Long-term growth of the non-closed 2PN perturbation

Determine whether the finite-time relative-distance perturbation generated by the non-closed 2PN acceleration exhibits unbounded long-term growth beyond the finite integration intervals studied for the Sun–Jupiter–Saturn and Sun–Mercury–Venus benchmark systems.

Background

The paper computes the leading relative-distance response driven by the non-closed contribution to the harmonic-gauge 2PN equations of motion for two isolated three-body benchmarks: Sun–Jupiter–Saturn over approximately 1,800 years and Sun–Mercury–Venus over approximately 50 years. In both cases, the perturbations change sign and remain oscillatory over the simulated intervals, although larger sampled amplitudes can occur at later times.

The available calculations do not establish the behavior of the perturbation over arbitrarily long times. In particular, the authors distinguish the absence of observed monotonic or secular growth within their finite intervals from the unresolved possibility of unbounded long-term growth. Addressing this question would require substantially wider integration intervals and potentially a broader range of N-body configurations.