This paper introduces a novel dynamical model, building upon the existing dynamical model for Deimos in the current numerical ephemerides, which only encompasses the simple libration effects of Deimos. The study comprehensively incorporates the rotational dynamics of Deimos influenced by the torque exerted by the major celestial bodies (Mars, the Sun) in the solar system within the inertial space. Consequently, a full dynamical model is formulated to account for the complete coupling between the rotation and orbit of Deimos. Simultaneously, employing precision orbit determination methods used for artificial satellites, we develop an adjustment model for fitting data to the complete model. The 12-order Adams–Bashforth–Moulton (ABM) integration algorithm is employed to synchronously integrate the 12 state variables of the full model to obtain the orbit of Deimos.The difference in the orbits obtained by integrating the full model over a period of 10 years and those obtained by the simplified model is at the order of 10 km. After precise orbit determination, this difference decreases to below 100 m, so numerical simulation results indicate that the full dynamical model and adjustment model are stable and reliable. Simultaneously, the integration of the Deimos third-order gravity field in the full model over a 10-year period induces only meter-level positional changes. This suggests that when constructing the complete model, the utilization of a second-order gravity field alone is sufficient. Compared to the simple model, the polar axis of Deimos in the inertial space exhibits a more complex oscillation in the full model. Additionally, the full model calculates that the minimum moment of inertia principal axis of Phobos has an amplitude of approximately 0.5 degrees in the longitude direction and does not exceed 2 degrees in the latitude direction. This work further advances the current dynamical model for Deimos and establishes the foundational model for the generation of a new set of precise numerical ephemerides for Deimos.

China is planning 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 enhances the 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 multilayered 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.

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.