HD 93129A is one of the hottest, most massive and luminous binary systems in the Galaxy, with a period longer than 100 yr. Non-thermal emission was reported with the ATCA, along with a ~30% flux increase between 2003 and 2009 from our current monitoring. The emission was interpreted as mainly coming from a colliding-wind region, which was mapped with the LBA. Optical studies indicate that the system is about to hit periastron in ~1 yr time, when we anticipate (i) radio flux shaped by free-free absorption at the colliding-wind region, (ii) unprecedented hard X-ray outbursts and (iii) probably gamma-ray emission. We propose to monitor HD 93129A with the LBA to trace the morphological changes from its emission along two 7-h epochs at S band and two epochs at C band. The evolution of its emission would allow us to unveil the orbital motion of the two stars (and thus clarify when the periastron passage takes place). The data would also allow us to characterize the wind colliding region and stellar winds around periastron. All this information would provide constraints to the current models that predit when the high energy emission would take place and could be observable by the current facilities. HD 93129A could become the second colliding wind binary exhibiting gamma-ray emission after Eta Car (and the only one displaying simultaneously non-thermal radio emission), challenging the limits on the highest energies that a wind collision region can exhibit.