Equilibrium Tidal Response of Jupiter: Detectability by the Juno Spacecraft

Abstract

An observation of Jupiter's tidal response is anticipated for the on-going Juno spacecraft mission. We combine self-consistent, numerical models of Jupiter's equilibrium tidal response with observed Doppler shifts from the Juno gravity science experiment to test the sensitivity of the spacecraft to tides raised by the Galilean satellites and the Sun. The concentric Maclaurin spheroid (CMS) method finds the equilibrium shape and gravity field of a rotating, liquid planet with the tide raised by a satellite, expanded in Love numbers (k nm ). We present improvements to CMS theory that eliminate an unphysical center of mass offset and study in detail the convergence behavior of the CMS approach. We demonstrate that the dependence of k nm with orbital distance is important when considering the combined tidal response for Jupiter. Conversely, the details of the interior structure have a negligible influence on k nm , for models that match the zonal harmonics J 2 , J 4 and J 6 , already measured to high precision by Juno. As the mission continues, improved coverage of Jupiters gravity field at different phases of Ios orbit is expected to yield an observed value for the degree-2 Love number (k 22 ) and potentially select higher-degree k nm . We present a test of the sensitivity of the Juno Doppler signal to the calculated k nm , which suggests the detectability of k 33 , k 42 and k 31 , in addition to k 22 . A mismatch of a robust Juno observation with the remarkably small range in calculated Io equilibrium k 22 = 0.58976±0.0001, would indicate a heretofore uncharacterized dynamic contribution to the tides.

Tidal Response and Shape of Hot Jupiters

“…For a distant perturber, the m = 2 moment dominates the expansion, but higher-order moments become more significant as a 0 /R increases. We note that the Jupiter and Saturn k 22 reported later for comparison defined k nm with q tid,e instead of q tid,0 (Wahl et al 2017a(Wahl et al , 2020.…”

“…S is added to Equation (1), and equipotential surfaces for the combined potential are evaluated on a 3D grid r(r, μ, f). Wahl et al (2020) updated the 3D CMS method by modifying W by subtracting out a linear term determined by an average force,…”

“…Hubbard (2013) introduced the CMS technique, a nonperturbative, iterative method for more precise calculations of selfconsistent shape and gravitational field. The CMS method was subsequently extended to three dimensions and applied to the cases of Jupiter and Saturn (Wahl et al 2016(Wahl et al , 2017aNettelmann 2019;Wahl et al 2020). In this work, we apply the CMS method to hot Jupiter exoplanets for the first time.…”

“…While more computationally expensive than the theory of figures, the CMS method correctly accounts for nonlinear effects that become relevant for extremely deformed planets, most notably effects on the order of the product of rotational and tidal perturbations (Wahl et al 2017a). These nonlinear effects lead to a splitting of the static k nm with degree m and an enhancement of k 22 that is significant for Jupiter and Saturn (Lainey et al 2017(Lainey et al , 2020Durante et al 2020;Wahl et al 2020).…”

Resolving the Latitudinal Short‐Scale Gravity Field of Jupiter Using Slepian Functions

“…3 of 12 10.1029/2020JE006416 The dynamical model used to integrate the Juno trajectory for orbit determination purposes accounts for several effects due to gravitational and nongravitational forces acting on the spacecraft. A nonexhaustive list is: the mass of Jupiter, the Sun and the other planets (Folkner, 2019); Jupiter's rotational parameters (Archinal et al, 2010); Jupiter's zonal harmonic coefficients from degree 2 to 12 (Iess et al, 2018); tidal perturbations caused by the Galilean satellites up to degree 6 (Wahl et al, 2020); the mass of the Galilean satellites (Jacobson, 2013); solar pressure radiation; Jupiter's albedo and thermal emission from the planet.…”