local gravitational field

We consider the method of constructing the local gravity field using technique called spherical cap harmonic analysis (SCHA). This approach involves using of  associated Legendre functions of integer degree and noninteger order. These functions form two sets of functions. They are mutually orthogonal over the spherical cap in each set. However, in general these functions are not orthogonal. Thus, for using both of these sets of functions it is traditionally used least squares method. However, for higher orders it is quite difficult to compute eigenvalues and norms of these functions.

We consider the method of constructing the local gravity field using nonorthogonal basic functions, which are solution of the Laplace equation in spherical cap or spherical segment. This approach involves using of associated Legendre functions of integer degree and noninteger order. These functions form two sets of functions. They are mutually orthogonal over the spherical cap in each set. Thus, for using both of these sets of functions it is traditionally used least squares method. However, for higher orders it is quite difficult to compute eigenvalues of these functions.