Some napkin/WolframAlpha math:
    if you wanted to use simple x,y,z coordinates,
    with the sun at the center
    and be able to represent locations at 30 AU (Neptune)
    with an accuracy of 1mm, e.g. 30AU vs 30.000...0001AU
    you'd need ~16 decimal digits of precision
    which is the same number of bits as a double (FP64)
    of course there's better ways to do this,
    in the surrounding smarter comments