  Hercules is a dwarf spheroidal satellite of the Milky Way, found at a
distance of about 138 kpc, and showing evidence of tidal disruption. It is very
elongated and exhibits a velocity gradient of 16 +/- 3 km/s/kpc. Using this
data a possible orbit of Hercules has previously been deduced in the
literature. In this study we make use of a novel approach to find a best fit
model that follows the published orbit. Instead of using trial and error, we
use a systematic approach in order to find a model that fits multiple
observables simultaneously. As such, we investigate a much wider parameter
range of initial conditions and ensure we have found the best match possible.
Using a dark matter free progenitor that undergoes tidal disruption, our
best-fit model can simultaneously match the observed luminosity, central
surface brightness, effective radius, velocity dispersion, and velocity
gradient of Hercules. However, we find it is impossible to reproduce the
observed elongation and the position angle of Hercules at the same time in our
models. This failure persists even when we vary the duration of the simulation
significantly, and consider a more cuspy density distribution for the
progenitor. We discuss how this suggests that the published orbit of Hercules
is very likely to be incorrect.
