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 conditionU ₀ =W ₀ . The computations using three different geopotential models yields the semi-major axis of the earth ellipsoid asa=6378145.4 metres for the flatteningf=1/298.2564. The corresponding equatorial gravity and the geopotential number are computed as γ_a=978029.59 mgals andU ₀=W ₀=6.26367371 10⁶ kgalmeters respectively.