Gravitational Time Dilation

Time passes more slowly by a factor of xx at plane cruising altitude of 12000 m12000 \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 xx differ from 1.000?1.000\ldots?

Useful Constants:

  • The radius of the earth is 6.37×106 m6.37 \times 10^6 \text{ m}.
  • The speed of light is 3×108 m/s3 \times 10^8 \text{ m}/\text{s}.
  • Newton's gravitational constant is 6.67×1011 Nm2/kg26.67 \times 10^{-11} \text{ N}\cdot \text{m}^2 / \text{kg}^2.
  • The mass of the earth is 5.97×1024 kg5.97\times 10^{24} \text{ kg}.

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