Marussi and the first formulation of Physical Geodesy as a Fixed-Boundary-Value Problem

The famous work of A.Marussi on the geometry of the Earth’s gravity field is known as intrinsic geodesy. This was aiming at describing all the relevant geodetic quantities in terms of the so called intrinsic coordinates and of their reciprocal relation. This has been done in a masterly way including all the interesting variables related to the curvatures of equipotential surfaces, which were in a sense the focus of this attention. However, hidden in Marussi’s equations, is the first formulation of the geodetic boundary-value problem in terms of a fixed-boundary problem This requires a proper understanding of the nature of such equations, as explained in the paper.