HD 98800 is a young ($sim10$ Myr old) and nearby ($sim45$ pc) quadruple system, composed of two spectroscopic binaries orbiting around each other (AaAb and BaBb), with a gas-rich disk in polar configuration around BaBb. While the orbital parameters of BaBb and AB are relatively well constrained, this is not the case for AaAb. A full characterisation of this quadruple system can provide insights on the formation of such a complex system. The goal of this work is to determine the orbit of the AaAb subsystem and refine the orbital solution of BaBb using multi-epoch interferometric observations with the VLTI/PIONIER and radial velocities. The PIONIER observations provide relative astrometric positions and flux ratios for both AaAa and BaBb subsystems. Combining the astrometric points with radial velocity measurements, we determine the orbital parameters of both subsystems. We refined the orbital solution of BaBb and derived, for the first time, the full orbital solution of AaAb. We confirmed the polar configuration of the circumbinary disk around BaBb. From our solutions, we also inferred the dynamical masses of AaAb ($M_{Aa} = 0.93 pm 0.09$ and $M_{Ab} = 0.29 pm 0.02$ M$_{odot}$). We also revisited the parameters of the AB outer orbit. Using the N-body simulation, we show that the system should be dynamically stable over thousands of orbital periods and that it made preliminary predictions for the transit of the disk in front of AaAb which is estimated to start around 2026. We discuss the lack of a disk around AaAb, which can be explained by the larger X-ray luminosity of AaAb, promoting faster photo-evaporation of the disk. High-resolution infrared spectroscopic observations would provide radial velocities of Aa and Ab (blended lines in contemporary observations), which would allow us to calculate the dynamical masses of Aa and Ab independently of the parallax of BaBb.
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