Enhancing Stellar Orbit Accuracy through the Radius Power Law Time Step Function Model

Accurately determining stellar orbits within astrophysical systems is paramount for understanding celestial mechanics. This study proposes a novel approach to enhance orbit accuracy by incorporating a radius power law time step function model. The methodology involves the numerical integration of the system's dynamics using a forward fourth-order symplectic integrator, combined with a time step function dependent on the distance of the test particle from the system's center. We conduct simulations on various astrophysical scenarios represented by conservative potentials, including point mass, Plummer, and Hernquist models. Our results demonstrate that employing a power-law time step function with an exponent of 1.5 significantly reduces phase-space error (measured by the ratio of radial to orbital periods) and improves orbit accuracy (measured by the gradient of the relative total energy drift). The method is easy to implement, computationally efficient, and adaptable to N-body and more general dynamical systems. Its solid theoretical basis and numerical reliability make it a practical tool for improving orbit accuracy in diverse astrophysical applications.