Measuring Ganymede’s Librations with Laser Altimetry

Gregor Steinbrügge,Alexander Stark,Robin Thor,Hauke Hussmann,Teresa Steinke

doi:10.3390/geosciences9070320

Abstract

Jupiter’s moon Ganymede might be in possession of a subsurface ocean located between two ice layers. However, from Galileo data it is not possible to unambiguously infer the thickness and densities of the individual layers. The upcoming icy satellite mission JUICE (JUpiter ICy moons Explorer) will have the possibility to perform more detailed investigations of Ganymede’s interior structure with the radio science experiment 3GM and the GAnymede Laser Altimeter (GALA). Here we investigate the possibility to derive the rotational state of the outer ice shell by using topography measured by laser altimetry. We discuss two different methods to invert synthetic laser altimetry data. Method 1 is based on a spherical harmonics expansion and Method 2 solves for B-splines on a rectangular grid. While Method 1 has significant limitations due to the omission of high degrees of the global expansion, Method 2 leads to stable results allowing for an estimate of the in-orbit measurement accuracy. We estimate that GALA can measure the amplitude of Ganymede’s librations with an accuracy of 2.5–6.6 μ rad (6.6–17.4 m at the equator). This allows for determining the thickness of an elastic ice shell, if decoupled from the deeper interior by a subsurface ocean, to about an accuracy of 24–65 km.

Highlights

Three of the Galilean satellites, Io, Europa, and Ganymede, are locked in a 1:2:4 orbital resonance.This Laplace resonance forces the satellites into eccentric orbits making them subject to strong, time-variable, gravitational forces exerted by Jupiter
We estimate that GAnymede Laser Altimeter (GALA) can measure the amplitude of Ganymede’s librations with an accuracy of 2.5–6.6 μrad (6.6–17.4 m at the equator)
For the inversion based on a spherical harmonic expansion we solved for the 7-day, 50-day, and 483-day period since similar frequencies (e.g., 7.05 d and 7.16 d) cannot be distinguished by the inversion routine

Summary

Introduction

Three of the Galilean satellites, Io, Europa, and Ganymede, are locked in a 1:2:4 orbital resonance This Laplace resonance forces the satellites into eccentric orbits making them subject to strong, time-variable, gravitational forces exerted by Jupiter. These forces trigger a response of the satellites dependent on their interior structure. Since the long axis is pointed towards the empty focus of the moons’ orbit around Jupiter, librational torques arise, which might force the ice shell to librate about their mean rotation axis [5] The amplitude of this physical libration depends on the interior structure of the respective satellite [4]

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Conclusion