  In a recent paper (Hajdukovic 2020a) quantum vacuum was considered as a
source of gravity and, the simplest phenomenon, the gravitational polarization
of the quantum vacuum by an immersed point-like body, was studied. In the
present paper, we have derived the effective gravitational charge density of
the quantum vacuum, caused by two point-like bodies. Among others, the obtained
result proves that quantum vacuum can have regions with a negative effective
gravitational charge density. Hence, quantum vacuum, the "ocean" in which all
matter of the Universe is immersed, acts as a complex fluid with a very
variable gravitational charge density that might include both positive and
negative densities; a crucial prediction that can be tested within the Solar
System. In general case of N>2 point-like bodies, immersed in the quantum
vacuum, the analytical solutions are not possible, and the use of numerical
methods is inevitable. The key point is that an appropriate numerical method,
for the calculation of the effective gravitational charge of the quantum vacuum
induced by N immersed bodies, might be crucial in description of galaxies,
without the involvement of dark matter or a modification of gravity. The
development of such a valuable numerical method, is not possible, without a
previous (and in this study achieved) understanding of the impact of a two-body
system.
