the literature [10]. This improvement is mostly enabled by the precision of Gaia astrometry [2,3], which limits the final uncertainties typically to be > 0.01 km³/s². However, on rare occasions very close encounters can be very well observed and lead to mass estimates with tiny uncertainties such as 0.039 0.001 km³/s² (445 Edna) or the smallest we found, 0.0032 0.0006 km³/s² (1952 Hesburgh). We did not find signal of mass estimates of Trojans, Centaurs or Trans-Neptunian Objects.

Main Belt Total Mass: The total mass of the main belt (sum of all a<4.6 au) is estimated to be 12.90  10⁻¹⁰ M_⊙, which is similar to previous estimates in the literature and consistent with the estimated errors.

Asteroid Densities: From the estimated masses, we derive updated density estimates for asteroids with well determined diameters and find consistency with their taxonomic types.

Conclusions: The latest Gaia data release allows us to estimate the masses of large main belt asteroids with higher precision and for more objects than previously attempted. We describe the details of the methodology and results in a journal publication. These mass estimates will improve the dynamical models of motion in the Solar System as well as our understanding of the densities of asteroids of given taxonomic classes.

Acknowledgments: This research was supported by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory, administered by Oak Ridge Associated Universities under contract with NASA. D.F, J.G. and R.P. conducted this research at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA (80NM0018D0004).

References:

[1] Baer, J. and Chesley, S. R., (2017) AJ, 154:76,
[2] Gaia Collaboration et al, (2023) A&A, 680, A37
[3] Farnocchia, D., et al (2024) AJ, 168:21
[4] Carry, B., (2012) PSS, 73(1), 98-118.
[5] Park, R.S., et al (2021) AJ, 161:105
[6] Eggl, S., et al (2020) Icarus, 339, 113596
[7] Vereš, P., et al (2017) Icarus, 139-149
[8] Fuentes-Muñoz, O., et al (2024) AJ, 167:290.
[9] Farnocchia, D., et al (2021) Icarus, 369, 114594
[10] Fienga, A., et al (2020) MNRAS, 492, 589-602

^[1] Publicly accessible at JPL’s Solar System Dynamics website, data accessed November 2024.