Variational formulation of the geodetic boundary value problem

A variational principle for the Stokesian boundary value problem is derived using the Euler-Lagrange theory. The resulting variational principle is then transformed into an equation determining the semi-major axis of the best fitting ellipsoid which fulfills the condition U 0 =W 0 . The computations using three different geopotential models yields the semi-major axis of the earth ellipsoid as a=6378145.4 metres for the flattening f=1/298.2564. The corresponding equatorial gravity and the geopotential number are computed as γa=978029.59 mgals and U 0=W 0=6.26367371 106 kgalmeters respectively