Combining Spherical Harmonics and Slepian Functions for Callisto’s Gravity Field Analysis

The JUpiter ICy moons Explorer (JUICE) is an ESA mission to investigate the Jovian system, with a primary focus on the potential habitability of subsurface oceans on Europa, Ganymede, and Callisto. Launched on 14 April 2023, JUICE will arrive at Jupiter in July 2031, when it will commence a comprehensive science phase, including multiple flybys of the icy moons and a 9-month orbital phase around Ganymede, partially conducted in a low-altitude (500–200 km) polar orbit.

The 3GM experiment (Gravity and Geophysics of Jupiter and the Galilean Moons) will employ precise radiometric tracking to determine the moons’ ephemerides, gravity fields, and tidal responses. For Callisto, 23 flybys will enable the reconstruction of its global gravity field up to approximately degree and order 7 and will support the estimation of gravity variations associated with eccentricity-driven tidal effects [1]. These gravity measurements are critical for detecting the presence of a subsurface ocean and for constraining the internal structure of the moon.

Callisto’s gravity field can be decomposed in spherical harmonics [2], which offer a global representation but are less effective when coverage is sparse or uneven, as is the case with flybys. In contrast, Slepian functions offer improved spatial localization and are better suited for capturing regional gravity anomalies [3].

The Slepian function approach presents therefore some advantages over conventional methods using spherical harmonics. It enables high-resolution spatial estimation of gravity fields in localized regions, even when observational data are limited. This method has proven effective in the Juno mission, where Slepian functions were used to represent the spatially confined gravity signal induced by the Great Red Spot's winds [4] and to resolve the short-scale latitudinal gravity structure of Jupiter [5].

We conducted numerical simulations incorporating all planned Callisto flybys and the associated tracking schedule, which includes three 6-hour tracking windows centered at –12, 0, and +12 hours relative to closest approach. Simulated range and range-rate observables were analyzed to compare gravity anomaly reconstructions based on spherical harmonics alone and in combination with Slepian functions. This analysis aims to identify the optimal approach for accurately modeling Callisto’s gravity field under realistic mission conditions.

References

[1] Cappuccio, Paolo & Di Benedetto, Mauro & Durante, Daniele & Iess, Luciano. (2022). Callisto and Europa Gravity Measurements from JUICE 3GM Experiment Simulation. The Planetary Science Journal. 3. 199. 10.3847/PSJ/ac83c4.

[2] Kaula, W.M., Theory of Satellite Geodesy, Blaisdell Publishing Company, Waltham Massachuset,1966.

[3] Slepian, David. “Some Comments on Fourier Analysis, Uncertainty and Modeling.” SIAM Review, vol. 25, no. 3, 1983, pp. 379–93. JSTOR, http://www.jstor.org/stable/2029386. Accessed 24 June 2024.

[4] Galanti, E., Kaspi, Y., Simons, F. J., Durante, D., Parisi, M., & Bolton, S. J. (2019). Determining the Depth of Jupiter's Great Red Spot with Juno: A Slepian Approach. Astrophysical Journal Letters, 874(2), Article 24. https://doi.org/10.3847/2041-8213/ab10864

[5] Parisi, Marzia & Galanti, Eli & Folkner, William & Kaspi, Yohai & Buccino, Dustin. (2020). Resolving the Latitudinal Short¿Scale Gravity Field of Jupiter Using Slepian Functions. Journal of Geophysical Research: Planets. 125. 10.1029/2020JE006416.