Is there a way to profile a cut on a sphere surface

I'm stumped, been trying to do this for 2 weeks now, think I'll go bald
before I figure it out so I'm asking the experts, it's got me beat and I'm
fast running out of time.
Here's the problem, I have a 100mm dia sphere and I want to machine a figure
of 8 track on the surface, say the track is 12mm wide x 6mm deep along the
centre line of the cut, the centre line of the "8" extends 45degrees across
the surface with a radius of say 12.5mm around the bends. The problem I
can't figure out is at any point of the centre axis of the cut must
intersect the centre point of the sphere ant the walls of the cut must be
parallel to this (think of it as a surface slot for a follower guide).
I've tried everthing I can think of, lofts, surface intersections, 3D cut's
but I can't get it, I'm thinking that SW can't do this, is it possible?
You help will be very very much appreciated.
Thanks in advance.
Brian