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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]

Sagot :

GinnyAnsweridn
### Solution:

To solve this problem, we need to convert the provided distances of the celestial objects from their original units into kilometers and, where appropriate, light-years.

#### Object A: 0.000001877 parsecs

Conversions
1 parsec = [tex]\( 31 \times 10^{12} \)[/tex] km.
1 parsec ≈ 3.262 light-years.

1. From parsecs to kilometers:

[tex]\[ \text{Distance in km} = \text{Distance in parsecs} \times \left(\text{km per parsec}\right) \][/tex]

[tex]\[ \text{Distance in km} = 0.000001877 \, \text{pc} \times 31 \times 10^{12} \, \text{km/pc} \][/tex]

[tex]\[ \text{Distance in km} = 58,187,000 \, \text{km} \][/tex]

2. From parsecs to light-years:

[tex]\[ \text{Distance in light-years} = \text{Distance in parsecs} \times \left(\text{light-years per parsec}\right) \][/tex]

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

[tex]\[ \text{Distance in light-years} = 0.000006122774 \, \text{ly} \][/tex]

#### Object B: 30.06 astronomical units (AU)

Conversion
1 AU = [tex]\( 1.5 \times 10^8 \)[/tex] km

1. From AU to kilometers:

[tex]\[ \text{Distance in km} = \text{Distance in AU} \times \left(\text{km per AU}\right) \][/tex]

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

[tex]\[ \text{Distance in km} = 4,509,000,000 \, \text{km} \][/tex]

#### Object C: 778.3 million kilometers

Conversion
1 million km = [tex]\( 10^6 \)[/tex] km

1. From million kilometers to kilometers:

[tex]\[ \text{Distance in km} = \text{Distance in million km} \times \left(\text{km per million km}\right) \][/tex]

[tex]\[ \text{Distance in km} = 778.3 \, \text{million km} \times 10^6 \, \text{km/million km} \][/tex]

[tex]\[ \text{Distance in km} = 778,300,000 \, \text{km} \][/tex]

### Summary of Results:
- Object A:
- Kilometers: [tex]\( 58,187,000 \, \text{km} \)[/tex]
- Light-years: [tex]\( 0.000006122774 \, \text{ly} \)[/tex]

- Object B:
- Kilometers: [tex]\( 4,509,000,000 \, \text{km} \)[/tex]

- Object C:
- Kilometers: [tex]\( 778,300,000 \, \text{km} \)[/tex]

These conversions represent the equivalent distances for each celestial object in the units provided.
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