An isotropic magnetized incident plasma will not, in general, appear isotropic to a detector located on an extended absorbing surface. For certain orientations of the external magnetic field and for a given look direction of the detector the helical particle trajectories intersect the surface before detection, so that the detector is effectively in the shadow of the surface. The shadow zones, i.e., the ranges of magnetic field directions for which particles are not observable by a given detector, grow larger as the ratio of the satellite radius to the particle cyclotron radius increases or as the look direction approaches the surface. In this paper we calculate analytically the shadow zones of small-aperture detectors on an infinite flat surface (i.e., in the limit of small particle gyroradii). The shadow zones include approximately one half of all possible external field orientations for a vertical detector. This effect may result in serious under-estimations of the frequency of observation of a particular plasma region, e.g., of the plasma sheet from a single lunar-based detector. Even for multiple- or large-aperture detectors, shadowing may cause wide variations between observed and actual pitch angle distributions. Since the flux to the surface is approximately isotropic only for magnetic fields within 35¿ of the surface normal, current balance calculations ignoring the magnetic field direction may overestimate the electron flux to the surface and thus under-estimate the equilibrium surface potential. In addition, the magnetic field may return photoelectrons to the surface, though not to the locality of origin. The surface potential could then be highly position dependent on a large body.