This has got to be the hardest, most patience-intensive project I've tried on photography. First, finding the camera settings; second, making sure the ball was in focus and framed properly. I had to wait for a bright-enough day and pick a darker background to make sure the spinning, planet-like, effect worked as desired. With such high shutter speeds there wasn't enough light coming into the camera. Even with a f1.8 lens I couldn't go no brighter than f4, otherwise a centimeter off and the ball would be out of focus. Lastly, I had to set the Nikon D7100 to shoot as jpeg (rather than raw) to make sure the continuous mode worked on its faster performance. Continuous mode is crucial, because, as you can imagine, framing the ball in a single click is impossible; you hold the trigger and let the camera fire continuously.

How to do it

• Set the desired aperture (f4 worked for me for a nice blurry background; the more blurry/darker the background, the more visible the water)
• Shutter speed is trial and error (higher shutter speeds are best to keep the ball's definition)
• With the two setups defined, I used the ISO to balance the picture
• Set the camera on continuous mode and ask someone to throw the ball as you press the trigger
• Practice, practice, practice

Settings

Camera: Nikon D7100 with a 1980's all-manual 50mm f1.8
Accessories: Tripod
Settings: Manual / continuous shooting (Ch mode on Nikon) / f4 / shutter speed 6400 / ISO 2000

I think the results turned out great for a test. Now that I know how it works, it's time to try all sorts of crazy high speed photos.

Edit.: For some reason @Liketu didn't upload all the photos, so here they are.