Select the correct answer from each drop-down menu. The distance between Earth and Mars is 225 million km. When converted using the conversion factor [tex]$1 AU =1.5 imes 10^8 km$[/tex], the distance between the planets is ____. The astronomical unit (AU) is ____ a light-year.

Question

Select the correct answer from each drop-down menu. The distance between Earth and Mars is 225 million km. When converted using the conversion factor [tex]$1 AU =1.5 	imes 10^8 km$[/tex], the distance between the planets is ____. The astronomical unit (AU) is ____ a light-year.

Anonymous · Answer

The distance between Earth and Mars is 1.5 AU, and an astronomical unit (AU) is smaller than a light-year. 
 ;

GinnyAnswer · Answer

Convert the distance between Earth and Mars from kilometers to AU: 225 × 1 0 6 km / ( 1.5 × 1 0 8 km/AU ) = 1.5 AU . 
 Compare the size of an AU to a light-year: 1 AU = 1.5 × 1 0 8 km and 1 light-year = 9.461 × 1 0 12 km . 
 Determine that an AU is smaller than a light-year. 
 The distance between the planets is 1.5 ​ AU, and the astronomical unit (AU) is s ma ll er t han ​ a light-year. 
 
 Explanation 
 
 Understanding the Problem We are given that the distance between Earth and Mars is 225 million km, which can be written as 225 × 1 0 6 km. We are also given that 1 AU (astronomical unit) is equal to 1.5 × 1 0 8 km. Our first task is to convert the distance between Earth and Mars from kilometers to AU. 
 
 Converting to AU To convert the distance from km to AU, we divide the distance in km by the conversion factor: Distance in AU = 1.5 × 1 0 8 km/AU Distance in km ​ Distance in AU = 1.5 × 1 0 8 km/AU 225 × 1 0 6 km ​ Distance in AU = 150 225 ​ = 1.5 So, the distance between Earth and Mars is 1.5 AU. 
 
 Comparing AU to a Light-Year Now, we need to determine if an AU is larger or smaller than a light-year. A light-year is the distance light travels in one year, which is approximately 9.461 × 1 0 12 km. We know that 1 AU is 1.5 × 1 0 8 km. To compare them, we can divide the length of a light-year by the length of an AU: 1 AU 1 light-year ​ = 1.5 × 1 0 8 km 9.461 × 1 0 12 km ​ = 63073.33 Since the result is much greater than 1, a light-year is much larger than an AU. Therefore, an AU is smaller than a light-year. 
 
 Final Answer Therefore, the distance between Earth and Mars is 1.5 AU, and an astronomical unit (AU) is smaller than a light-year.

Examples 
 Understanding the vast distances in space can be challenging. Using astronomical units (AU) helps simplify these distances relative to the Earth-Sun distance. For example, when planning interplanetary missions, knowing the distances in AU allows scientists and engineers to estimate travel times, fuel requirements, and communication delays. This makes space travel more manageable and comprehensible.

Select the correct answer from each drop-down menu. The distance between Earth and Mars is 225 million km. When converted using the conversion factor [tex]$1 AU =1.5 \times 10^8 km$[/tex], the distance between the planets is . The astronomical unit (AU) is a light-year.

Answer (2)

Select the correct answer from each drop-down menu. The distance between Earth and Mars is 225 million km. When converted using the conversion factor [tex]$1 AU =1.5 \times 10^8 km$[/tex], the distance between the planets is ____. The astronomical unit (AU) is ____ a light-year.

Answer (2)

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Select the correct answer from each drop-down menu. The distance between Earth and Mars is 225 million km. When converted using the conversion factor [tex]$1 AU =1.5 \times 10^8 km$[/tex], the distance between the planets is . The astronomical unit (AU) is a light-year.