The recent Gaia Data Release 3 has revealed a catalogue of more than eight hundred thousand binary systems. The release provides orbital solutions for half of the systems, with the majority of them being unresolved astrometric binaries. However, some astrophysical parameters that can only be derived from the relative orbit and spectroscopic data, such as the spectral type and the mass of each companion, remain unknown in most of them. The purpose of this work is to develop a methodology that allows to obtain those fundamental stellar parameters, and those related to the geometry and thus ephemeris of the system, in order to know if it can be optically resolved. To obtain precise values for each component, we propose an analytic algorithm to estimate the only two possible relative orbits and pairs of masses of main-sequence astrometric binaries using all the available astrometric, photometric and spectroscopic data in the Gaia DR3. In some cases, it is possible to select the solution that is more aligned with the rest of the data. We deduce not only the two possible values of the individual spectral types, masses and effective temperatures for each binary but also the size of the telescope necessary to resolve their components. The workflow of our algorithm as well as the ESMORGA (Ephemeris, Stellar Masses, and relative ORbits from GAia) catalogue with individual masses, spectral types, and effective temperatures for 49530 binaries derived from its application is also presented.