The new observations of GOCE present a challenge to
develop new calculation methods that take into account
the sphericity of the Earth. We address this problem by
using a discretization with a series of tesseroids. There
is no closed formula giving the gravitational fields of
the tesseroid and numerical integration methods must be
used, such as the Gauss Legendre Cubature (GLC). A
problem that arises is that the computation times with the
tesseroids are high. Therefore, it is important to optimize
the computations while maintaining the desired accuracy.
This optimization was done using an adaptive computation
scheme that consists of using a fixed GLC order and
recursively subdividing the tesseroids. We have obtained
an optimum ratio between the size of the tesseroid and
its distance from the computation point. Furthermore, we
show that this size-to-distance ratio is different for the
gravitational attraction than for the gravity gradient tensor.
