The young T Tauri star WW Cha was recently proposed to be a close binary object with strong infrared and submillimeter excess associated with circum-system emission. This makes WW Cha a very interesting source for studying the influence of dynamical effects on circumstellar as well as circumbinary material. We derive the relative astrometric positions and flux ratios of the stellar companion in WW Cha from the interferometric model fitting of observations made with the VLTI instruments AMBER, PIONIER, and GRAVITY in the near-infrared from 2011 to 2020. For two epochs, the resulting uv-coverage in spatial frequencies permits us to perform the first image reconstruction of the system in the K band. The positions of nine epochs are used to determine the orbital elements and the total mass of the system. We find the secondary star orbiting the primary with a period of T=206.55 days, a semimajor axis of a=1.01 au, and a relatively high eccentricity of e=0.45. Combining the orbital solution with distance measurements from Gaia DR2 and the analysis of evolutionary tracks, the dynamical mass of Mtot=3.20 Msol can be explained by a mass ratio between ~0.5 and 1. The orbital angular momentum vector is in close alignment with the angular momentum vector of the outer disk as measured by ALMA and SPHERE. The analysis of the relative photometry suggests the presence of infrared excess surviving in the system and likely originating from truncated circumstellar disks. The flux ratio between the two components appears variable, in particular in the K band, and may hint at periods of triggered higher and lower accretion or changes in the disks structures. The knowledge of the orbital parameters, combined with a relatively short period, makes WW Cha an ideal target for studying the interaction of a close young T Tauri binary with its surrounding material, such as time-dependent accretion phenomena.
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