A High-Precision Dynamical Model of Callisto: Incorporating Rotation Effects within Multi-Layer Internal Structure Models

TL;DR

This work advances Callisto ephemerides by introducing a high-precision dynamical model that fully couples Callisto’s rotation with its orbital motion. The authors first reproduce the current ephemeris-style simple model, incorporating N-body forces, Jupiter’s non-spherical gravity and rotation, Galilean perturbations, librations, and General Relativity, then build a full rotation–orbit coupling model using a rigid-body rotation framework with Euler-Liouville dynamics and a 12-variable state transition structure. Data-fitting against NOE-5-2023 demonstrates that the full model achieves tight agreement, with residuals shrinking to about $\sim$25 meters when adjusted, underscoring the significance of rotational effects for precision ephemerides. They further assess tidal effects under multi-layer internal structures (two-layer and three-layer) through a tide potential and Love numbers, finding meter-scale differences over a decade, which indicates that internal-structure constraints are essential for maximum accuracy. Overall, the full model provides a robust platform for Tianwen-4 data analysis and a route to refining Callisto’s gravity field and interior structure in future missions, including JUICE.

Abstract

China is planing to launch the Tianwen-4 mission around the year 2030, with its aim being the exploration of Jupiter and its moon, Callisto. Within the realm of deep space exploration, the accuracy of ephemerides is of great importance. Current ephemerides employ a simplified rotation model for Callisto, which this study addresses by proposing a novel dynamical model. This model enhancesthe existing orbital dynamics by integrating Callisto's rotational motions influenced by gravitational torques from the Sun, Jupiter, and other Galilean moons within an inertial frame, capturing the intricate coupling between Callisto's orbital and rotational dynamics. The study establishes a full dynamical model by deriving analytical expressions for this coupling and developing an adjustment model for data fitting using precise orbit determination methods. Furthermore, the influence of tidal effects on Callisto's motion is investigated, considering its multi-layered internal structure. Results demonstrate that the difference between the newly established full model and the model in current ephemerides is on the order of tens of meters. When calculating the impact of different internal structures of Callisto on its orbit, the influence of three-layered and two-layered structures is on the order of meters, suggesting that the development of a high-precision dynamical model requires additional constraints on the internal structure of Callisto. This research provides a novel alternative for a new generation of precise numerical ephemerides for Callisto. Additionally, these findings provide a testing platform for the data from the Tianwen-4 mission.

Figures (13)

• Figure 1: The Euler angles for the transformation between JCRS and the Jupiter-fixed coordinate system Yang2017DeterminationOT. Precession angle($\phi$): The angle at which Jupiter rotates around the Z-axis of the fixed coordinate system; Nutation angle($\theta$): The angle at which Jupiter rotates around the X-axis obtained after the first rotation (the intersection line of Jupiter's celestial coordinate system and the equatorial plane of the fixed coordinate system); Spin angle($\psi$): The angle at which the rigid body rotates around the Z-axis obtained after the second rotation.
• Figure 2: The influence of the gravitational fields of the three Galilean satellites (Io, Europa, and Ganymede) on Callisto’s orbit. The ordinate $\mathit{\Delta}P$ represents the difference between the orbit that includes the perturbations of the Galilean satellites and the calculated orbit that does not, with the unit being meters; the abscissa represents the integration duration starting from the J2000 epoch.
• Figure 3: The integration starts at the J2000 epoch. By reproducing the dynamical model from the current ephemeris, we calculate and compare the orbital differences with the position of Callisto from NOE-5-2023 ephemeris. The ordinate shows positional differences (in kilometers), and the abscissa represents the integration duration (in years).
• Figure 4: The integration commences at the J2000 epoch. The reproduced dynamical model is subjected to data fitting using position and velocity data of Callisto from the NOE-5-2023 ephemeris. The ordinate depicts positional differences (in kilometers), while the abscissa represents the integration duration (in years).
• Figure 5: After fitting the reproduced model of Callisto to the NOE-5-2023 ephemeris, the differences in the x, y, and z directions between the calculated results and the positions of Callisto in the NOE-5-2023 ephemeris.