At first glance, you might think that a light year is a measure of time because it has the word year in it. A light year is actually a measure of distance that uses light as a reference. If you ever tell a friend that your distance is five minutes away, you also use time as a measure of distance. The distance between the stars in this universe is very far. So astronomers use light years as a larger unit than miles and kilometers. To calculate the actual distance of a light year, you just need to multiply the speed of light by the number of seconds in a year.
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Method 1 of 2: Calculating One Light Year
Step 1. Determine the light year
A light year is a measure of the distance equivalent to how far light travels in one Earth year. Because the entire universe is so far apart, astronomers use light years. Without light years, discussing the distance between two stars would require the use of long and irregular numbers.
Another measure of distance that you may encounter while studying astronomy is the parsec. This size is equal to 3.26 light years. Parsec is another way to simplify the numbers used to calculate and discuss astronomical distances
Step 2. Write a formula for distance
Using the general physics formula, distance equals speed times time or d = r x t, you can calculate how far a light year is: Light Year = (speed of light) x (one year). Since the speed of light is denoted by the variable “c”, you can rewrite the equation as d = c x t, where d is the distance one light year, c is the speed of light and t is time.
- If you want to know the distance of a light year in kilometers, you need to find the speed of light in kilometers per second. If you want miles, you need to find the speed of light in miles per second.
- You must know the number of seconds in an Earth year for this calculation.
Step 3. Determine the speed of light
Light in a vacuum travels at 186,000 miles per second. This amount is equivalent to 299,792 kilometers per second or 670,616,629 miles per hour. Here we will use speed in miles per second.
For this calculation we will use the speed of light, c, equal to 186,000 miles per second. This number can be rewritten in scientific notation as 1.86 x 105 miles per second.
Step 4. Count the number of seconds in a year
To find the number of seconds in a year, perform a series of multiplication unit conversions. To convert years to seconds, multiply the number of days in a year times the number of hours in a day, times the number of minutes in an hour, times the number of seconds in a minute.
- 1 year x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute = 31,536,000 seconds.
- Again, we can rewrite this number using scientific notation as 3, 154 x 107.
Step 5. Plug the variables into the formula and solve
Now that you've determined the variables for the speed of light and time, you can plug them into the formula d = c x t and find the distance one light year. Replace c with 1.86 x 105 miles per second and time with 3.154 x 107 second.
- d = c x t
- d = (1,86 x 105) x (3, 154 x 107 second)
- d = 5, 8 x 1012 or 5.8 trillion miles.
Step 6. Calculate the distance in kilometers
If you want to calculate in kilometers, simply replace the speed of light with the speed in kilometers per second: 3.00 x 105. The time in seconds remains the same as no conversion is required.
- d = c x t
- d = (3,00 x 105) x (3, 154 x 107 second)
- d = 9, 46 x 1012 or 9.5 trillion kilometers.
Method 2 of 2: Converting Distances To Light Years
Step 1. Determine the distance you want to change
Before starting, make sure that whatever distance you're working on is in miles (if using imperial units) or in kilometers if using common units of measurement. There's no point in converting short distances into light years, but it's fine if you're curious.
- To convert feet to miles, remember that a mile equals 5,280 feet: x feet (1 mile/5,280 ft) = miles.
- To convert meters to kilometers, simply divide by 1000: x m (1 km/1000 m) = km.
Step 2. Determine the right conversion factor
You need to identify the unit of distance that you want to convert to light years. If you're converting from kilometers to light years, use a different conversion factor than you used to convert from miles.
- To convert from kilometers to light years, use: 1 light year /(9, 46 x 1012 km).
- To convert miles to light years, use: 1 light year/(5.88 x 1012 miles).
Step 3. Multiply the initial distance by the conversion factor
Once you've determined the correct conversion factor, multiply the initial distance to get the distance in light years. If the number is large, we recommend using scientific notation.
- For example: If it is known that an object is approximately 14.2 x 1014 miles from Earth, how far is it in light years?
- Use the mile conversion factor: 1/(5.88 x 1012)
- Multiply: (14, 2 x 1014) x (1/(5, 88 x 1012)) = 2, 41 x 102 = 241 light years.
- The object is 241 light years away.
Step 4. Ask for help
You can always ask for help from teachers and fellow students. There are also plenty of resources on the internet and in textbooks to help you convert distances into light years. Don't hesitate to ask for additional help if needed.
