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We are impressed by the direct Hubble Space Telescope size measurement of Xena.... Measuring the size of such a tiny and moving object is a very difficult task. We were pleased to learn that our claim that 2003UB313 is larger than Pluto
A wide range of values of q has been measured for solar system objects, ranging from 0.2 to over 1.2. We had chosen 0.9 because this is an average value found for Pluto, which we thought to be an appropriate analogon.
Assuming the reference star to be single is a good guess, but is far from certain. Roughly half of all stars are multiple systems, and a faint field star such as the one chosen for the measurement is likely to be distant enough (more than 1000 light years)
Given the inherent uncertainties in both methods, the actual size of 2003 UB313 is not established beyond reasonable doubt by either the MAMBO or HST measurements.