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The growing population of man-made objects with the build up ofmega-constellations not only increases the potential danger to all spacevehicles and in-space infrastructures (including space observatories), butabove all poses a serious threat to astronomy and dark skies. Monitoring ofthis population requires precise satellite characterization, which is is achallenging task that involves analyzing observational data such as position,velocity, and light curves using optimization methods. In this study, wepropose and analyze the application of two optimization procedures to determinethe parameters associated with the dynamics of a satellite: one based on theTheory of Functional Connections (TFC) and another one based on the Nelder-Meadheuristic optimization algorithm. The TFC performs linear functionalinterpolation to embed the constraints of the problem into a functional. Inthis paper, we propose to use this functional to analytically embed theobservational data of a satellite into its equations of dynamics. After that,any solution will always satisfy the observational data. The second procedureproposed in this research takes advantage of the Nealder-Mead algorithm, thatdoes not require the gradient of the objective function, as alternativesolution. The accuracy, efficiency, and dependency on the initial guess of eachmethod is investigated, analyzed, and compared for several dynamical models.These methods can be used to obtain the physical parameters of a satellite fromavailable observational data and for space debris characterization contributingto follow-up monitoring activities in space and astronomical observatories.

Theory of Functional Connections and Nelder-Mead optimization methods applied in satellite characterization