Using photos to map a 3D sphere onto a 2d map/plane?

[GregKochPhoto]

I have a physical sphere with a pattern on it that I've photographed from every angle and I'm trying to figure out how to merge those images into a 2D surface. Photo Merge doesn't work well when I simply rotate the object but keep the camera stationary. I think I might need to move the camera through an arc to photograph the sphere, but that wouldn't give me every part of the surface to translate into a map of the sphere.

Are there any tips on getting Photoshop to translate these photos to a plane? I know there will be distortion, but I'm hoping there's some way within Photoshop to do this regardless.

[Myra Ferguson]

I was able to make the following image:

from the pictures of the globe in this image:

It's not perfect, but with a possibly more overlapping images of the globe and some cleanup of the details, you could fix some of the issues with it.

Here are the steps I used:

1. Remove the background.
2. Separate each globes onto separate layers
3. Export the separate globes as PNGs.
4. Convert each globe in its new PNG to a Smart Object.
5. Apply Filter > Distort > Spherize... as a Smart Filter to each globe (I used -50 but I wound up applying that same amount a second time).
6. Rasterize each of the globes (You could duplicate them and then rasterize them so that you have a back up in case you need to make changes. They have to be rasterized for Photomerge.).
7. Save the globes.
8. Go to File > Automate > Photomerge... set to Auto with all the separate globe files as source files with all 4 options at the bottom of Photomerge selected.