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, H_lim, as a function of semi-major axis. Our method requires fewer assumptions and decisions to be made in its application, making results more transportable and reproducible amongst studies that implement it, as well as scalable to much larger datasets of asteroids expected in the next decade with the Vera C.~Rubin Observatorys Legacy Survey of Space and Time (LSST). Using the values of H_lim(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 to using a conservative single value of H_lim, an approach often adopted in previous studies. Additionally, by fitting a simple, physically motivated model of H_lim(a) to 7e5 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.
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