  `Star G', near the center of the supernova remnant of Tycho's SN1572, has
been claimed to be the ex-companion star of the exploding white dwarf, thus
pointing to the progenitor being like a recurrent nova. This claim has been
controversial, but there have been no confident proofs or disproofs.
Previously, no has seriously addressed the question as to the exact explosion
site in 1572. We now provide accurate measures of the supernova position by two
radically different methods. Our first method is to use the 42 measured angular
distances between the supernova in 1572 and bright nearby stars, with
individual measures being as good as 84 arc-seconds, and all resulting in a
position with a 1-$\sigma$ error radius of 39 arc-seconds (including systematic
uncertainties). Our second method is to use a detailed and realistic expansion
model for 19 positions around the edge of the remnant, where the swept-up
material has measured densities, and we determine the center of expansion with
a chi-square fit to the 19 measured radii and velocities. This method has a
1-$\sigma$ error radius of 7.5 arc-seconds. Both measures are substantially
offset from the geometric center, and both agree closely, proving that neither
has any significant systematic errors. Our final combined position for the site
of 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 the
8.2-$\sigma$ confidence level. Our new position lies mostly outside the region
previously searched for ex-companion stars.
