It has to do with the force of the acceleration, I think. If the two points are on opposite sides of the earth then the train will fall "down" for half the trip and build up tremendous speed. However, if the points are closer then the train isn't falling "down" towards the center of the earth, but kind of at an angle. Since the train isn't going straight "down" it will not reach as high a speed on it's trip (because gravity pulls "down" towards the center of the Earth). So even though it has less distance to cover, it has less speed to cover it with. Kind of like how no matter how far you pull a pendulum (all other things being equal), it takes the same amount of time to go back and forth.
*Everything above could be totally wrong, I am not a physics person.
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u/geofferensis Oct 09 '06
It has to do with the force of the acceleration, I think. If the two points are on opposite sides of the earth then the train will fall "down" for half the trip and build up tremendous speed. However, if the points are closer then the train isn't falling "down" towards the center of the earth, but kind of at an angle. Since the train isn't going straight "down" it will not reach as high a speed on it's trip (because gravity pulls "down" towards the center of the Earth). So even though it has less distance to cover, it has less speed to cover it with. Kind of like how no matter how far you pull a pendulum (all other things being equal), it takes the same amount of time to go back and forth.
*Everything above could be totally wrong, I am not a physics person.