  We construct a non-relativistic limit of ten-dimensional N=1 supergravity
from the point of view of the symmetries, the action, and the equations of
motion. This limit can only be realized in a supersymmetric way provided we
impose by hand a set of geometric constraints, invariant under all the
symmetries of the non-relativistic theory, that define a so-called `self-dual'
Dilatation-invariant String Newton-Cartan geometry. The non-relativistic action
exhibits three emerging symmetries: one local scale symmetry and two local
conformal supersymmetries. Due to these emerging symmetries the Poisson
equation for the Newton potential and two partner fermionic equations do not
follow from a variation of the non-relativistic action but, instead, are
obtained by a supersymmetry variation of the other equations of motion that do
follow from a variation of the non-relativistic action. We shortly discuss the
inclusion of the Yang-Mills sector that would lead to a non-relativistic
heterotic supergravity action.
