This is not as elegant a solution, but...
If you were on a planet with just the right mass and diameter, you're hardest throw in the right direction would allow the ball to orbit the planet once (or twice, etc. depending on the constants just mentioned).
here's why that's a problem. the earth's diameter is about 7900 miles. when the ball is thrown it will not only be traveling around the world but also falling. what that means is that the ball has to travel 7900 miles before it falls 6 feet. with some physics (or a stop watch) we find that an object falls to the earth from 6 feet in about 0.61 seconds. convert 7900 miles per 0.61 seconds to mph and you get 46,622,951 mph!! earth's escape velocity is 25000 mph. so once you threw the ball at 47,000,000 mph it would just keep going out into space instead of curving around the earth.