Hi I'm trying to create a sphere that is shaded in the following way but for the life of me can't get it quite right... What am I missing??

I've tried everything... Circular gradients. Shapes the blurs. Nothing is working... :(

While the original looks like it´s made from at least 2 overlapping gradients I tried a more simple approach with one radial gradient. No idea if you need the noisy look also:

Oh very clever! No the noise is just an artefact of the scanning... Is there anyway to get the sort of conical shape going?

Not with one single gradient - perhaps with a mesh gradient but seems quite elaborate.

Polygon

Not with one single gradient - perhaps with a mesh gradient but seems quite elaborate.

It is challenging, but there are ways to split any irregular shaped object into small areas filled with the same linear gradient. 

Example for conic gradients: 

https://openclipart.org/detail/230797/conic-spectrum-3

https://openclipart.org/detail/229796/conic-gradient-3

https://openclipart.org/detail/191874/conic-gradient

https://openclipart.org/detail/350650/interlocking-rings-animated

Having said that, I'd definitely not recommend trying to draw such from scratch if you just started.