Surprisingly, this star's position has not been reliably measured to high precision. Most standard ground-based measurements (and maybe the Hipparcos/Tycho data too) are perturbed by bright and asymmetric ejecta from the 1840 and 1890 eruptions, at all radii from 0.1 to 8 arcsec. This statement applies also to radio observations, which cannot even see the stellar wind proper because an amorphous region 0.3"–1" across is optically thick at wavelengths longer than 1 cm.
At Minnesota we have estimated the star's position from a combination of old photographic plates, CCD images made with a 0.9-m telescope at Cerro Tololo, and HST/WFPC2 images. The result in J2000 coordinates is —
RA = 10h 45m 03.563s, dec = -59° 41' 04.14" in the ICRS (Hipparcos/Tycho) system, RA = 10h 45m 03.643s, dec = -59° 41' 04.22" in the ZZZQ catalog that we use for HST acquisitions (see below). Expected r.m.s. uncertainty is around ± 0.15" along each axis relative to the overall set of ZZZQ stars, or ± 0.25" (maybe 0.20") for each coordinate in an absolute grid such as the ICRS.
This position, measured independently, matches that given in the Tycho Catalog very well; but in principle the latter shouldn't be trusted for this purpose, because of the reasons noted above. (Eta has an astrometric-quality rating of 9, poor, in that catalog. We've found that Tycho data for stars rated '9' are erratic in this region, with some discrepancies far worse than expected.)
If anyone is interested in doing so, the position measurement can be improved by combining numerous existing HST acquisition and image data. We haven't had enough time to do it.
In 1989, when some of us first planned HST observations of Eta Car, the HST Guide Star Catalog (GSC) was unsatisfactory. For this region the original GSC used Schmidt plates where most of the relevant stars were hidden by nebulosity, and the plate scale was inadequate. Therefore we prepared a "special catalog" ZZZQ of acquisition and guide stars in the vicinity of Eta, and have been using it for HST observations ever since.
Partial list of ZZZQ stellar positions (ascii text file with explanations).
Automated Plate Scanner (APS) www site
Figure showing Eta's equatorial coordinates as functions of time (line drawing, B&W GIF file).
Taking precession into account, in ancient times this object was visible much farther north than it is today. If Eta had any major eruptions then like the protracted 19th-century outburst, it would have been noticed — and remembered — in ancient Egypt, Mesopotamia, and China. Unfortunately those cultures generally recorded planets' movements rather than stellar outbursts. Is it possible that any records of such an event might survive somewhere?