Ray tracing in relativistic astrometry: stellar positions, stellar motion and error budget

摘要

In a series of papers (see de Felice et al 2004 Astrophys. J. 607 580-95, and references therein) a relativistic astrometric model, termed RAMOD, was developed, with the purpose of deducing from the observations made by the satellite GAIA the position and motion of the stars of our galaxy. In this model, the solar system is assumed to be the only source of gravity; moreover, since GAIA is expected to provide data with an accuracy of a microarcsecond in the measurements of angles, the model has been conceived to include terms of the order O(c(-3)) - with c being the vacuum light velocity - in order to reach the same accuracy. Since RAMOD is operated by a numerical code, it can produce numerical solutions only; some analytical form of the solutions is yet needed, in order to write down and solve the error equations. Using variational methods, in this paper we provide an analytical solution which agrees with the numerically determined one to the same order of accuracy and in the same operational conditions of the satellite. Thanks to this approach, we are also able both to identify the position of a star with only one integration from observations made at two different satellite positions and to derive the coordinate components of the stellar motion - if detectable - simply by iterating the above procedure of position measurements after a suitable interval of the orbital time. Finally, we also determine the uncertainties of the solutions - the error budget - arising from the statistical errors of the boundary conditions. The relations linking the errors in the solutions with the uncertainties of the observables are known as 'condition equations'.