Question

to solve a problem using the equation for kepler’s third law, enrico must convert the average distance of mars from the sun from meters into astronomical units. how should he make the conversion?
multiply the average distance by 1.5 × 10¹¹
multiply 1.5 × 10¹¹ by the average distance
divide the average distance by 1.5 × 10¹¹
divide 1.5 × 10¹¹ by the average distance

Explanation:

1. Recall the definition of an astronomical unit (AU): 1 AU is the average distance from the Earth to the Sun, which is approximately \( 1.5 \times 10^{11} \) meters.
2. To convert a distance \( d \) (in meters) to astronomical units, we use the formula: \( \text{Distance in AU} = \frac{d}{1\ \text{AU in meters}} \).
3. Substituting the value of 1 AU (\( 1.5 \times 10^{11} \) meters) into the formula, we get \( \text{Distance in AU} = \frac{\text{Average distance of Mars (in meters)}}{1.5 \times 10^{11}} \). So we divide the average distance (in meters) by \( 1.5 \times 10^{11} \) to get the distance in astronomical units.

Answer:

C. divide the average distance by \( 1.5 \times 10^{11} \)