Shading on a dome using gradients

I have an axonometric drawing of a dome on top of a cylinder, and I need to shade this to show lighting and form. My best attempts are using a radial gradient for the top spherical section, and a freeform line gradient for the cylinder, but I can't achieve a smooth transistion between the two.

Whilst I'm happy with the top section, I'm unsure how to go about this to creat the effect I'm after, though I suspect that using two seperate gradients may be complicating things.