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 $c=299,792,458m/s$.

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:

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