  We study moduli dependent threshold corrections to gravitational couplings in
the case of the heterotic string compactified on a symmetric orbifold, for
untwisted moduli, extending previous analysis on gauge couplings. Like in the
gauge case, the contribution comes entirely from the spacetime $N=2$ sector. As
a byproduct, this calculation provides a simple derivation of the trace anomaly
coefficients for the different fields coupled to gravity.
