How big is a lightyear exactly?

Odd questions occur to me once in a while. For example, I recently started wondering how big a lightyear actually is. It's of course the distance light travels in a year, but exactly how long is a year? The word is ambiguous.

You might have learned in school that a year is the time it takes for the Earth to orbit the Sun. That's more precisely a "sidereal" year (from a Latin word for "star"), which lasts 365.25636 days. But for many purposes we're more interested in the "tropical" year, the time period from one March equinox to the next, because that determines the cycle of the seasons. It's not the same as the sidereal year because it's affected by wobbling of the Earth's rotational axis. It currently runs about 365.242189 days but the length isn't perfectly constant.

Ideally, we'd like our calendar to be in sync with the seasons. For many centuries the standard European calendar was the Julian calendar, introduced by Julius Caesar in 45 BCE. That calendar gives most years 365 days with an extra day every fourth year. (Actually, the Romans managed to misunderstand the rule for a while, making every third day a leap year, until August Caesar straightened them out.) The average Julian calendar year is 365.25 days long, pretty close to a tropical year, but slightly too long, enough to build up three days of error every four centuries, which eventually led Pope Gregory XIII to introduce the slightly different Gregorian calendar in 1582. It skips three leap years in every four centuries, giving it an average length of 365.2425 days, still a little too long, but only by a day in several thousand years.

(A lot of non-Catholic countries using the Julian calendar continued to do so for a while. Britain and its empire stayed on the Julian one into the 1700s, Russia didn't switch over until after the Tsar was overthrown, and Greece didn't adopt the Gregorian calendar until 1923. Incidentally, Caesar had the authority to decree a new calendar because managing it was part of his job as the head priest of the official Roman religion. His title was "pontifex maximus," literally, the greatest "bridge-builder." Pope Gregory was likewise a Roman pontiff, though obviously not of the same religion.)

But I digress. To answer the original question, it turns out that the International Astronomical Union defines a lightyear as the distance light travels in an average Julian year, that is, 365.25 days. A day has 24 hours, each with 60 minutes of 60 seconds, so if you know how fast light travels in a second, you can work out the length of a year in seconds by multiplying it all out. (If I did it right, there are 31,557,600 seconds in 365.25 days.)

You may remember the speed of light as 186,000 miles per second, but that's not exact. Because the length of a meter is now defined in terms of the speed of light, light travels exactly 299,792,458 meters per second, exactly. (If you don't want to memorize that, 300 million meters per second is really, really close.)

Multiply the speed of light in meters per second by the number of seconds in a Julian year and you'll get the length of a lightyear in meters: 9,460,730,472,580,800.

You can even work it out in inches if you want. The U.S., Britain, and other countries had slightly different standards for yards, feet, and inches prior to 1959, but that year compromised on Canada's definition, which made the inch exactly 2.54 centimeters. A meter is 39.3701 inches, so multiply that by 9,460,730,472,580,800 and you'll get the number of inches in a lightyear. I'll let you work that out.

Incidentally, if you type a phrase like "1 lightyear in inches" into a Google search, Google will return the answer (at least to a few significant figures) and an on-screen calculator. Google does a lot of calculations and conversions for you this way (type "1 million dollars in euros" for example). This is a pretty useful trick to know, and probably the only practical piece of information in this entire post.

In verifying all this I came across a bit of trivia I recall reading somewhere before but had managed to forget: As you may recall an "astronomical unit" (AU) is the average distance of the Earth from the Sun, which makes it convenient for describing distances between bodies inside the solar system. The EarthSky website points out (here) that the number of astronomical units in a lightyear (about 63241.1) is by coincidence very similar to the number of inches in a statute mile (63360). Hence if you were to make a map with the Earth one inch from the Sun, a lightyear would be about a mile, and on the same map the closest star other than the Sun would be about 4 1/4 miles away.

That would be a big map. Reminds me of the person who asked a reference librarian if the library had a globe, and when the librarian pointed one out complained that it was too small. "Do you have one that's life-size?" The librarian replied, "Yes, but it's in use."

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