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. (C) 2017 Elsevier Inc. All rights reserved.

Twelve years ago the Catalina Sky Survey discovered Earth's first known natural geocentric object other than the Moon, a few-meter diameter asteroid designated 2006 RH120. Despite significant improvements in ground-based telescope and detector technology in the past decade the asteroid surveys have not discovered another temporarily-captured orbiter (TCO; colloquially known as minimoons) but the all-sky fireball system operated in the Czech Republic as part of the European Fireball Network detected a bright natural meteor that was almost certainly in a geocentric orbit before it struck Earth's atmosphere. Within a few years the Large Synoptic Survey Telescope (LSST) will either begin to regularly detect TCOs or force a re-analysis of the creation and dynamical evolution of small asteroids in the inner solar system. The first studies of the provenance, properties, and dynamics of Earth's minimoons suggested that there should be a steady state population with about one 1- to 2-m diameter captured objects at any time, with the number of captured meteoroids increasing exponentially for smaller sizes. That model was then improved and extended to include the population of temporarily-captured flybys (TCFs), objects that fail to make an entire revolution around Earth while energetically bound to the Earth-Moon system. Several different techniques for discovering TCOs have been considered but their small diameters, proximity, and rapid motion make them challenging targets for existing ground-based optical, meteor, and radar surveys. However, the LSST's tremendous light gathering power and short exposure times could allow it to detect and discover many minimoons. We expect that if the TCO population is confirmed, and new objects are frequently discovered, they can provide new opportunities for (1) studying the dynamics of the Earth-Moon system, (2) testing models of the production and dynamical evolution of small asteroids from the asteroid belt, (3) rapid and frequent low delta-v missions to multiple minimoons, and (4) evaluating in-situ resource utilization techniques on asteroidal material. Here we review the past decade of minimoon studies in preparation for capitalizing on the scientific and commercial opportunities of TCOs in the first decade of LSST operations.

Radar observations can be used to obtain accurate orbital elements for near-Earth objects (NEOs) as a result of the very accurate range and range rate measureables. These observations allow the prediction of NEO orbits further into the future and also provide more information about the properties of the NEO population. This study evaluates the observability of NEOs with the EISCAT 3D 233 MHz 5 MW high-power, large-aperture radar, which is currently under construction. Three different populations are considered, namely NEOs passing by the Earth with a size distribution extrapolated from fireball statistics, catalogued NEOs detected with ground-based optical telescopes and temporarily captured NEOs, i.e. mini-moons. Two types of observation schemes are evaluated, namely the serendipitous discovery of unknown NEOs passing the radar beam and the post-discovery tracking of NEOs using a priori orbital elements. The results indicate that 60-1200 objects per year, with diameters D > 0.01 m, can be discovered. Assuming the current NEO discovery rate, approximately 20 objects per year can be tracked post-discovery near the closest approach to Earth. Only a marginally smaller number of tracking opportunities are also possible for the existing EISCAT ultra-high frequency (UHF) system. The mini-moon study, which used a theoretical population model, orbital propagation, and a model for radar scanning, indicates that approximately seven objects per year can be discovered using 8 %-16% of the total radar time. If all mini-moons had known orbits, approximately 80-160 objects per year could be tracked using a priori orbital elements. The results of this study indicate that it is feasible to perform routine NEO post-discovery tracking observations using both the existing EISCAT UHF radar and the upcoming EISCAT 3D radar. Most detectable objects are within 1 lunar distance (LD) of the radar. Such observations would complement the capabilities of the more powerful planetary radars that typically observe objects further away from Earth. It is also plausible that EISCAT 3D could be used as a novel type of an instrument for NEO discovery, assuming that a sufficiently large amount of radar time can be used. This could be achieved, for example by time-sharing with ionospheric and space-debris-observing modes.