Satellite radio, unlike satellite television, doesn’t make use of dishes, so you don't need to install a dish on your car. The main reason is bandwidth, but suffice it to say that satellite radio uses small, non-directional antennas that are similar to many satellite phones you may have seen.
Both terrestrial radio and satellite radio use omnidirectional antennas, which can be contrasted with the directional antennas used by satellite television services. However, your existing car antenna that’s designed to receive AM and FM signals isn’t capable of receiving satellite radio transmissions.
The issue is that the FM broadcast band occupies part of the very high frequency (VHF) radio spectrum, the AM band utilizes part of the medium frequency (MF) band, and satellite radio occupies the S-band.