  We calculate the $\eta^\prime$-meson energy spectrum in the $\Upsilon (1S)
\to \eta^\prime g g g \to \eta^\prime X$ decay in the leading-order
perturbative QCD in the static-quark limit for the orthoquarkonium.Our
principal result is the extraction of parameters of the $\eta^\prime g^* g$
effective vertex function (EVF) involving a virtual and a real gluon from the
available data on the hard part of the $\eta^\prime$-meson energy spectrum. The
perturbative-QCD based framework provides a good description of the available
CLEO data, allowing one to constrain the lowest Gegenbauer coefficients
$B^{(q)}_2$ and $B^{(g)}_2$ of the quark-antiquark and gluonic distribution
amplitudes of the $\eta^\prime$-meson. The resulting constraints are combined
with the existing ones on these coefficients from an analysis of the
$\eta^\prime - \gamma$ transition form factor and the requirement of positivity
of the EVF, yielding $B^{(q)}_2 (\mu_0^2) = -0.008 \pm 0.054$ and $B^{(g)}_2
(\mu_0^2) = 4.6 \pm 2.5$ for $\mu_0^2 = 2 GeV^2$. This reduces significantly
the current uncertainty on these coefficients.
