To calculate how many times further Voyager 1 has traveled compared to Apollo 13, we'll need the distances traveled by both spacecraft.
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Voyager 1 is approximately 14.1 billion miles from Earth as of 2023, which can be expressed in scientific notation: \[ 14.1 \text{ billion} = 14.1 \times 10^9 \text{ miles} \]
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Apollo 13, which traveled to the Moon, covered a distance of approximately 400,000 kilometers during its mission. To convert this distance to miles, we use the conversion factor where 1 kilometer is approximately 0.621371 miles: \[ 400,000 \text{ km} \times 0.621371 \text{ miles/km} \approx 248,548 \text{ miles} \] In scientific notation, this can be expressed as: \[ 2.48548 \times 10^5 \text{ miles} \]
Now, we need to divide the distance traveled by Voyager 1 by the distance traveled by Apollo 13:
\[ \text{Ratio} = \frac{\text{Distance traveled by Voyager 1}}{\text{Distance traveled by Apollo 13}} = \frac{14.1 \times 10^9 \text{ miles}}{2.48548 \times 10^5 \text{ miles}} \]
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Performing the division step-by-step:
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Start with the numbers: \[ \frac{14.1}{2.48548} \approx 5.67 \quad \text{(for practical purposes, we'll use a calculator for this)} \]
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Now, for the powers of 10: \[ 10^9 \div 10^5 = 10^{9-5} = 10^4 \]
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Combining both parts: \[ \frac{14.1 \times 10^9}{2.48548 \times 10^5} \approx 5.67 \times 10^4 \]
So, the final answer, in exact scientific notation, is: \[ \approx 5.67 \times 10^4 \]
Thus, Voyager 1 has traveled approximately \(5.67 \times 10^4\) times further than Apollo 13.