Gravitational Time Dilation

Time passes more slowly by a factor of \(x\) at plane cruising altitude of \(12000 \text{ m}\) above the Earth's surface, compared to the time experienced by an object at infinity. At approximately how many places after the decimal point does \(x\) differ from \(1.000\ldots\)?

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Useful constants:

• The radius of the Earth is \(6.37 \times 10^6 \text{ m}\).

• The speed of light is \(3 \times 10^8 \text{ m}/\text{s}\).

• Newton's gravitational constant is \(6.67 \times 10^{-11} \text{ N}\cdot \text{m}^2 / \text{kg}^2\).

• The mass of the earth is \(5.97\times 10^{24} \text{ kg}\).