Research on Higher-Order Gravitational Potential Gradients of Fundamental Mass Bodies in Cylindrical and Ellipsoidal Coordinates

• Applicant: Dr.-Ing. Xiaole Deng
• Subject Area: Geodesy, Photogrammetry, Remote Sensing, Geoinformatics, Cartography
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 549821068

In recent years, there has been significant progress in understanding gravitational effects, advancing from low-order to higher-order gravitational potential gradients in theoretical geodesy and geophysics. This progress is largely thanks to successful measurements of third-order gradients in laboratory settings. While theoretical expressions for higher-order gravitational potential gradients in Cartesian and spherical coordinates have been developed, the same hasn't been achieved for cylindrical and ellipsoidal coordinates. This project aims to fill this gap by developing theoretical expressions for third- and fourth-order gravitational potential gradients in cylindrical and ellipsoidal coordinates. Specifically, this project will focus on a vertical cylindrical prism, a vertical cylindrical shell, an ellipsoidal prism, and an ellipsoidal shell. Additionally, this project will derive detailed expressions for transforming first-order up to fourth-order gravitational potential gradients among Cartesian, cylindrical, and spherical coordinates. To ensure their correctness, all derived expressions for coordinate transformation will undergo self-validation using a proposed transformation cycle method. This project will also explore the superposition error elimination effect for cylindrical and ellipsoidal shells when discretized into prisms. Furthermore, the project will compare the gravitational potential and its gradients across different coordinates (Cartesian, spherical, cylindrical, and ellipsoidal) for fundamental mass bodies. This analysis will highlight the unique characteristics of each coordinate system. Importantly, our proposal introduces the novel concept of the transformation cycle method for self-validating all coordinate transformation expressions. This method hasn't been explored in theoretical geodesy and geophysics before. Overall, this comprehensive analysis will provide a strong foundation for the practical application of fundamental mass bodies in gravitational fields across various coordinate systems.

• DFG Programme: Research Grants