  The Poincare and Poincare-Weyl gauge theories of gravitation with Lagrangians
quadratic on curvature and torsion in post-Riemannian spaces with the Dirac
scalar field is discussed in a historical aspect. The various hypothesizes
concerning the models of a dark matter with the help of a scalar field are
considered. The new conformal Weyl-Dirac theory of gravitation is proposed,
which is a gravitational theory in Cartan-Weyl space-time with the Dirac scalar
field representing the dark matter model. A static spherically symmetric
solution of the field equations in vacuum for a central compact mass is
obtained as the metrics conformal to the Yilmaz-Rosen metrics. On the base of
this solution one considers a radial movement of an interplanetary spacecraft
starting from the Earth. Using the Newton approximation one obtains that the
asymptotic line-of-sight velocity in this case depends from the parameters of
the solution, and therefore one can obtain on basis of the observable data the
values of these parameters.
