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Time Elapsed on a Clock

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A good approximation to the metric outside the surface of the Earth is provided.

It may be thought of as the familiar Newtonian gravitational potential. Here G is newton's constant and M is the mass of the earth. For this problem o may be assumed to be small.

Imagine a clock on the surface of the Earth at distance R1 from the Earth's center, and another clock on a tall building at distance R2 from the Earth's center. Calculate the time elapsed on each clock as a function of the coordinates time t. Which clock moves faster?

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Solution Summary

The solution uses relativity and an approximation metric to calculate the time elapsed on a clock.