Comparison of mean and osculating stability in the vicinity of the (2:1) tesseral resonant surface

• Context: long-term evolution of artificial satellite.
• Problem: investigation of the possible effects of the short periodic terms neglected during the averaging procedure.
• Case study: the 2:1 tesseral resonance.
• Methods: confrontation of Osculating and Mean Fast-Lyapunov Indicator stability maps.
• Conclusion: chaos is robust to the averaging procedure and numerical methods used to propagate the motion.

We confront stability results over long time scales, considering alternately the averaged and the non-averaged theory to propagate the equations of motion of a celestial body orbiting the vicinity of the (2:1) tesseral resonant surface. This confrontation is performed using Fast Lyapunov Indicator stability maps. The benefit of such maps is threefold: (i) to reveal the whole phase space architecture and the consequences of the resonance overlap when several combinations of tesseral resonant parameters are accounted for, (ii) to perform a stability analysis on a whole phase space region, and (iii) to have a clear view of the possible impacts of the short-periodic effects removed during the averaging procedure. Our detailed numerical investigations conclude that the tesseral chaos is robust to the averaging procedure and the numerical methods used to propagate the equations of motion over such long time scales.