Answer
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Step 1:I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Understand Time Dilation
Time passes differently in space due to Einstein's theory of relativity. The time difference depends on the relative velocity and gravitational field strength.
Step 3:: Recall the Time Dilation Formula
- $$c$$ is the speed of light ($$3 \times 10^{8}$$ m/s)
The time dilation formula is: Where:
Step 4:: Consider Orbital Velocity
For astronauts in low Earth orbit, the velocity is approximately $$7.66 \times 10^{3}$$ m/s.
Step 5:: Calculate Time Dilation
\Delta t' = \frac{1}{\sqrt{1 - \frac{(7.66 \times 10^{3})^{2}}{(3 \times 10^{8})^{2}}}}
Plugging in the values:
Step 6:: Perform Calculation
After calculation, this results in approximately 1.0000004 hours on Earth for every 1 hour in space.
Final Answer
Note: The time difference is extremely small due to the relatively low orbital velocity of spacecraft compared to the speed of light.
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