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You can back out the information you need, if you can take a picture of the ball at a known distance from the camera. If you treat them as fixed (which they probably are as long as you don't change zoom or lenses on your camera), then it's one number, focal length / sensor height that is constant.
If you take a picture of your ball at a known distance, then you can solve the equation for the unknown constant, and then use that in all your future calculations. Measure carefully, or better yet, take multiple pictures at different known distances and average the results together.
