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.
| Celestial Objects | Distance from the Star |
|---|---|
| object A | 0.000001877 pc |
| object B | 30.06 AU |
| object C | 778.3 million km |
Conversion factors:
[tex]$1 AU =1.5 \times 10^8 km$[/tex]
1 light-year [tex]$=9.5 \times 10^{12} km$[/tex]
1 parsec [tex]$=31$[/tex] trillion km, or about 3.262 light-years
Answer (2)
The distances of three celestial objects from a star were converted into kilometers, astronomical units (AU), and light-years (ly). Object A is equivalent to 58170.00 km, 0.0003879 AU, and 0.0000061 ly. Object B and C were similarly converted, providing a comprehensive understanding of distances in different units.
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Converts the distance of object A from parsecs to kilometers, astronomical units, and light-years.
Converts the distance of object B from astronomical units to kilometers, parsecs, and light-years.
Converts the distance of object C from kilometers to astronomical units, parsecs, and light-years.
Presents the converted distances for all three objects in the requested units.
Explanation
Given Data and Conversion Factors We are given the distances of three celestial objects from a star in different units and asked to convert them to other units using the provided conversion factors. Let's start by listing the given information:
Object A: 0.000001877 pc Object B: 30.06 AU Object C: 778.3 million km = 778.3 × 1 0 6 km
Conversion factors: 1 AU = 1.5 × 1 0 8 km 1 light-year = 9.5 × 1 0 12 km 1 parsec = 31 × 1 0 12 km = 3.262 light-years
Object A Conversions Now, let's convert the distance of Object A from parsecs to kilometers, astronomical units, and light-years.
To kilometers: 0.000001877 pc × 1 pc 31 × 1 0 12 km = 58187000 km
To astronomical units: 0.000001877 pc × 1 pc 31 × 1 0 12 km × 1.5 × 1 0 8 km 1 AU = 1.5 × 1 0 8 58187000 AU = 0.387913333 AU
To light-years: 0.000001877 pc × 1 pc 3.262 light-years = 0.000006122774 light-years
Object B Conversions Next, let's convert the distance of Object B from astronomical units to kilometers, parsecs, and light-years.
To kilometers: 30.06 AU × 1 AU 1.5 × 1 0 8 km = 4509000000 km
To parsecs: 30.06 AU × 1 AU 1.5 × 1 0 8 km × 31 × 1 0 12 km 1 pc = 31 × 1 0 12 4509000000 pc = 0.0001454516 pc
To light-years: 30.06 AU × 1 AU 1.5 × 1 0 8 km × 9.5 × 1 0 12 km 1 light-year = 9.5 × 1 0 12 4509000000 light-years = 0.0004746316 light-years
Object C Conversions Finally, let's convert the distance of Object C from kilometers to astronomical units, parsecs, and light-years.
To astronomical units: 1 778.3 × 1 0 6 km × 1.5 × 1 0 8 km 1 AU = 5.188666667 AU
To parsecs: 1 778.3 × 1 0 6 km × 31 × 1 0 12 km 1 pc = 0.0000251065 pc
To light-years: 1 778.3 × 1 0 6 km × 9.5 × 1 0 12 km 1 light-year = 0.0000819263 light-years
Final Results In summary: Object A:
0.000001877 pc = 58187000 km = 0.387913333 AU = 0.000006122774 light-years
Object B:
30.06 AU = 4509000000 km = 0.0001454516 pc = 0.0004746316 light-years
Object C:
778.3 × 1 0 6 km = 5.188666667 AU = 0.0000251065 pc = 0.0000819263 light-years
Examples
Understanding astronomical distances is crucial in space exploration and astrophysics. For instance, when planning a mission to a distant exoplanet, scientists use these conversions to determine travel time, fuel requirements, and communication strategies. Knowing the distances in various units like AU, light-years, and parsecs helps in comparing these distances to known scales, such as the size of our solar system or the distance to nearby stars. This ensures accurate navigation and efficient resource management for interstellar travel.
