Linear emulator approach for bound orbits under the influence of the Paczynski-Wiita potential

Abstract

We studied orbits under the influence of the Paczynski-Wiita pseudo-Newtonian potential. This potential results in a modified Binet equation that is nonlinear. We can approximate this nonlinearity by using the least squares method to produce a linear emulator. We showed that this approximation produces orbits that precesses over time, outperforming the standard linear Taylor series approximation.