What is the exact measurement of a light year? I searched google for the answer in meters and came up with $9.461\cdot 10^{15}$ meters. When I calculated the answer considering $299\,792\,458 \;\text{m/s}$ as the speed of light, I came up with:

$$ 299\,792\,458 \times 365 \times 24 \times 3\,600 = 9\,454\,254\,955\,508\,926 \;\text{m} $$ Why is there such a gap? Did I miss something to add in the equation or is it just wrong?

  • $\begingroup$ 9,460,514,622,032,012 meters is not quite correct; it assumes a year of about 365.2417 days. $\endgroup$ Aug 29 '16 at 21:44

By convention, astronomy uses the Julian Year for the computation of a light year:

Although there are several different kinds of year, the IAU regards a year as a Julian year of 365.25 days (31.5576 million seconds) unless otherwise specified.

Wikipedia gives the length as

$31 557 600 s \times 299 792 458 m/s = 9 460 730 472 580 800 m$ (exactly)

The reason that it's exact (and not subject to experimental error) is that the metre itself is defined in terms of the speed of light, so the quantities are fixed by definition.

  • 2
    $\begingroup$ One way to avoid this ambiguity would be to lookup the length of a lightsecond (where second is a well-defined SI unit) and then convert that into whatever notion of years you care about. But for astronomy purposes you probably just want to use the usual convention. $\endgroup$ Aug 29 '16 at 13:39

You're forgetting that one year is not 365 days, but 365.2422 or something close to that.

That change will give you a number much much closer to the google provided number.

  • $\begingroup$ Ah got it now.. the calculator rounded the darn answer for some reason. $\endgroup$
    – CipherBot
    Aug 29 '16 at 6:12
  • $\begingroup$ There's always websites on the internet who simplifies a lot of things, this is one such example. Not surprised actually. $\endgroup$
    – CipherBot
    Aug 29 '16 at 6:22
  • 2
    $\begingroup$ See Toby's answer. $\endgroup$ Aug 29 '16 at 21:42
  • $\begingroup$ His days per year is wrong, and his answer didn't answer the op either. However it is a nice explanation/calculation of a light year. $\endgroup$
    – LaserYeti
    Aug 30 '16 at 3:11
  • $\begingroup$ The average length of a year on the Gregorian calendar (over a 400-year leap-year cycle) is exactly 365.2425 days. Astronomically, it's between 365.2416 and 365.2428 days depending on which moment of Earth's orbit you're measuring it from. $\endgroup$
    – dan04
    Sep 1 at 22:32

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