How many astronomical units make up one light year?

Explanation

To find out how many astronomical units (AU) make up one light year (ly), we need to use the definitions of both units and perform some calculations. Here’s a step-by-step solution:

### Step 1: Understand the definitions
- **Astronomical Unit (AU)**: The average distance from the Earth to the Sun, which is approximately \(1.49 \times 10^8\) kilometers.
- **Light Year (ly)**: The distance that light travels in one year, which is approximately \(9.46 \times 10^{12}\) kilometers.

### Step 2: Set up the relationship
We want to find out how many astronomical units are in one light year. This can be expressed mathematically as:
\[ \text{Number of AUs in 1 ly} = \frac{\text{Distance in 1 ly}}{\text{Distance in 1 AU}} \]

### Step 3: Substitute the values
Substituting the known values into the equation:
\[ \text{Number of AUs in 1 ly} = \frac{9.46 \times 10^{12} \text{ km}}{1.49 \times 10^{8} \text{ km}} \]

### Step 4: Perform the calculation
Now, we can simplify the fraction:
\[ \text{Number of AUs in 1 ly} = \frac{9.46}{1.49} \times \frac{10^{12}}{10^{8}} = \frac{9.46}{1.49} \times 10^{4} \]

Calculating \( \frac{9.46}{1.49} \):
\[ \frac{9.46}{1.49} \approx 6.35 \]

Thus, we have:
\[ \text{Number of AUs in 1 ly} \approx 6.35 \times 10^{4} \]

### Conclusion
Therefore, there are approximately \(6.35 \times 10^{4}\) astronomical units in one light year.

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