To convert the distance from light-years to miles, we can follow these steps:

Step 1: Determine the distance light travels in one year.

1 light-year is the distance light travels in one year. The speed of light is $3.00 \times 10^8$ meters per second.

We first calculate how many seconds there are in one year: $1 \text{ year} = 365.25 \times 24 \times 60 \times 60 = 31,557,600 \text{ seconds}.$

Now, we calculate the distance light travels in one year in meters: $\text{Distance in one year} = (3.00 \times 10^8 \text{ m/s}) \times (31,557,600 \text{ s}) = 9.46728 \times 10^{15} \text{ meters}.$

Step 2: Convert meters to miles.

We use the conversion factor: 1 mile = 1609.34 meters.

$\text{Distance in one light-year} = \frac{9.46728 \times 10^{15} \text{ meters}}{1609.34 \text{ meters/mile}} = 5.87863 \times 10^{12} \text{ miles}.$

Step 3: Multiply by 4.0 light-years.

The distance from Alpha Centauri to Earth is 4.0 light-years, so:

$\text{Distance} = 4.0 \times 5.87863 \times 10^{12} \text{ miles} = 2.35145 \times 10^{13} \text{ miles}.$

Therefore, the distance from Alpha Centauri to Earth is approximately $2.35 \times 10^{13}$ miles.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the significance of using light-years in astronomical measurements?
2. How can we calculate the time it would take a spacecraft to travel one light-year?
3. What are some other methods of measuring astronomical distances?
4. How do distances in parsecs compare to those in light-years?
5. Can light-year distances vary depending on the observer’s frame of reference?

Tip: When dealing with very large numbers, scientific notation makes it easier to manage and communicate distances clearly.