  We compute the leading post-Newtonian and quantum corrections to the Coulomb
and Newtonian potentials using the full modern arsenal of on-shell techniques;
we employ spinor-helicity variables everywhere, use the Kawai-Lewellen-Tye
(KLT) relations to derive gravity amplitudes from gauge theory and use
unitarity methods to extract the terms needed at one-loop order. We stress that
our results are universal and thus will hold in any quantum theory of gravity
with the same low-energy degrees of freedom as we are considering. Previous
results for the corrections to the same potentials, derived historically using
Feynman graphs, are verified explicitly, but our approach presents a huge
simplification, since starting points for the computations are compact and
tedious index contractions and various complicated integral reductions are
eliminated from the onset, streamlining the derivations. We also analyze the
spin dependence of the results using the KLT factorization, and show how the
spinless correction in the framework are easily seen to be independent of the
interacting matter considered.
