The distance from the Earth to the Sun is about \( 1.5 \times 10^{8} \mathrm{~km} \), while the distance from the Earth to the moon is about \( 3.8 \times 10^{5} \mathrm{~km} \). If a scale model of the solar system is constructed so that the distance from the Earth to the Sun is 100 meters, what will be the distance from the Earth to the moon?
\( 0.25 \mathrm{~m} \)
\( 6.36 \mathrm{~m} \)
39, \( 474 \mathrm{~m} \)
\( 39.5 \mathrm{~m} \)

Answer

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Answer

Calculate \(d_{Moon}\): \(d_{Moon} = 0.2533 \mathrm{~m}\)

Steps

Step 1 ：Set up a proportion:\(\frac{d_{Moon}}{100} = \frac{3.8 \times 10^5}{1.5 \times 10^8}\)

Step 2 ：Solve for \(d_{Moon}\):\(d_{Moon} = 100 \times \frac{3.8 \times 10^5}{1.5 \times 10^8}\)

Step 3 ：Calculate \(d_{Moon}\): \(d_{Moon} = 0.2533 \mathrm{~m}\)