  A correlator of the vector current of a heavy quark is computed analytically
near threshold in the next-to-next-to-leading order in perturbative and
relativistic expansion that includes $\al_s^2$, $\al_sv$ and $v^2$ corrections
in the coupling constant and velocity of the heavy quark to the nonrelativistic
Coulomb approximation. Based on this result, the numerical values of the
$b$-quark pole mass and the strong coupling constant are determined from the
analysis of sum rules for the $\Upsilon$ system. The next-to-next-to-leading
corrections are found to be of order of next-to-leading ones.
