Planes of dwarf galaxies and the cosmic web in the local universe Galaxies like the Milky Way and our neighbor Andromeda host systems of smaller satellite galaxies. In these two galaxies, there is significant evidence that many of their satellites sit on a vast, thin, co-rotating planes. A similarly flattened structure was recently spotted around Centaurus A, one of the few galaxies close enough to the MW such that it is possible to measure accurate distances to the swarm of gas-poor, low luminosity dwarf galaxies that cluster around it. It has been argued that in the standard (ΛCDM) model of cosmology such planes are unexpected. Numerical simulations suggest that satellites are beamed towards galaxies within the plane defined by the principal axis of collapse of the surrounding velocity shear field so that their spatial distribution is associated with the filaments of the cosmic web. Recent advances in the mapping of the local velocity field allow us to test the assertion that the orientation of flattened satellite systems is dictated by the velocity shear tensor. We show that both planes of M31 satellites as well as those around CenA are nearly perfectly aligned with the eigenvector of their local shear tensor that corresponds to fastest collapse, calculated from the Cosmicflows-2 survey. The MW’s satellite plane alignment is not as perfect, likely indicative of its lower mass. The Local Group itself resides in a filament stretched by the Virgo cluster and compressed predominantly by the Local Void. Centaurus A lives on the edge of this filament. The alignment of planes of satellites with the principal shear of the ambient velocity field substantiates the standard ΛCDM model and suggests that the large scale velocity field directly influences the orientation of very nearby satellite galaxies.