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Throw the ball

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New thought for the day! I was thinking about this while sitting in the bus this morning trying to avoid looking at the girl beside me.

Suppose you throw a ball up to the sky. And supposed that you threw it no faster than 11 Km/s. So the ball will "come back" down at you eventually. (which is why I put the 11 Km/s i.e. escape velocity restriction)

Most people would draw a parabola describing the path that this ball will take. That's a very interesting observation, and completely wrong.
The ball is actually going on a straight line. Well, ok, it's not VERY straight because of wind and air resistance and stuff, but if you take out the air facter, the path of ball is as straight as it could be. It's just that you and the earth happen to be present at both ends of this straight line.

You don't believe me? Ok, put 2 air planes in centre of south pole, and let them go in opposite directions STRAIGHT ahead. They're going in opposite directions, right? And they're going straight path, the engine is ONLY forcing them forward. And yet, the two airplanes will collide in the centre of north pole.

There, so they happen to be present at both ends of a straight line, even through the straight lines where in opposite directions.

If you're wondering why I thought about this in the bus, well, it's because I'm a mathematician and this is exactly what General Relativity says. Except in more technical terms...
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Actually, I don't think it would be exactly parabolic due to the inconstant acceleration due to gravity (assuming you throw it up at that velocity, and ignoring air resistance). I'm too lazy to actually compute if it would make that much of a difference, but the normal derivations (integrations) used in the basic mechanics formulae don't apply without constant acceleration.

If you don't have the constant acceleration, you have to integrate the equation another step, which yields a cubic function, which is not necessarily parabolic.

What was this about a female..?

EDIT: Oh dammit. You said "no faster" not "faster". Check out that hot girl over there!

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Andy, Rob: You guys didn't notice that Pouya neglected to say "...trying to avoid looking at the hot girl beside me."

Obviously she was fat and ugly and Pouya had to distract himself to keep from retching. Good save there Pouya

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Is a geodesic really thought of as a straight line? I just thought of it as the path that maximizes the proper time experienced by an object on that path.

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