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 Objects & 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:
$1 AU =1.5 \times 10^8 km$
1 light-year $=9.5 \times 10^{12} km$
1 parsec $=31$ trillion km , or about 3.262 light-years

Convert the distance of Object A from parsecs to kilometers, astronomical units, and light-years.
Convert the distance of Object B from astronomical units to kilometers, parsecs, and light-years.
Convert the distance of Object C from kilometers to astronomical units, parsecs, and light-years.
Summarize the converted distances for each object in the specified units.

Explanation

Given Information and Objective 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 A U = 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

Converting Object A's Distance Now, let's convert the distance of Object A from parsecs to kilometers, astronomical units, and light-years.

To kilometers: 0.000001877 p c × ( 31 × 1 0 12 km /1 p c ) = 58187000 km
To astronomical units: 0.000001877 p c × ( 31 × 1 0 12 km /1 p c ) × ( 1 A U /1.5 × 1 0 8 km ) = 58187000 km / ( 1.5 × 1 0 8 km / A U ) = 0.387913333 A U
To light-years: 0.000001877 p c × ( 3.262 l i g h t − ye a rs /1 p c ) = 0.000006122774 light-years

Converting Object B's Distance Next, let's convert the distance of Object B from astronomical units to kilometers, parsecs, and light-years.

To kilometers: 30.06 A U × ( 1.5 × 1 0 8 km /1 A U ) = 4509000000 km
To parsecs: 30.06 A U × ( 1.5 × 1 0 8 km /1 A U ) × ( 1 p c /31 × 1 0 12 km ) = 4509000000 km / ( 31 × 1 0 12 km / p c ) = 0.0001454516 p c
To light-years: 30.06 A U × ( 1.5 × 1 0 8 km /1 A U ) × ( 1 l i g h t − ye a r /9.5 × 1 0 12 km ) = 4509000000 km / ( 9.5 × 1 0 12 km / l i g h t − ye a r ) = 0.0004746316 light-years

Converting Object C's Distance Finally, let's convert the distance of Object C from kilometers to astronomical units, parsecs, and light-years.

To astronomical units: 778.3 × 1 0 6 km × ( 1 A U /1.5 × 1 0 8 km ) = 778300000 km / ( 1.5 × 1 0 8 km / A U ) = 5.18866667 A U
To parsecs: 778.3 × 1 0 6 km × ( 1 p c /31 × 1 0 12 km ) = 778300000 km / ( 31 × 1 0 12 km / p c ) = 0.0000251065 p c
To light-years: 778.3 × 1 0 6 km × ( 1 l i g h t − ye a r /9.5 × 1 0 12 km ) = 778300000 km / ( 9.5 × 1 0 12 km / l i g h t − ye a r ) = 0.0000819263 light-years

Final Results Here's a summary of the converted distances:

Object A:

58,187,000 km
0.387913333 AU
0.000006122774 light-years

Object B:

4,509,000,000 km
0.0001454516 pc
0.0004746316 light-years

Object C:

5.18866667 AU
0.0000251065 pc
0.0000819263 light-years

Examples
Understanding the vast distances in space requires converting between different units like kilometers, astronomical units, parsecs, and light-years. For instance, when planning a mission to a distant exoplanet, scientists use these conversions to calculate travel time, fuel requirements, and communication delays. Knowing that a planet is 5 light-years away helps engineers design spacecraft with sufficient life support and communication systems that can function for decades. These unit conversions are not just theoretical exercises but essential tools for space exploration and astronomical research.

Answered by GinnyAnswer | 2025-07-08

The distances of three celestial objects were converted into various units based on given conversion factors. Object A's distance was calculated in km, AU, and light-years; Object B's and Object C's distances were also converted into respective units. This process highlights the importance of unit conversion in astrophysics for understanding celestial distances.
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Answered by Anonymous | 2025-07-12