I'm trying to have this cell fractured sphere have each piece/object have it's own Z Orientation pointing to the center of the sphere. I've attempted doing this manually by setting a custom orientation through the Edit mode> Normals orientation then saving it as a custom to use in object mode. It appears to work, but the F curves animation set to Z Location seems to be using the Global Z and I can't seem to find where I can change that to my custom one. Is there a better way of doing this? A script perhaps, as I'll be doing this for 32+ objects of the sphere.
Because the fcurves (like PGmath has indicated) are in global-space, you might be able to get done what you want with a small work-around:
For each piece of your sphere, add an empty at the center of the sphere and parent that one piece to it. Then rotate each empty such that the sphere-piece is directly below the empty. Apply the rotation to the empty, then manually rotate the empty back so the sphere-piece is back to its original location/orientation.
Any subsequent changes to the z-rotation of the sphere-piece should cause the rotation you are looking for. If you need an example .blend, I might be able to put one together and post it later today.