2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/1366We present theoretical analysis of the astrometric searches for extrasolar planets with the Space Interferometry Mission (SIM). Particularly, we derive a model for the future measurements with SIM and discuss the problem of reliable estimation of orbital elements of planets. For this purpose we propose a new method of data analysis and present a numerical test of its application on simulated SIM astrometric measurements of $\upsilon$ Andromedae planetary system. We demonstrate that our approach allows successfull determination of its orbital elements.30 pages, 9 fig,, AASTeX, an additional file with macrosAstrophysicstext