Oh. Well, silly me. I did double check that it's inverse-square, but apparently not deeply enough - the energy is, but the amplitude isn't. Which makes sense if I think about it a little more (it's basically a spring, so energy ~ displacement^2)

For other readers, this poster's correction is right, here's an astronomy SA thread on it. https://astronomy.stackexchange.com/questions/34761/why-does...

I swear, the one time I try posting outside my areas of expertise :D