  A rare eclipse of the mysterious object Epsilon Aurigae will occur in
2009-2011. We report an updated single-lined spectroscopic solution for the
orbit of the primary star based on 20 years of monitoring at the CfA, combined
with historical velocity observations dating back to 1897. There are 518 new
CfA observations obtained between 1989 and 2009. Two solutions are presented.
One uses the velocities outside the eclipse phases together with mid-times of
previous eclipses, from photometry dating back to 1842, which provide the
strongest constraint on the ephemeris. This yields a period of 9896.0 +/- 1.6
days (27.0938 +/- 0.0044 years) with a velocity semi-amplitude of 13.84 +/-
0.23 km/s and an eccentricity of 0.227 +/- 0.011. The middle of the current
on-going eclipse predicted by this combined fit is JD 2,455,413.8 +/- 4.8,
corresponding to 2010 August 5. If we use only the radial velocities, we find
that the predicted middle of the current eclipse is nine months earlier. This
would imply that the gravitating companion is not the same as the eclipsing
object. Alternatively, the purely spectroscopic solution may be biased by
perturbations in the velocities due to the short-period oscillations of the
supergiant.
