Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand Time Dilation
Time passes differently in space due to Einstein's theory of relativity. Specifically, time moves more slowly for objects moving at high velocities or in strong gravitational fields.
Step 3:: Consider Orbital Velocity
The International Space Station (ISS) orbits at approximately $$7.66 \times 10^{3} \mathrm{~m/s}$$ (kilometers per hour).
Step 4:: Apply Time Dilation Formula
- $$c$$ is speed of light ($$3 \times 10^{8} \mathrm{~m/s}$$)
The time dilation formula is: Where:
Step 5:: Calculate Time Difference
\Delta t' = \frac{1}{\sqrt{1 - \frac{(7.66 \times 10^{3})^{2}}{(3 \times 10^{8})^{2}}}}
Plugging in values:
Step 6:: Compute the Ratio
After calculation, this results in approximately 1.0000005 years on Earth per 1 year in space.
Final Answer
Approximately 1.0000005 Earth years equal 1 year in space, meaning an astronaut ages only microseconds slower than someone on Earth during a typical space mission.
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