Observational completion limit of minor planets from the asteroid belt to Jupiter Trojans

With the growing numbers of asteroids being discovered, identifying an observationally complete sample is essential for statistical analyses and for informing theoretical models of the dynamical evolution of the solar system. We present an easily implemented method of estimating the empirical observational completeness in absolute magnitude, Hlim, as a function of semimajor axis. Our method requires fewer assumptions and decisions to be made in its application, making results more transportable and reproducible among studies that implement it, as well as scalable to much larger data sets of asteroids expected in the next decade with the Vera C.?Rubin Observatory's Legacy Survey of Space and Time. Using the values of Hlim(a) determined at high resolution in semimajor axis, a, we demonstrate that the observationally complete sample size of the main belt asteroids is larger by more than a factor of 2 compared with using a conservative single value of Hlim, an approach often adopted in previous studies. Additionally, by fitting a simple, physically motivated model of Hlim(a) to ~7×105 objects in the Minor Planet Database, our model reveals statistically significant deviations between the main belt and the asteroid populations beyond the main belt (Hungarias, Hildas, and Trojans), suggesting potential demographic differences, such as in their size, eccentricity, or inclination distributions.