Evolution of Mean Orbital Spacing in Planetary and Satellite Systems under Tidal Dissipation and Nebular Drag

Abstract

The approximately geometric spacing of orbital distances in planetary and regular satellite systems has long been recognized, yet its dynamical evolution remains poorly constrained. In this paper, we investigate the secular evolution of the mean distance ratio of secondaries under the combined effects of primary tidal dissipation and nebular gas drag. A general analytical framework is derived linking the initial and final mean distance ratios to system parameters and to the physical characteristics of the dominant dissipative processes. Applying this formalism to the Solar System planets and to the regular satellites of Jupiter, Saturn, and Uranus, we show that primary tidal interactions produce only negligible changes in mean distance ratios over timescales comparable to the age of the Solar System. Similarly, nebular gas drag during the protoplanetary and circumplanetary disk phases leads to limited deviations over a broad range of disk models and lifetimes. These results suggest that, within the assumptions adopted, the mean distance ratio evolves only weakly and may preserve information about primordial system configurations established during early disk evolution. The approximate conservation of this quantity may therefore provide a useful diagnostic for constraining the formation and early dynamical evolution of planetary and satellite systems, with potential implications for the architecture of exoplanetary systems.