A satellite in orbit is moving at a much higher velocity than most of the ambient molecules, so that it leaves a wake swept nearly free of gas. A concave shield with a large opening into this wake can thus contain a region of low pressure for experiments and provide a high speed pump for experiment outgassing. Potential experiments in this environment include the production of ultrapure materials and deposition of thin films. It is possible to set bounds on the flux density within a wake shield relative to the externally incident flux density on the shield opening. The upper bound of this ratio, for an aft‐facing shield, is simply 1.0, corresponding to a Maxwellian incident flux. The lower bound for a hemispherical shield is 0.5, when the incident flux is all concentrated on the edge around the opening. The lower bound for cylinders of various L/R ratios with the same edge concentration is also very near 0.5. The total flux on a hemisphere from an internal isotropic point source is 1.0 to 1.5 times the flux leaving the point, depending on its location.