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How big is fair territory?

Mistake by the Lake Sporting Times, a blog devoted to the lowly Cleveland sports scene, has deduced that fair territory for Jacobs Field extends to all of the Earth's surface, if the lines hug the surface of the Earth. That's because, Corey from MBTLST concludes, someone on the Indians might circumnavigate the Earth with a home run and thus the lines would encompass the rest of the surface of the Earth.

... Of course, this entire discussion is pretty ridiculous, you have to admit. After all, any spot on Earth is technically in Jacobs Field fair territory. Take Buffalo, NY. On the Great Lakes regional map above, it appears to be in foul ground, just a little bit too far to the right. However, a Travis Hafner home run could land in Buffalo if it were hit down the left field line hard enough to travel about 24,500 miles, almost orbiting the Earth once. ...

He made this Google map for us.


fair territory global.jpg

But here is my problem with his claim. If the lines hug the surface of the globe, they must -- at exactly a quarter of the way around the globe from the endpoint of Jacobs Field's home plate -- start to converge again. They would meet again twice -- half way around the world and again at the back corner of the plate.

Take a ball and draw a straight line around it. Then draw another straight line around the same ball, but at a 90-degree angle from the original line. The first spot of convergence is half way around the world from the home plate. The second spot of convergence is home plate. You have outlined a space on the ball that constitutes one half of the surface of the ball and shaped like an hour glass.

So a home run hit around the world would most likely land in foul territory. Fair territory gets very small very fast as the ball approaches its starting point. Lesson: don't hit a ball around the world. It's a much better deal to hit it a quarter or three-quarters as far instead. That's where fair territory is widest. Maybe choke up a bit on the bat.

But consider this: A ball hit hard enough to orbit the Earth does not travel in a straight line. It travels in three dimensions. Hit it hard enough and it escapes the gravitational pull of the Earth and enters space, shooting off at a strange tangent (probably dipping a bit along the way as gravity bends its trajectory).

It's not clear from baseball rules, but what if the foul lines are not supposed to hug the surface of the Earth? What if they are supposed to be actual lines in three-dimensional space rather than borders on the Earth? That would mean that they would slowly rise from the Earth as the Earth curves. Imagine fair territory as a plane that sits at a tangent to the globe, shooting off straight from Cleveland into space, expanding infinitely, and thus encompassing one eighth of the universe!

Dude.

If that were the case, a ball hit from Cleveland that hugged the earth and thus orbited it (like Bugs Bunny's line drive in that cartoon does, coming back with stickers from around the world), would in fact be a foul ball almost as soon as it left Jacobs Field.

That means -- think about it -- when Barry Bonds hits a home run out of Pac Bell Park (or whatever they are calling it these days) and it lands in the San Francisco Bay, BELOW the level of the field, he has actually hit a foul ball.

I think it's time Major League Baseball clarify its rules about fair and foul territory in infinite space. Hank Aaron's record hangs in the balance.

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