A triaxial reference ellipsoid for the Earth

We present a new, physically motivated triaxial reference ellipsoid for the Earth. It is an equipotential surface in the gravity field and closely approximates the geoid, akin to the conventional reference ellipsoid of revolution. According to Bursa and Fialova (Studia Geophysica et Geodaetica 37(1):1-13, 1993), the triaxial reference ellipsoid is uniquely, but not exclusively, specified by the body's total mass, the dynamic form factors of polar and equatorial flattening, the longitude of the equatorial major axis, the rotation rate, and the designated surface potential. We model the gravity field using triaxial ellipsoidal harmonics. While they are rarely considered practical for near-spherical planets, we leverage an intrinsic property that ellipsoidal harmonics yield an exact expression for the constant potential on a triaxial ellipsoid. A practical procedure is proposed to solve for the ellipsoidal parameters that converge iteratively to fulfill the exact condition of equipotentiality. We present the solution for the Earth Gravitational Model 2008.

Automated summary

We propose a new physically motivated triaxial reference ellipsoid for the Earth, which closely approximates the geoid and is an equipotential surface in the gravity field. The ellipsoid is uniquely specified by various factors including the Earth's total mass, dynamic form factors, and rotation rate. We use triaxial ellipsoidal harmonics to model the gravity field and present a practical procedure to iteratively solve for the ellipsoidal parameters.