  In the last experiment with the PK-3 Plus laboratory onboard the
International Space Station, interactions of millimeter-size metallic spheres
with a complex plasma were studied~[M. Schwabe {\it et al.}, New J. Phys. {\bf
19}, 103019 (2017)]. Among the phenomena observed was the formation of cavities
(regions free of microparticles forming a complex plasma) surrounding the
spheres. The size of the cavity is governed by the balance of forces
experienced by the microparticles at the cavity edge. In this article we
develop a detailed theoretical model describing the cavity size and demonstrate
that it agrees well with sizes measured experimentally. The model is based on a
simple practical expression for the ion drag force, which is constructed to
take into account simultaneously the effects of non-linear ion-particle
coupling and ion-neutral collisions. The developed model can be useful for
describing interactions between a massive body and surrounding complex plasma
in a rather wide parameter regime.
