  We prove orientation results for evaluation maps of moduli spaces of rational
stable maps to del Pezzo surfaces over a field, both in characteristic $0$ and
in positive characteristic. These results and the theory of degree developed in
a sequel produce quadratically enriched counts of rational curves over
non-algebraically closed fields of characteristic not $2$ or $3$. Orientations
are constructed in two steps. First, the ramification locus of the evaluation
map is shown to be the divisor in the moduli space of stable maps where image
curves have a cusp. Second, this divisor is related to the discriminant of a
branched cover of the moduli space given generically by pairs of points on the
universal curve with the same image.
