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 \(1.000\ldots?\)

\(\)
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 \(5.97\times 10^{24} \text{ kg}\).
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