  We derive the torque on a spheroid of an arbitrary aspect ratio $\kappa$
sedimenting in a linearly stratified ambient. The analysis demarcates regions
in parameter space corresponding to broadside-on and edgewise (longside-on)
settling in the limit $Re, Ri_v \ll 1$, where $Re = \rho_0UL/\mu$ and $Ri_v
=\gamma L^3g/\mu U$, the Reynolds and viscous Richardson numbers, respectively,
are dimensionless measures of the importance of inertial and buoyancy forces
relative to viscous ones. Here, $L$ is the spheroid semi-major axis, $U$ an
appropriate settling velocity scale, $\mu$ the fluid viscosity, and
$\gamma\,(>0)$ the (constant)\,density gradient characterizing the stably
stratified ambient, with $\rho_0$ being the fluid density taken to be a
constant within the Boussinesq framework. A reciprocal theorem formulation
identifies three contributions to the torque: (1) an $O(Re)$ inertial
contribution that already exists in a homogeneous ambient, and orients the
spheroid broadside-on; (2) an $O(Ri_v)$ hydrostatic contribution due to the
ambient linear stratification that also orients the spheroid broadside-on; and
(3) a hydrodynamic contribution arising from the perturbation of the ambient
stratification by the spheroid whose nature depends on $Pe$; $Pe = UL/D$ being
the Peclet number with $D$ the diffusivity of the stratifying agent. For $Pe
\gg 1$, the hydrodynamic contribution is $O(Ri_v^{\frac{2}{3}}$) in the Stokes
stratification regime characterized by $Re \ll Ri_v^{\frac{1}{3}}$, and orients
the spheroid edgewise regardless of $\kappa$. The differing orientation
dependencies of the inertial and large-$Pe$ hydrodynamic stratification torques
imply that the broadside-on and edgewise settling regimes are separated by two
distinct $\kappa$-dependent critical curves in the
$Ri_v/Re^{\frac{3}{2}}-\kappa$ plane. The predictions are consistent with
recent experimental observations.
