NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2025 Sep 18, 09:44 -0700
Ian Staniforth https://navlist.net/Spherical-triangles-versus-plane-triangles-Staniforth-sep-2025-g57813 drew attention to Andoyer's method (cf Meeus, Astronomical Algorithms p.85) for computing ellipsoidal distances.
This method was the one used in LORAN position finding where obviously the true geodesic distance is needed for an accurate fix. (see https://www.loran-history.info/research/loran_a/referencess/mit_volume_iv_loran.pdf p 171). It is an expansion to first order in the Earth's flattening, f ≈1/298.
A wealth of information on LORAN can be found at https://www.loran-history.info/default.htm
Andoyer derived the method in 1927 and it was published posthumously in Bulletin Géodésique in 1932. Lambert pushed the result in 1942 in the Journal of the Washington Academy of Sciences and states that he had equivalent formulas several years before the publication but did not publish them then. The method is often called the Andoyer-Lambert formula or simply Lambert's formula.
Expansions to higher orders in f are known https://arxiv.org/abs/1109.4448 .
Robin Stuart
