  Recent observational studies have demonstrated that the majority of satellite
galaxies tend to orbit their hosts on highly flattened, vast, possibly
co-rotating planes. Two nearly parallel planes of satellites have been
confirmed around the M31 galaxy and around the Centaurus A galaxy, while the
Milky Way also sports a plane of satellites. It has been argued that such an
alignment of satellites on vast planes is unexpected in the standard
({\Lambda}CDM) model of cosmology if not even in contradiction to its generic
predictions. Guided by {\Lambda}CDM numerical simulations, which suggest that
satellites are channeled towards hosts along the axis of the slowest collapse
as dictated by the ambient velocity shear tensor, we re-examine the planes of
local satellites systems within the framework of the local shear tensor derived
from the Cosmicflows-2 dataset. The analysis reveals that the Local Group and
Centaurus A reside in a filament stretched by the Virgo cluster and compressed
by the expansion of the Local Void. Four out of five thin planes of satellite
galaxies are indeed closely aligned with the axis of compression induced by the
Local Void. Being the less massive system, the moderate misalignment of the
Milky Way's satellite plane can likely be ascribed to its greater
susceptibility to tidal torques, as suggested by numerical simulations. The
alignment of satellite systems in the local universe with the ambient shear
field is thus in general agreement with predictions of the {\Lambda}CDM model.
