PhongNodeMaterial with lower alpha the further fragment is from mesh origin?

I’m wondering how I might apply an alpha gradient (or any sort of gradient in general) to a Mesh starting with a PhongNodeMaterial. I am curious in general how to do it with shader code, but I also want to explore the NodeMaterial system.

As a huristic for the gradient, I would like more alpha the further we are from the Mesh’s local origin. Say at distance 0 we have full opacity, and by distance 10 we have full opacity.

How might we do this with the NodeMaterial system?