  Context: One of the greatest uncertainties in modelling the mass-exchange
phases during the evolution of a binary system is the amount of mass and
angular momentum that has been lost from the system. To constrain this problem,
a favourable, evolved and detached real binary system is valuable as an example
of the end result of this process. Aims: We study the 52-day post-mass-exchange
eclipsing binary V643 Ori from complete uvby light curves and high-resolution
spectra. V643 Ori is a double-lined, circular orbit, synchronized binary
showing total primary eclipses. Results: We determine accurate masses of 3.3
and 1.9 M(Sun) and radii of 16 and 21 R(Sun). The masses and radii are
incompatible with undisturbed post-main-sequence evolution. Conclusions: We
have attempted to simulate the past evolutionary history of V643 Ori under both
conservative and non-conservative Case B mass transfer scenarios. In the
non-conservative case we varied the amounts of mass and angular momentum loss
needed to arrive at the present masses in a circular 52-day orbit, keeping the
two stars detached and synchronized as now observed, but without following the
evolution of other stellar properties in any detail. Multiple possible
solutions were found. Further attempts were made using both the BSE formalism
and the binary MESA code in order to track stellar evolution more closely, and
make use of the measured radii and temperatures as important additional
constraints. Those efforts did not yield satisfactory solutions, possibly due
to limitations in handling mass transfer in evolved stars such as these. We
remain hopeful that future theoreticians can more fully model the system under
realistic conditions.
