Sarahgarland81idn
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Arrange the distances between Earth and various celestial objects in order from least to greatest. Use the conversion table to help you.

\begin{tabular}{|l|l|}
\hline
\multicolumn{2}{|c|}{Conversion Table} \\
\hline
1 AU & [tex]$1.5 \times 10^8$[/tex] km \\
\hline
1 ly & [tex]$63,000$[/tex] AU \\
\hline
1 pc & [tex]$3.262$[/tex] ly \\
\hline
\end{tabular}

- Distance to Neptune at the farthest: 4.7 billion km
- Distance to the star Betelgeuse: 640 ly
- Distance to the star VY Canis Majoris: [tex]$3.09 \times 10^8$[/tex] AU
- Distance to the galaxy Large Magellanic Cloud: 49,976 pc

Sagot :

GinnyAnsweridn
Certainly! Let's systematically convert each distance to a common unit, in this case, kilometers, to arrange them in order from least to greatest.

1. Distance to Neptune:
- Already provided in kilometers: [tex]\( 4.7 \times 10^9 \)[/tex] km

2. Distance to Betelgeuse (640 light-years):
- 1 light-year (ly) = 63,000 astronomical units (AU)
- 1 AU = [tex]\( 1.5 \times 10^8 \)[/tex] km
- Convert light-years to astronomical units:
[tex]\( 640 \, \text{ly} \times 63,000 \, \text{AU/ly} = 40,320,000 \, \text{AU} \)[/tex]
- Convert astronomical units to kilometers:
[tex]\( 40,320,000 \, \text{AU} \times 1.5 \times 10^8 \, \text{km/AU} = 6.048 \times 10^{15} \)[/tex] km
- Distance to Betelgeuse: [tex]\( 6.048 \times 10^{15} \)[/tex] km

3. Distance to VY Canis Majoris (3.09 [tex]\(\times 10^8\)[/tex] AU):
- 1 AU = [tex]\( 1.5 \times 10^8 \)[/tex] km
- Convert astronomical units to kilometers:
[tex]\( 3.09 \times 10^8 \, \text{AU} \times 1.5 \times 10^8 \, \text{km/AU} = 4.635 \times 10^{16} \)[/tex] km
- Distance to VY Canis Majoris: [tex]\( 4.635 \times 10^{16} \)[/tex] km

4. Distance to the Large Magellanic Cloud (49,976 parsecs):
- 1 parsec (pc) = 3.262 light-years (ly)
- 1 light-year (ly) = 63,000 astronomical units (AU)
- 1 AU = [tex]\( 1.5 \times 10^8 \)[/tex] km
- Convert parsecs to light-years:
[tex]\( 49,976 \, \text{pc} \times 3.262 \, \text{ly/pc} = 162,949.512 \, \text{ly} \)[/tex]
- Convert light-years to astronomical units:
[tex]\( 162,949.512 \, \text{ly} \times 63,000 \, \text{AU/ly} = 10,265,818,056 \, \text{AU} \)[/tex]
- Convert astronomical units to kilometers:
[tex]\( 10,265,818,056 \, \text{AU} \times 1.5 \times 10^8 \, \text{km/AU} = 1.5405551784 \times 10^{18} \)[/tex] km
- Distance to the Large Magellanic Cloud: [tex]\( 1.5405551784 \times 10^{18} \)[/tex] km

Now, let's arrange these distances from least to greatest:

1. Distance to Neptune: [tex]\( 4.7 \times 10^9 \)[/tex] km
2. Distance to Betelgeuse: [tex]\( 6.048 \times 10^{15} \)[/tex] km
3. Distance to VY Canis Majoris: [tex]\( 4.635 \times 10^{16} \)[/tex] km
4. Distance to the Large Magellanic Cloud: [tex]\( 1.5405551784 \times 10^{18} \)[/tex] km
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