Exact measurement of a light year

  • 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?

    9,460,514,622,032,012 meters is not quite correct; it assumes a year of about 365.2417 days.

  • 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.

    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.

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Content dated before 7/24/2021 11:53 AM