Distance Traveled in a Light Year

Problem Statement

Astronomical distances are sometimes described in terms of light years. As you might guess, a light year is the distance that light in a vacuum will travel in one year. How many meters is one light year? The speed of light in a vacuum is $c=299,792,458m/s$.

I Need a Hint!

Start by converting a year to seconds (use 365.25 days per year). Then use the speed of light to figure out the distance traveled.

Solution

We can solve this problem using dimensional analysis. Let’s start by calculating the number of seconds in a year:

$$(1year)\left(\frac{365.25days}{1year}\right)\left(\frac{24hours}{1day}\right)\left(\frac{60minutes}{1hour}\right)\left(\frac{60seconds}{1minute}\right)=31,557,600seconds$$

Now we can multiply by the speed of light to get the final answer:

$$\left(299,792,458m/s\right)\left(31,557,600s\right)=9,460,730,472,580,800m\approx 9.46\times 10^{15}m$$