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, , 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 (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 , an approach often adopted in previous studies. Additionally, by fitting a simple, physically motivated model of (a) to ∼7נ10⁵ 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.

随着越来越多的小行星被发现，确定一个观测完整的样本对于统计分析和为太阳系动力学演化的理论模型提供信息至关重要。我们提出了一种易于实现的方法，用于估计绝对幅度的经验观测完整性，作为半长轴的函数。我们的方法在其应用中需要更少的假设和决策，使结果在实施它的研究中更具可移植性和可重复性，并且可扩展到预计在未来十年内使用 Vera C.Rubin Observatory’s Legacy 进行的更大的小行星数据集时空调查。使用在半长轴上以高分辨率确定的( a )值，a，我们证明，与使用保守的单一值 相比，主带小行星的观测完整样本量大了 2 倍以上，这是以前研究中经常采用的方法。此外，通过将( a )的简单、物理动机模型拟合到小行星数据库中的∼7נ10 ⁵天体，我们的模型揭示了主带与主带外小行星种群（匈牙利、希尔达斯和特洛伊木马）之间的统计显着偏差)，表明潜在的人口差异，例如大小、离心率或倾斜度分布。