Select the correct answer.
Venus is an average distance of 108.2 million kilometers from the Sun. Use the conversion factor [tex]$1 AU =1.5 \times 10^8 km$[/tex] to convert this distance from kilometers to astronomical units. Choose the closest answer.
A. [tex]$0.72 AU$[/tex]
B. 1.25 AU
C. 3.56 AU
D. 45.63 AU
E. 96.12 AU
Answer (2)
The average distance of Venus from the Sun is approximately 0.72 astronomical units (AU) when converted from kilometers using the conversion factor. Therefore, the correct answer is A. 0.72 AU .
;
Divide the distance of Venus from the Sun in kilometers by the conversion factor to get the distance in AU.
Perform the calculation: 1.5 × 1 0 8 108.2 × 1 0 6 = 0.721333...
Round the result to two decimal places: 0.72 AU.
The closest answer from the given options is 0.72 A U .
Explanation
Understanding the Problem We are given that Venus is an average distance of 108.2 million kilometers from the Sun. We are also given that 1 AU (astronomical unit) is equal to 1.5 \t × 1 0 8 km. Our objective is to convert the distance of Venus from the Sun from kilometers to astronomical units.
Setting up the Conversion To convert the distance from kilometers to AU, we need to divide the distance in kilometers by the conversion factor. That is, D i s t an c e A U = C o n v ers i o n F a c t or D i s t an c e km In our case, D i s t an c e km = 108.2 × 1 0 6 km and C o n v ers i o n F a c t or = 1.5 × 1 0 8 km/AU.
Calculating the Distance in AU Now, we perform the calculation: D i s t an c e A U = 1.5 × 1 0 8 108.2 × 1 0 6 = 150 108.2 = 0.721333... Rounding to two decimal places, we get 0.72 AU.
Selecting the Correct Answer Comparing our result with the given options, we see that the closest answer is 0.72 AU.
Examples
Understanding astronomical units helps us grasp the vast distances in space. For instance, if we're designing a mission to Venus, knowing its distance from the Sun in AU allows us to calculate travel time and fuel requirements more intuitively. Similarly, when studying exoplanets, expressing their orbital distances in AU provides a relatable scale, making it easier to compare their potential habitability to planets in our solar system. This unit simplifies complex calculations and enhances our understanding of cosmic distances.
