Using high-precision astrometric optical observations from the Walter Baade Magellan Telescope in conjunction with high-resolution very long baseline interferometric (VLBI) radio imaging with the Very Long Baseline Array (VLBA), we have located the core of the X-ray binary system XTE J1752-223. Compact radio emission from the core was detected following the state transition from the soft to the hard X-ray state. Its position to the south-east of all previously-detected jet components mandated a re-analysis of the existing VLBI data. Our analysis suggests that the outburst comprised at least two ejection events prior to 2010 February 26. No radio-emitting components were detected to the south-east of the core at any epoch, suggesting that the receding jets were Doppler-deboosted below our sensitivity limit. From the ratio of the brightness of the detected components to the measured upper limits for the receding ejecta, we constrain the jet speed to be greater than 0.66c and the inclination angle to the line of sight to be less than 49 degrees. Assuming that the initial ejection event occurred at the transition from the hard intermediate state to the soft intermediate state, an initial period of ballistic motion followed by a Sedov phase (i.e. self-similar adiabatic expansion) appears to fit the motion of the ejecta better than a uniform deceleration model. The accurate core location can provide a long time baseline for a future proper motion determination should the system show a second outburst, providing insights into the formation mechanism of the compact object.
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