Question

question 14 (multiple choice worth 3 points) oss.01the diagram below shows the position of the sun and two galaxies, g1 and g2. the distance between the sun and galaxy g1 is represented by y. what is the value of y in km?
options:
100 billion km
100 million km
500 billion km
500 million km

Explanation:

Step1: Recall the conversion of AU to km

1 AU is approximately \( 1.5 \times 10^{8} \) km. But we can also use the given total distance between Sun and G2 (300 billion km) and the distance between G1 and G2 (1333 AU) to find Y. First, let's find the distance between Sun and G2 in AU. Wait, alternatively, we know that the distance between Sun and G2 is 300 billion km, and between G1 and G2 is 1333 AU. Let's convert 300 billion km to AU.

But maybe a simpler way: We know that 1 AU is about \( 1.5 \times 10^{8} \) km. Let's check the options. Let's see the distance between G1 and G2 is 1333 AU. Let's convert 1333 AU to km: \( 1333 \times 1.5 \times 10^{8} \) km \( \approx 2 \times 10^{11} \) km (since \( 1.5 \times 10^{8} \times 1333 \approx 2 \times 10^{11} \)). Wait, 300 billion km is \( 3 \times 10^{11} \) km. Wait, maybe the total distance from Sun to G2 is 300 billion km, and from G1 to G2 is 1333 AU. Let's find the distance from Sun to G1 (Y) as total distance minus G1 - G2 distance. But first, convert 1333 AU to km.

1 AU = \( 1.5 \times 10^{8} \) km. So 1333 AU = \( 1333 \times 1.5 \times 10^{8} \) km \( \approx 2 \times 10^{11} \) km (since 13331.5≈2000, so 20001e8=2e11). The total distance from Sun to G2 is 300 billion km = \( 3 \times 10^{11} \) km. So Y = 3e11 - 2e11 = 1e11 km = 100 billion km.

Alternatively, we know that 1 AU is approximately 150 million km (1.5e8 km). So 1333 AU is 1333*150 million km ≈ 200,000 million km = 200 billion km. Then total distance from Sun to G2 is 300 billion km, so Y = 300 - 200 = 100 billion km.

Step2: Match with options

The option 100 billion km is present.

Answer:

100 billion km (the option corresponding to this, e.g., if the first option is "100 billion km", then the answer is that option. Assuming the first option is "100 billion km", the answer is: A. 100 billion km)