Dynamical and numerical modeling of NEOs orbits using a quintessence-like space-time framework

In this work, we investigate a novel approach for determining the orbits of Near-Earth Objects (NEOs) using a modified version of a Kiselev space-time, which incorporates a matter quintessence-like component. This method focuses on the nonnull geodesics of the space-time metric, with particular emphasis on varying two key parameters: the normalization factor c and the range factor w, within the limits suggested by previous studies in the specialized literature. Our primary objective is to develop a model that can accurately calculate the orbit of a NEO-based solely on two orbital parameters: its eccentricity and semimajor axis. To achieve this, we have implemented a numerical code that takes these two parameters as input values, adjusting the parameters c and w to generate a corresponding orbit. The model was applied to five well-known and potentially hazardous NEOs — (99942) Apophis, (101955) Bennu, (2024) YR4, (2000) SG344 and (2024) BY15 — whose orbital parameters were compared with observational data and results from other numerical models. A fitting procedure based on the L-BFGS-B optimization algorithm was implemented to determine the optimal values of c and w, minimizing the root-mean-square (RMS) radial error with respect to the Keplerian orbit. The fitted values clustered around [Formula: see text] and [Formula: see text], consistent with quintessence-like scenarios and cosmological bounds. The results show that the quintessence-modified relativistic framework is capable of reproducing the orbits of diverse NEOs with kilometer-scale accuracy. Radial error curves and Euclidean error distributions confirm the robustness of the method across different eccentricities, including highly eccentric cases such as (2024) BY15. This approach therefore offers a straightforward yet effective method for calculating NEO orbits, requiring only basic input parameters while still providing reliable results. The findings suggest that matter quintessence-like models could be a useful tool for studying the orbital dynamics of NEOs in a relativistic framework and may serve as a testbed for probing exotic matter effects at solar system scales.