The solar wind interaction with the non-magnetic Venerean ionospheric obstacle is unique. Ionospheric models of this interaction have primarily been in two dimensions that do not allow for changes in the orientation of the solar wind magnetic field near the obstacle. Analysis of high resolution magnetic field data from the Pioneer Venus Orbiter spacecraft has revealed field rotations that are observed to occur in conjunction with the dayside ionopause. These rotations are a result of the velocity shear at the ionopause and indicate the alignment of the magnetic field with the radial day to night flow of ionospheric plasma. A new configuration of the dayside magnetic field draping has been derived from these results. In addition, a new current system to account for this changing field orientation has been determined and is discussed in relation to current systems derived from previous models. These new aspects of the dayside solar wind interaction at Venus can be applied to other similar solar system objects. Assuming Mars also represents a non-magnetic obstacle to the flow, as past experimental observations indicate, the field diagnostics discovered here make it possible to probe the structure of the Martian ionosphere using magnetometer data in the absence of ion mass spectrometer data. These results will play a major role in predictive modeling and data analysis for future Mars missions.