Tesseral Harmonics of Jupiter from Static Tidal Response

Abstract

The Juno Orbiter is measuring the three-dimensional gravity field perturbation of Jupiter induced by its rapid rotation, zonal flows, and tidal response to its major natural satellites. This paper aims to provide the contributions to the tesseral harmonics coefficients Cnm, Snm, and the Love numbers knm to be expected from static tidal response in the gravity field of rotating Jupiter. For that purpose, we apply the method of Concentric Maclaurin Ellipsoids. As we are interested in the variation of the tidal potential with the longitudes of the moons, we take into account the simultaneous presence of the satellites Io, Europa, and Ganymede. We assume coplanar, circular orbits with normals parallel to Jupiter's spin axis. The planet-centered longitude of Io in the three-moon case is arbitrarily assumed φ = 0. Under these assumptions we find maximum amplitudes and fluctuations of 3.5 × 10−8 ± 15% for C22. For the Love numbers, the largest variation of 10% to 20% is seen in k42 and k62, whereas the values k2, k33, and k44 fall into narrow ranges of 0.1% uncertainty or less. In particular, we find , where is the static tidal response to lone Io. Our obtained gravity field perturbation leads to a maximum equatorial shape deformation of up to 28 m. We suggest that should Juno measurements of the knm deviate from those values, it may be due to dynamic or dissipative effects on Jupiter's tidal response. Finally, an analytic expression is provided to calculate the tesseral harmonics contribution from static tidal response for any configuration of the satellites.