Assume that at the vanishing point of the golden spiral is an axis coming directly out of the screen that is orthogonal to the plane of the spiral (like you're looking down the barrel of a rifle)

Now assume that the spiral itself is a visual representation of the path of a particle moving away from you AND in a perfect circle about the aforementioned axis.

At what speed would a particle be having to travel away from an observer to create this "flat" 2D golden ratio?