Solution of the Dirichlet and Stokes exterior boundary problems for the Earth's ellipsoid

Abstract.

 The accuracy of the well-known boundary condition with a radial derivative is improved up to 5×10⁻⁵ by means of a small change of the absolute term. A transformation of the condition by means of Dini's method makes it possible to pass to a condition associated with Dirichlet's problem for an auxiliary function which is harmonic outside the Earth's ellipsoid. A new method of the solution of Dirichlet's problem enables an integral equation with a small kernel to be obtained. Therefore, the solution of the integral equation can be obtained easily through iteration steps or even without iterations. The solution of the integral equation determines the disturbing potential and the mixed gravity anomaly outside of the ellipsoid.