based on your web page I see your a programmer.
All you have to do is compute the tangent points of contact at the radius and depth of position. Then circular interpolate the profile.
Figure out your chip load based on material and speeds then you should be able to create a spread sheet to pump out the code.
It's just math, not hard, just tedious.
just have to make sure the cutter you choose will reach the full diameter without the shank hitting and long enough to get to the bottom.
That hole will need to be flushed out during the cut as it will pack up fast. And several roughing passes would be advised as those cutters are not made for heavy loads. Might be better to use the center of the sphere as a separate offset so you can call it 0,0,0 then you can use the scaling features of mach3 and using the finish routine just scale it down for the roughing passes. So reference all dimensions from the center of the sphere
I advise, go slow and a use a good rigid setup, have fun
the blue lines are the tangent angle back to the center of the cutter ball.