Simulation of Stepwise Gravity Field Estimation for Phobos in MMX QSO Operations

The Martian Moons eXploration (MMX) mission is a JAXA-led sample return mission scheduled for launch in 2026, aiming to reveal the origin and evolution of the Martian moons, Phobos and Deimos. In particular, detailed proximity observations of Phobos are planned. Our objective is to precisely determine the orbit of the MMX spacecraft and the gravity field of Phobos using radiometric tracking, laser ranging, and landmark observations, and ultimately to estimate the internal density structure of Phobos based on these results.

After arriving in the Martian system, the MMX spacecraft will be inserted into a Quasi-Satellite Orbit (QSO) around Phobos, from which detailed observations will be conducted. To ensure spacecraft safety, mission operations begin from a high-altitude QSO and gradually transition to lower-altitude QSOs while updating operational parameters required for navigation and observation. In this study, based on the planned mission profile, we investigate a strategy for stepwise gravity field estimation of Phobos during the gradual orbital descent of the MMX spacecraft.

The proposed approach sequentially updates the gravity field solution at each orbital altitude using all observational data accumulated up to that stage, enabling the estimation of the best available gravity field and spacecraft orbit solutions before entering lower-altitude operational phases. This is particularly important because low-degree gravity coefficients, which contribute most strongly to the gravity acceleration, can be progressively refined during the early mission phases, thereby improving the estimation of higher-degree gravity terms from lower-altitude observations with greater sensitivity. Such a sequential strategy is expected to enhance both the robustness and stability of gravity field recovery.

To evaluate this concept, numerical simulations were performed using predefined “true” shape and internal density structure models of Phobos. The nominal true shape model was based on Ernst et al. (2023), modified so that the center of figure coincides with the center of mass. A geometrically similar model with a slightly different scale was also used to simulate scale factor estimation. For the internal density structure, we assumed a model containing a density anomaly beneath Stickney crater, from which the corresponding gravity field was computed and used to propagate the spacecraft trajectory. Simulated Doppler, LIDAR (Light Detection and Ranging), and landmark observation data were generated from the resulting “true” trajectory, with random Gaussian noise added to each observation type to represent realistic measurement errors.

Gravity field coefficients and spacecraft orbit parameters were estimated from the simulated observations using initial values of the spacecraft state vectors, shape model scale factor, gravity coefficients, and libration amplitude that were intentionally offset from the true solution to reproduce realistic operational uncertainties. The simulations were performed using the GINS software package developed by CNES.

The results show that the proposed stepwise gravity field estimation approach is significantly more effective than a non-sequential estimation method. In simulations without the stepwise approach, the gravity field estimation tended to diverge, whereas the sequential estimation strategy provided stable and convergent solutions throughout the gradual orbital descent. These results demonstrate that the stepwise approach is essential for robust gravity field recovery during MMX operations around Phobos.

Reference

Ernst, C. M., et al.: High-resolution shape models of Phobos and Deimos from stereophotoclinometry, Earth Planets Space, 75, 103, https://doi.org/10.1186/s40623-023-01814-7, 2023.