Answer :
To rewrite the distances between a star and three celestial objects in different, but equivalent, units, follow these steps:
### 1. Distance to Object A: 0.000001877 parsecs (pc)
- Convert parsecs to kilometers:
Using the conversion factor, [tex]\(1 \text{ pc} = 31 \times 10^{12} \text{ km}\)[/tex]:
[tex]\[ \text{Distance in km} = 0.000001877 \text{ pc} \times 31 \times 10^{12} \text{ km/pc} = 58187000.0 \text{ km} \][/tex]
- Convert parsecs to light-years:
Using the conversion factor, [tex]\(1 \text{ pc} = 3.262 \text{ light-years}\)[/tex]:
[tex]\[ \text{Distance in light-years} = 0.000001877 \text{ pc} \times 3.262 \text{ light-years/pc} = 6.122774 \times 10^{-6} \text{ light-years} \][/tex]
### 2. Distance to Object B: 30.06 Astronomical Units (AU)
- Convert AU to kilometers:
Using the conversion factor, [tex]\(1 \text{ AU} = 1.5 \times 10^{8} \text{ km}\)[/tex]:
[tex]\[ \text{Distance in km} = 30.06 \text{ AU} \times 1.5 \times 10^{8} \text{ km/AU} = 4509000000.0 \text{ km} \][/tex]
### 3. Distance to Object C: 778.3 million kilometers (km)
- Convert million kilometers to kilometers:
[tex]\[ \text{Distance in km} = 778.3 \text{ million km} \times 10^{6} \text{ km/million km} = 778300000.0 \text{ km} \][/tex]
- Convert kilometers to parsecs:
Using the conversion factor, [tex]\(1 \text{ pc} = 31 \times 10^{12} \text{ km}\)[/tex]:
[tex]\[ \text{Distance in pc} = \frac{778300000.0 \text{ km}}{31 \times 10^{12} \text{ km/pc}} = 2.5106451612903225 \times 10^{-5} \text{ pc} \][/tex]
### Summary of Converted Distances:
- Object A:
- [tex]\(0.000001877 \text{ pc}\)[/tex]
- Equivalent to 58,187,000.0 km
- Equivalent to [tex]\(6.122774 \times 10^{-6}\)[/tex] light-years
- Object B:
- [tex]\(30.06 \text{ AU}\)[/tex]
- Equivalent to 4,509,000,000.0 km
- Object C:
- 778.3 million km
- Equivalent to 778,300,000.0 km
- Equivalent to [tex]\(2.5106451612903225 \times 10^{-5} \text{ pc}\)[/tex]
These conversions provide equivalent representations of the distances in different units, making it easier to understand and compare these distances in various astronomical contexts.
### 1. Distance to Object A: 0.000001877 parsecs (pc)
- Convert parsecs to kilometers:
Using the conversion factor, [tex]\(1 \text{ pc} = 31 \times 10^{12} \text{ km}\)[/tex]:
[tex]\[ \text{Distance in km} = 0.000001877 \text{ pc} \times 31 \times 10^{12} \text{ km/pc} = 58187000.0 \text{ km} \][/tex]
- Convert parsecs to light-years:
Using the conversion factor, [tex]\(1 \text{ pc} = 3.262 \text{ light-years}\)[/tex]:
[tex]\[ \text{Distance in light-years} = 0.000001877 \text{ pc} \times 3.262 \text{ light-years/pc} = 6.122774 \times 10^{-6} \text{ light-years} \][/tex]
### 2. Distance to Object B: 30.06 Astronomical Units (AU)
- Convert AU to kilometers:
Using the conversion factor, [tex]\(1 \text{ AU} = 1.5 \times 10^{8} \text{ km}\)[/tex]:
[tex]\[ \text{Distance in km} = 30.06 \text{ AU} \times 1.5 \times 10^{8} \text{ km/AU} = 4509000000.0 \text{ km} \][/tex]
### 3. Distance to Object C: 778.3 million kilometers (km)
- Convert million kilometers to kilometers:
[tex]\[ \text{Distance in km} = 778.3 \text{ million km} \times 10^{6} \text{ km/million km} = 778300000.0 \text{ km} \][/tex]
- Convert kilometers to parsecs:
Using the conversion factor, [tex]\(1 \text{ pc} = 31 \times 10^{12} \text{ km}\)[/tex]:
[tex]\[ \text{Distance in pc} = \frac{778300000.0 \text{ km}}{31 \times 10^{12} \text{ km/pc}} = 2.5106451612903225 \times 10^{-5} \text{ pc} \][/tex]
### Summary of Converted Distances:
- Object A:
- [tex]\(0.000001877 \text{ pc}\)[/tex]
- Equivalent to 58,187,000.0 km
- Equivalent to [tex]\(6.122774 \times 10^{-6}\)[/tex] light-years
- Object B:
- [tex]\(30.06 \text{ AU}\)[/tex]
- Equivalent to 4,509,000,000.0 km
- Object C:
- 778.3 million km
- Equivalent to 778,300,000.0 km
- Equivalent to [tex]\(2.5106451612903225 \times 10^{-5} \text{ pc}\)[/tex]
These conversions provide equivalent representations of the distances in different units, making it easier to understand and compare these distances in various astronomical contexts.
