What is the precise distance in miles of a light year?

Question

I saw a figure given in a magazine recently, but it looked a bit off and was only to the first 5 figures. I calculated it more precisely by hand, since my calculators won't deal with so many digits. I just wanted to check my calculations with anyone else who has done it. To get a precise answer, one must know the precise speed of light in miles per second and the precise number of seconds in a year. The figure in the magazine is a bit high because it evidently used 365.25 days for a solar year. That is only an approximation, as a bit of research on century adjusments of the Gregorian calendar will show.

I said miles, not meters or kilometers. I have enough work without doing that conversion. I thought one could understand the basics. Where does one think we usually use the speed of light? I was checking exact distances to certain stars. I am not illiterate, people, so give me credit for knowing something, and don't be smart alecs, please. Someone is on the right track with the right speed in miles per second, but he uses 365.25 days per year, that is too much. I think he can figure it out.

Answer 1

A "light-year" is a standard defined distance. It does not depend on the length of a year, any more than a "foot" of measurement depends on any one actual human foot.

A "light-year", by definition (or at least by IAU recommendation), is the distance traveled by light in a vacuum in 365.25 days. In SI units, it is exactly

299792458 x 365.25 x 24 x 60 x 60 meters.
= 9,460,730,472,580,800 meters (exactly).

For "miles", we need to use the U.S. survey mile, which is 5280 survey feet, each of 1200 / 3937 meters. Note that this is not the customary foot, which is 0.3048 meters. Survey miles are used for measuring road miles and land acreage in the US.

1 light-year = 5,878,613,615,932.848484... survey miles.

Or you could use the international mile, with 1 foot = 0.3049 meters. Then we get:
1 light-year = 5,878,625,373,183.607730851825... international miles. The fractional part is 849 / 1397 (exactly).

If you really care about the length of a light-year to an accuracy of better than 5 digits, then you need to study up on units of measurement in the context of general relativity, and such things as "TDB", "TT", and "TCB" units. Also study "comoving", "proper" and "coordinate" distances. It took me over a year to get a basic understanding.

Distances to stars are not known to any better than 4 or 5 significant digits, no matter what units you are using.

Answer 2

Hi. Start in metric.The speed of light = 299 792 458 m / s. We know what a meter is but how many seconds? Depends on how you measure a second and in what frame of reference. I find 31,556,925.9747 as an agreed standard on the number on seconds in a year. I'll let you do the arithmetic.
Oh heck, 9 458 540 318 542 952.7126 meters = 5.87726447 × 10^12 miles. Roughly.

Answer 3

The IAU recommends the Julian year be the "year" used for this definition, and that year is 365.25 days long.

The official length of a light year is 5,878,625,373,183.61 statute miles.

The speed of light is defined very exactly as 299,792,458 metres per second. Since scientists (regardless of country) use the metric/SI system, its natural that a scientific value is in meters.
In imperial units, the speed of light is 670,616,629.2 miles per hour or about 186,282.397 miles per second.

And perhaps you're a little miffed at the answers you have received, but there is no need to be rude.

Answer 4

1 light year = 5 898 499 814 135 . 0 miles
That conversion factor is accurate to the nearest tenth of a mile, assuming a standard tropical year and the recommended value for the speed of light in vacuum.

Answer 5

If you want to be that precise then you will need to tell us in which year the light will be travelling and through what medium!

Speed of light in a vacuum is 299 792 458 m / s

Answer 6

Figure: Speed of light is 186,282.3960 miles per second.

So, multiply by 60 seconds, by 60 minutes, by 24 hours by 365.25 days:

186,282.3960 miles per second X 31557600 =
5,878,625,340,009.6 Miles per year.

Answer 7

5,878,625,373,183.61 statute miles

See http://en.wikipedia.org/wiki/Light_year

Answer 8

what they said i don't have my calculator next to me.