Theoretical research progress of gravitational field modeling in Earth science and deep-space exploration

Modeling the gravitational field of irregular celestial bodies is a common problem currently faced by the researchers in the fields of Earth science and deep space exploration. This paper reviews the developmental history of gravitational field modeling theory in these two fields. It summarizes research progress in the last decade, focusing on multipole expansion and potential-flow simulation theories. The gravitational field multipole expansion theory introduces the complex algebraic function commonly used in electromagnetism and quantum mechanics to the gravitational field modeling research field, which can express the (internal and external) gravitational field of celestial bodies more concisely. The calculation rules and mathematical tools from the complex function theory make solving the gravitational dynamics problems in Earth and planetary science more convenient. The potential-flow simulation theory is proposed on top of the equivalence of the Earth's external gravitational vector field and the potential-flow velocity field. That is, both are source- and curl-free vector fields. It introduces the numerical algorithms of computational fluid dynamics to model the external gravitational fields of celestial bodies. Because the potential-flow simulation theory is not established based on the perturbation theory, it can overcome the divergence problem of conventional methods, especially when inverting for the gravitational field of an irregularly shaped celestial body. The two theories expand the theoretical research of gravitational field modeling by using seemingly irrelevant knowledge from other research fields, and such methodology is instructive for Earth or deep-space science researchers to make subsequent theoretical improvements. Moreover, we also systematically categorize, compare, and analyze the existing gravitational field modeling methods based on the mathematical definition of the gravitational field, as well as its variants, and summarize their advantages and disadvantages, helping to select proper gravitational field modeling methods for the Earth and deep-space science researchers.