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A Secular Relativistic Model For Solar System's Numerical Simulations

Using Gauss' averaged equations, we compute the secular relativistic effects generated by the Sun on the argument of the perihelion and the mean anomaly of an orbit. Then we test different alternative simpler models that have been proposed to reproduce the secular relativistic effects in the orbital elements. Generally, models introduce artificial perturbations that are velocity-independent but that depend on the heliocentric distance. If these perturbations are set as an impulse in a constant timestep integrator, when the particle approaches perihelion the generated impulse could be very strong and badly sampled, originating a spurious orbital evolution. In order to overcome this setback, we propose two new models based on a constant, distance-independent, perturbation. With these models we obtain the correct secular drift in the argument of perihelion and the expected secular orbital evolution is reproduced. We also discuss with some detail the secular effect generated on the mean anomaly by different models.