Abstract
This paper presents the application of recent ansatz for estimation of stability of the Laplace resonance for Galilean moons (Io, Europa, Ganymede). We estimate over time the eccentricity + semi-major axis in a binary system experiencing the net tidal friction, including the additional tidal heating which comes from the transformation of net transfer of angular momentum between the Galilean moons of Jupiter (due to dynamical features of the Laplace resonance). Presumably, there should be a net transfer of angular momentum between Io and Europa (for the reason that tidal heating on Ganymede seems to be negligible with respect to Io and Europa). We established the fact that Laplace resonance should be valid and stable on a timescale of centuries in the future, but there might be chaotic perturbations less than 0.1\% for the accuracy of such phenomenon. Moreover, the presented ansatz can be used to predict a scheme for optimizing the maneuvers of spacecrafts in the vicinity of Ganymede (due to absence of net transfer of angular momentum between Ganymede and other Galilean moons). The main conclusion stems from previously suggested approach (\cite{ershkov2017tidal.
Highlights
The Laplace resonance is known to be one of the old famous problems in celestial mechanics, besides we should especially note that a lot of great scientists have been reporting their researches related to this phenomenon during the last 200 years.In accordance with (Peale et al 1979) the Galilean satellites are numbered in the conventional manner with 1 to 4 corresponding respectively to Io, Europa, Ganymede, and Callisto
Since any energy dissipation in the satellite decreases E and since we have E < 0, and Laplace resonance (1) helps to maintain Io’s orbital eccentricity (e) at a stable and constant value (0.0041, according to the data of astrometric observations (Ershkov 2017a)), we find from (2) that there should be a net transfer of angular momentum between the Galilean moons of Jupiter – due to dynamical features of the Laplace resonance (1)
As for scientific originality of the current research (in comparison with the results of work (Ershkov 2017a)), the aforementioned analysis let us conclude that there is a net transfer of angular momentum between Io and Europa, which results in the tidal heating
Summary
The Laplace resonance is known to be one of the old famous problems in celestial mechanics, besides we should especially note that a lot of great scientists have been reporting their researches related to this phenomenon during the last 200 years. Since any energy dissipation in the satellite decreases E and since we have E < 0, and Laplace resonance (1) helps to maintain Io’s orbital eccentricity (e) at a stable and constant value (0.0041, according to the data of astrometric observations (Ershkov 2017a)), we find from (2) that there should be a net transfer of angular momentum between the Galilean moons of Jupiter – due to dynamical features of the Laplace resonance (1). It should be a net transfer of angular momentum between Io and Europa (for the reason that tidal heating on Ganymede seems to be negligible with respect to Io and Europa). Where the scale-factor a0 should be given by the initial conditions
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