A generalized model of luminosity of space objects for improving the efficiency of observation planning, and experiments on model's formation in the Tiraspol observatory

Abstract

The range of space objects’ luminosity is wide and goes beyond the limiting magnitudes of telescopes. Present model of luminosity does not take into account failed attempts of measurements. It cases overestimation of the model parameters. In fact, as actual estimates correspond to conditional distribution law, they, in general, depend on limiting magnitude. To avoid bias of estimates, the criterion was proposed and analytical and numerical algorithms were developed. In this work the description of generalized model of luminosity of space objects and its testing are presented. The algorithm of estimation parameters of the model was programmed and successfully simulated. The results of tests, when space objects with luminosity close to limiting magnitude are observed, and a comparison of estimates obtained by the proposed algorithm with estimates based on the existing model are proposed in the work. The comparison shows that algorithm estimates parameters more accurately due to the fact that the generalized model takes into account the presence of unobserved "tails" of the distribution law. The results of testing algorithm on real data from Tiraspol Observatory and suggestions for other observatories engaged in monitoring near-Earth space objects to fulfill similar activities are also mentioned. Implementation of these recommendations helps to get a greater amount of information for parameters' estimation of generalized model of luminosity for a greater number of space objects. It is expected that proposed model will improve the efficiency of observation planning of telescopes with different limiting magnitude at the stage of distribution tasks between them.