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The table shows the distances between a star and three celestial objects. Use the conversion factors to rewrite the distances in different, but equivalent, units.

\begin{tabular}{|l|l|}
\hline
Celestial Object & Distance from the Star \\
\hline
Object A & 0.000001877 pc \\
\hline
Object B & 30.06 AU \\
\hline
Object C & 778.3 million km \\
\hline
\end{tabular}

Conversion factors:
[tex]\[ 1 \, \text{AU} = 1.5 \times 10^8 \, \text{km} \][/tex]
[tex]\[ 1 \, \text{light-year} = 9.5 \times 10^{12} \, \text{km} \][/tex]
[tex]\[ 1 \, \text{parsec} = 31 \, \text{trillion km} \, \text{or about} \, 3.262 \, \text{light-years} \][/tex]

Rewrite the distances in equivalent units:

[tex]\[
\begin{array}{ll}
\text{Distance to Object A:} & \square \\
\text{Distance to Object B:} & \square \\
\text{Distance to Object C:} & \square \\
\end{array}
\][/tex]

Example conversions:
[tex]\[ 0.0001458 \, \text{pc} \][/tex]
[tex]\[ 5.2 \, \text{AU} \][/tex]
[tex]\[ 57.91 \, \text{million km} \][/tex]



Answer :

GinnyAnswer
To rewrite the distances of the celestial objects in different units, follow these steps for each conversion.

### Distance to Object A
- The distance from the star to object A is given as 0.000001877 parsecs (pc).
- We need to convert this distance to light-years (ly).
- 1 parsec is approximately 3.262 light-years.

[tex]\[ \text{Distance to Object A in light-years} = 0.000001877 \, \text{pc} \times 3.262 \, \text{ly/pc} \][/tex]

[tex]\[ \text{Distance to Object A in light-years} = 6.122774 \times 10^{-6} \, \text{ly} \][/tex]

So, the distance to object A is approximately [tex]\( 6.122774 \times 10^{-6} \)[/tex] light-years.

### Distance to Object B
- The distance from the star to object B is given as 30.06 astronomical units (AU).
- We need to convert this distance to kilometers (km).
- 1 AU is approximately [tex]\( 1.5 \times 10^8 \)[/tex] km.

[tex]\[ \text{Distance to Object B in kilometers} = 30.06 \, \text{AU} \times 1.5 \times 10^8 \, \text{km/AU} \][/tex]

[tex]\[ \text{Distance to Object B in kilometers} = 4509000000.0 \, \text{km} \][/tex]

So, the distance to object B is approximately [tex]\( 4509000000.0 \)[/tex] kilometers.

### Distance to Object C
- The distance from the star to object C is given as 778.3 million kilometers.
- We need to convert this distance to astronomical units (AU).
- 1 AU is approximately [tex]\( 1.5 \times 10^8 \)[/tex] km.
- The given distance in kilometers is [tex]\( 778.3 \times 10^6 \)[/tex] km.

[tex]\[ \text{Distance to Object C in AU} = \frac{778.3 \times 10^6 \, \text{km}}{1.5 \times 10^8 \, \text{km/AU}} \][/tex]

[tex]\[ \text{Distance to Object C in AU} = \frac{778.3 \times 10^6}{1.5 \times 10^8} \][/tex]

[tex]\[ \text{Distance to Object C in AU} = 5.188666666666666 \, \text{AU} \][/tex]

So, the distance to object C is approximately [tex]\( 5.188666666666666 \)[/tex] astronomical units.

Summarizing, the distances converted are:
- Object A: [tex]\( 6.122774 \times 10^{-6} \)[/tex] light-years.
- Object B: 4,509,000,000.0 kilometers.
- Object C: 5.188666666666666 astronomical units.

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