Personally, I would recommend moving the camera around the car, over rotating the car in front of the camera. This way, you don't need to worry at all about blank backgrounds or anything else. When you move the camera around the car, the background and the ground underneath the car will all move correctly in relationship to the car and will only help Photosynth calculate the camera positions.
In other words, Photosynth's prime directive is to determine the relative distances between all of the feature points in the images which it believes are the same in multiple images. When all objects that you care about seeing a point cloud of are stationary (i.e. a stationary car in a stationary room), you will get a point cloud of a car in a point cloud of a room and where the car's shiny surface makes for fewer image features, the rest of the stationary environment will help Photosynth keep its bearings.