Towards exact relativistic theory of Earth's geoid undulation
Sergei Kopeikin (University of Missouri, USA), Elena Mazurova (Moscow, State University of Geodesy, Cartography, Russia), Alexander Karpik, (Siberian State Geodetic Academy, Russia)
TL;DR
This paper develops a relativistic extension of the Earth's geoid model using covariant geometric methods, deriving new equations that incorporate general relativity effects into geodesy calculations.
Contribution
It introduces a covariant definition of the anomalous gravity potential and formulates a relativistic Bruns equation for geoid height calculation.
Findings
Derivation of a covariant Laplace equation for gravity potential
Formulation of a relativistic Bruns equation for geoid height
Discussion of relativistic effects beyond Newtonian approximation
Abstract
The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulate differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.