Absolute gravimetry in a shifted Legendre basis

A formalism, based on standard least squares techniques, is presented in which analytic expressions can be derived for the study of the influence of hypothetic perturbations in absolute gravimetry. The model function derived from the equation of motion of the test mass and possible perturbations is expanded in an orthogonal basis composed of the shifted Legendre polynomials, and projections onto the model space and the space orthogonal to this serve to isolate the contributions to the model parameters and to the residuals. The part of the perturbation remaining in the orthogonal space can be compared with those retrieved from the residuals of the fit of the model function to the experimental data. The analysis of the structure of these residuals is a major means of Gaining information about the character of the perturbations. Finally, some explicit examples are given and a discussion concerning how such an analysis can be made is included.