In this work we reviewed the Gauss method to infer the orbits of minor bodies of the solar system, as the identification of optimization parameters to infer the orbital elements of two asteroids near to the Earth (NEAs): 5587 (1990 SB) and 4953 (1990 MU)), already cataloged and named by the Minor Planet Center - MPC. We used the database of JPL - Horizons and also included an analysis using data of Gaia Data Release 3 (DR3). We did an statistic analysis between distribution of points correspondent to orbital elements that we obtained and the inferred by the Jet Propulsion Laboratory-JPL. When data is crossed with the orbital parameters of Small-Body Database (JPL), we analyzed the deficiency grades of the method by statistic comparation with state vector method between orbital elements inferred with the implemented method and the accepted by the community, obtaining a relative error for the orbits calculated of 0.424149% and 0.416237% for the body 5587 (1990SB), and 0.257968% and 0.223521% for the body 4953 (1990MU). The first error value mentioned corresponds to an orbit calculated with the database JPL- Horizons, and the second value to an orbit calculated with the database Gaia (DR3), for each body in study. In the first phases of implementation of the code, it was found that the restrictions of the traditional method are overcome under the additional parameters that are proposed, resulting in orbits that are better approximated than those determined by NASA Team at the time of observation corresponding to the collection of data for the different bodies analyzed in the framework of this work.The best approximations are established with respect to the calculation of the orbital elements through the numerical solutions incorporated in the NASA SPICE kernel in python for a period of 100 years, with a step of 1 month. We found that our data are quite close to the curves that represent the variations of each of the 5 orbital elements involved in our analysis, namely: a, e, i, ω, Ω. Finally, it should be noted that our method could contribute to the estimation of orbits for minor bodies of the Solar System from observational data, which could easily be taken by using small telescopes. Thus, it would enrich processes that seek to expand the coverage of observatories focused on estimating the orbits of minor bodies in the solar system.