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`Star G', near the center of the supernova remnant of Tycho's SN1572, hasbeen claimed to be the ex-companion star of the exploding white dwarf, thuspointing to the progenitor being like a recurrent nova. This claim has beencontroversial, but there have been no confident proofs or disproofs.Previously, no has seriously addressed the question as to the exact explosionsite in 1572. We now provide accurate measures of the supernova position by tworadically different methods. Our first method is to use the 42 measured angulardistances between the supernova in 1572 and bright nearby stars, withindividual measures being as good as 84 arc-seconds, and all resulting in aposition with a 1-$\sigma$ error radius of 39 arc-seconds (including systematicuncertainties). Our second method is to use a detailed and realistic expansionmodel for 19 positions around the edge of the remnant, where the swept-upmaterial has measured densities, and we determine the center of expansion witha chi-square fit to the 19 measured radii and velocities. This method has a1-$\sigma$ error radius of 7.5 arc-seconds. Both measures are substantiallyoffset from the geometric center, and both agree closely, proving that neitherhas any significant systematic errors. Our final combined position for the siteof the 1572 explosion is J2000 $\alpha$=0h 25m 15.36s, $\delta=64^{\circ} 8'40.2"$, with a 7.3 arc-second 1-sigma uncertainty. Star G is rejected at the8.2-$\sigma$ confidence level. Our new position lies mostly outside the regionpreviously searched for ex-companion stars.

Newly Determined Explosion Center of Tycho's Supernova and the Implications for Proposed Ex-Companion Stars of the Progenitor