Modeling the artificial night sky brightness at short distances from streetlights

•The artificial night sky brightness is produced by scattering of anthropogenic light.•Scattering takes place from the eye of the observer along the whole line of sight.•Nearby streetlights contribute strongly in the first few meters from the eye.•The basic zenith brightness near the sources decreases as the inverse of the distance.•The presence of obstacles or elevated sources modulates this dependence.