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 $5.97\times 10^{24} \text{ kg}$.

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