Astronomical distances are measured in light-years (1 light year is the distance traveled by light in 1 year; the speed of light is 3.00 x 108 m/s).  The distance from Alpha Centauri to the Earth is 4.0 light-years.  What is the distance in miles?

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.

Astronomical distances are measured in light-years (1 light year is the distance traveled by light in 1 year; the speed of light is 3.00 x 10^8 m/s). The distance from Alpha Centauri to the Earth is 4.0 light-years. What is the distance in miles?

Learn how to calculate the distance from Alpha Centauri to Earth in miles by converting light-years using the speed of light and unit conversions. This problem explains key concepts like scientific notation and unit conversions, suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation