  The dynamics of Mars' obliquity are believed to be chaotic, and the
historical ~3.5 Gyr (late-Hesperian onward) obliquity probability density
function (PDF) is high uncertain and cannot be inferred from direct simulation
alone. Obliquity is also a strong control on post-Noachian Martian climate,
enhancing the potential for equatorial ice/snow melting and runoff at high
obliquities (> 40{\deg}) and enhancing the potential for desiccation of deep
aquifers at low obliquities (< 25{\deg}). We developed a new technique using
the orientations of elliptical craters to constrain the true
late-Hesperian-onward obliquity PDF. To do so, we developed a forward model of
the effect of obliquity on elliptic crater orientations using ensembles of
simulated Mars impactors and ~3.5 Gyr-long Mars obliquity simulations. In our
model, the inclinations and speeds of Mars crossing objects bias the preferred
orientation of elliptic craters which are formed by low-angle impacts.
Comparison of our simulation predictions with a validated database of elliptic
crater orientations allowed us to invert for best-fitting obliquity history. We
found that since the onset of the late-Hesperian, Mars' mean obliquity was
likely low, between ~10{\deg} and ~30{\deg}, and the fraction of time spent at
high obliquities > 40{\deg} was likely < 20%.
