Question

solar winds have an influence all the way to about 160 au from the sun. about how many kilometers is that?
○ 24,000,000,000 km
○ 48,000,000,000 km
○ 240,000,000,000 km
○ 480,000,000,000 km

Explanation:

Step1: Recall the conversion of AU to km

1 Astronomical Unit (AU) is approximately equal to \( 1.5\times10^{8} \) kilometers.

Step2: Calculate the distance in km for 160 AU

We need to multiply the number of AU (160) by the conversion factor. So, the distance \( d = 160\times1.5\times 10^{8} \) km.
First, calculate \( 160\times1.5=240 \). Then, \( 240\times 10^{8}=2.4\times 10^{10} \) km? Wait, no, wait: \( 1.5\times 10^{8}\times160 = 1.5\times160\times 10^{8}=240\times 10^{8}=2.4\times 10^{10} \)? Wait, no, \( 10^{8}\times240 = 240\times10^{8}=2.4\times 10^{10} \)? Wait, no, 240,000,000,000 is \( 2.4\times 10^{11} \)? Wait, I made a mistake. Let's recalculate:

1 AU \( \approx 1.5\times 10^{8} \) km.

So 160 AU \( = 160\times1.5\times 10^{8} \) km.

\( 160\times1.5 = 240 \), so \( 240\times 10^{8} \) km. But \( 240\times 10^{8}=2.4\times 10^{2}\times 10^{8}=2.4\times 10^{10} \)? Wait, no, 10^8 times 240: 240,000,000,000 is 2.4×10^11? Wait, no, 10^8 is 100,000,000. 240×100,000,000 = 24,000,000,000? Wait, no: 240 × 100,000,000 = 24,000,000,000? Wait, 100,000,000 is 1e8. 240 × 1e8 = 2.4e2 × 1e8 = 2.4e10 = 24,000,000,000? Wait, no, 2.4e10 is 24,000,000,000? Wait, 1e9 is 1,000,000,000. So 2.4e10 is 24,000,000,000? Wait, no, 2.4×10^10: 10^10 is 10,000,000,000. So 2.4×10,000,000,000 = 24,000,000,000. Wait, but the options have 24,000,000,000; 48,000,000,000; 240,000,000,000; 480,000,000,000.

Wait, maybe I used the wrong conversion factor. Wait, actually, 1 AU is approximately 1.5×10^8 km? Wait, no, 1 AU is approximately 149,597,870.7 km, which is approximately 1.5×10^8 km (1.5×10^8 = 150,000,000). So 160 AU: 160 × 1.5×10^8 = 240×10^8 = 2.4×10^10 = 24,000,000,000 km? Wait, but 2.4×10^10 is 24,000,000,000? Wait, 10^10 is 10,000,000,000. So 2.4×10,000,000,000 = 24,000,000,000. So the first option is 24,000,000,000 km. Wait, but let's check again.

Wait, 1 AU ≈ 1.5×10^8 km.

160 AU = 160 1.5×10^8 km = (1601.5) ×10^8 km = 240 ×10^8 km = 2.4×10^10 km = 24,000,000,000 km.

So the answer should be 24,000,000,000 km.

Answer:

24,000,000,000 km (corresponding to the first option: 24,000,000,000 km)