Contribution of PRIDE VLBI to the JUICE-Europa Clipper moons&#8217; ephemerides solution
Authors: Fayolle Sam (M.S.) , Dirkx Dominic (D.) , Cimo Giuseppe (G) , Gurvits Leonid (L.I.) , Lainey Valery (V.) , Visser Pieter (P.N.A.M.) 
Published: July 2024

Context and rationaleIn the 2030s, JUICE and Europa Clipper radio-science will provide the most accurate measurements to date of the Galilean satellites&#8217; dynamics. A refined ephemerides estimation, by bringing tighter constraints on the moons&#8217; current orbits and migration rates, will be invaluable to our understanding of their origin and thermal-orbital history. In particular, improved ephemerides solutions provide a natural way to characterise tidal dissipation in both Jupiter and its moons, whose combined effect drives the long-term evolution of the entire Galilean system [1].However, achieving a robust and consistent solution that reaches the extremely low uncertainty levels predicted by current simulations [2,3] will be challenging in practice. This would require our models to adequately reproduce both the spacecraft and moons&#8217; dynamics with an accuracy well below the formal errors given by present analyses [4]. In the past, similar dynamical modelling inconsistencies complicated the reconstruction of a global solution for the orbits of Titan [5] and Dione [6] from Cassini&#8217;s flybys. In the JUICE-Europa Clipper case, the combination of 1) the Galilean system&#8217;s specific orbital configuration, 2) the extremely high accuracy of the radio-science measurements, 3) JUICE&#8217;s unique mission profile will put an even more stringent requirement on the quality of our models. The strongly coupled dynamics of the moons &#8211; due to the Laplace resonance between Io, Europa, and Ganymede &#8211; would indeed ideally require a balanced data set. Despite the complementarity of the JUICE and Europa Clipper tours, this will still be far from being the case (no flyby at Io, vs. an incredibly accurate characterisation of Ganymede thanks to JUICE&#8217;s orbital phase).Overcoming the above-mentioned modelling challenges to eventually attain a statistically consistent solution will therefore require proceeding gradually, starting with local (i.e., per flyby) estimations of the flyby moon&#8217;s state - to be carefully analysed and validated - before a global solution can be reconstructed. In our analyses, we investigate the role that JUICE&#8217;s Planetary Radio Interferometry and Doppler Experiment (PRIDE) [7] can play in this perspective, to complement the dedicated radio-science instrument, 3GM on JUICE [8] and the radio-science and gravity experiment on Europa Clipper [9]. PRIDE will provide independent VLBI (Very Long Baseline Interferometry) measurements of the spacecraft&#8217;s angular position in the ICRF (International Celestial Reference Frame), complementing the line-of-sight constraints from classical radio-science (i.e., range and Doppler) [10]. We here assess the contribution of PRIDE VLBI to the moons&#8217; ephemerides determination, regarding both possible solution improvements and validation opportunities.Analysis setupWe first simulated VLBI measurements for JUICE (single-spacecraft VLBI) in various data acquisition and quality scenarios (including realistic biases driven by the radio sources available as calibrators). In particular, we considered two different VLBI noise budgets, based on the statistical properties of existing data sets [11,12,13,14]: a &#8220;good&#8221; quality VLBI case, with a random (Gaussian) noise of ~ 0.25 nrad, and a &#8220;poor&#8221; quality VLBI case with a noise level set to ~ 0.75 nrad.Furthermore, the simultaneous presence of JUICE and Europa Clipper in the Jovian system opens opportunities for the concurrent VLBI tracking of both spacecraft, a technique already demonstrated for Martian orbiters [15]. The resulting measurements, referred to as dual-spacecraft VLBI, yield very accurate constraints on the relative position of JUICE and Europa Clipper. When performed temporally close to both a JUICE flyby and a Europa Clipper flyby, they will also contain valuable information on the relative motion of the Galilean satellites themselves. We identified 11 opportunities for such promising dual-spacecraft VLBI observations (see Fig. 1), and also assessed their contribution to the moons&#8217; ephemerides determination.We performed covariance analyses with and without VLBI, for both local (per flyby) and global moons&#8217; state estimations, the former representing a necessary intermediate step before the latter can eventually be achieved.ResultsWe showed that PRIDE VLBI can bring a significant improvement to the satellites&#8217; local state solutions, most notably in the out-of-plane (normal) direction. This is illustrated in Fig. 2, which compares the per-flyby formal position uncertainties for each flyby moon obtained with and without VLBI. Fig 2 corresponds to the results for single-spacecraft VLBI tracking of JUICE. Comparable improvements are observed with dual-spacecraft VLBI. On the other hand, the VLBI contribution to the moons&#8217; global ephemerides estimation will remain limited. Once such a global estimation is successfully conducted, adding VLBI data cannot further improve the solution beyond what can be attained with Doppler and range only.The implications of our results are, nonetheless, not limited to the absolute improvement of the local state solutions, as the latter also underlines PRIDE&#8217;s critical importance for the reconstruction of consistent and highly accurate global ephemerides. Reduced errors for the moon&#8217;s local, per-flyby state solutions will indeed facilitate detecting possible modelling inconsistencies, and identifying their possible causes (spacecraft or moons&#8217; dynamics). The PRIDE VLBI data set therefore represents a powerful and critical means to improve, complement, and validate the classical radio-science solution. As such, it can play a key role in progressing from local estimates towards a robust, unprecedentedly accurate global solution for the moons&#8217; dynamics.&#160;The complete methodology and results of our analyses have been published here: https://doi.org/10.1016/j.icarus.2024.116101References[1] Lainey et al. (2009) Nature, 459.7249:957-959.[2] Fayolle et al. (2023) Astronomy &amp; Astrophysics, 677:A42.[3] Magnanini et al. (2024), Astronomy &amp; Astrophysics, in press.[4] Fayolle et al. (2022) Planetary and Space Science, 219:105531.[5] Durante et al. (2019) Icarus, 326:123&#8211;132.[6] Zannoni et al. (2020) Icarus, 345:113713.[7] Gurvits et al. (2023) Space Science Reviews, 219(8):79[8] Iess et al. Space Science Reviews, in preparation.[9] Mazarico et al. (2023) Space Science Reviews, 219.4:30.[10] Dirkx et al. (2017) Planetary and Space Science, 147:14&#8211;27.[11] Pradel et al. (2006) Astronomy &amp; Astrophysics, 452(3):1099&#8211;1106.[12] Duev et al. 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