The math shouldn't be that difficult. Assuming we know the other bodies actually orbit around the Sun, and we're simply making Earth the fixed reference point, you should just have a pretty simple ellipse for planets farther out than Earth. The orbital math would stay the same, you just have to add in the rotational motion of the Sun around the earth. The center of each planet's orbit is simply making it's own circle around Earth. So, most planets would just have a slightly bigger elliptical path (far enough that I don't think they'd create the loops like below, but I didn't do any math on it!). Planets closer to the sun than the Earth would be different, as their revolution is contained inside the Earth-Sun circle. Their path would look more like a continuous looping path like so:
Spirograph - The Extra Large "Galaxy" size.