Observations from the PHOBOS spacecraft suggest that, for the most part, the Martian magnetotail is induced instead of intrinsic. In this paper, test particle techniques are used to determine how the associated ion wake might appear to detectors behind Mars if it is produced primarily by planetary ions picked up by the solar wind in the dayside exosphere. The results suggest that low energy (<10 keV) pickup ions populate the inner wake, while a more energetic component is present in the outer magnetosheath and adjacent solar wind. The latter has a finite gyroradius related spatial asymmetry controlled by the interplanetary field orientation. This asymmetry is analogous to, but stronger than, that which appears in Venus ion wake observations because of the smaller obstacle size and weaker interplanetary field at Mars.