Solar System Scaling / Phaeton

We were hanging up the glow-in-the dark planets Avery received as a christmas/birthday gift. Of course they had to be in order. Of course they had to be scaled accurately. And of course I had to look up what the relative distances were since I couldn’t remember (although I did suspect it scaled exponentially as distance increased). Here’s what it looks like:

Looks pretty pretty exponential to me. So what does it look like on a log scale?

Indeed. Actually, let’s put the geometric mean distance of the asteroid belt onto the plot.

Well, that’s a pretty nice log-linear line if I’ve ever seen one. So each planet is like 1.8-fold [earth-distances to the sun] further than the previous planet. Definitive proof for the existence of Phaeton.