The Lense-Thirring effect on the Galilean moons of Jupiter

The perspectives of detecting the general relativistic gravitomagnetic Lense-Thirring effect on the orbits of the Galilean moons of Jupiter induced by the angular momentum ${\boldsymbol{S}}$ of the latter are preliminarily investigated. Numerical integrations over one century show that the expected gravitomagnetic signatures of the directly observable right ascension $\alpha$ and declination $\delta$ of the satellites are as large as tens of arcseconds for Io, while for Callisto they drop to the $\simeq 0.2\,\mathrm{arcseconds}$ level. Major competing effects due to the mismodeling in the zonal multipoles $J_\ell,\,\ell=2,\,3,\,4,\,\ldots$ of the Jovian non-spherically symmetric gravity field and in the Jupiter's spin axis ${\boldsymbol{\hat{k}}}$ should have a limited impact, especially in view of the future improvements in determining such parameters expected after the completion of the ongoing Juno mission in the next few years. On the other hand, the masses of the satellites, responsible of their mutual $N-$body perturbations, should be known better than now. Such a task should be accomplished with the future JUICE and Clipper missions to the Jovian system. Present-day accuracy in knowing the orbits of the Jovian Galilean satellites is of the order of 10 milliarcseconds, to be likely further improved thanks to the ongoing re-reduction of old photographic plates. This suggests that, in the next future, the Lense-Thirring effect in the main Jovian system of moons might be detectable with dedicated data reductions in which the gravitomagnetic field is explicitly modeled and solved-for.