The exact values of a lightyear and the speed of light.

[PTNLemay]

The value of c is pretty well established on account of how often it's quoted, 299 792 458 m/s. But I'm less certain about the length of a light year. Google tells me it's 9.4605284 x10^15 meters.

V = D/T and T = D/V, so that would make the "year" in question 31 556 925.96 seconds. But wikipedia says that the lightyear is based on a Julian year, which is 365.25 x 86400 seconds. That's 31 557 600 seconds. It's not a very big difference, but somewhere someone rounded too much and it resulted in a discrepancy, so which value is correct?

[christok]

The speed of light is not a measured quantity. It is the definition of the metre.

1 second = 9 192 631 770 oscillations of a caesium atom in an atomic clock, by definition.

299 792 458 metres = distance light travels in 1 second, by definition.

1 day = 86400 seconds, by definition (for scientific purposes). It isn't, of course, equal to a solar day (which varies in length) but it is a nearby and historically justified round number which may be used with SI values.

I must be a real nerd. I didn't look any of those up.

According to the Big Orange Book*, one light-year is "the distance travelled by light through a vacuum in one Julian year: 1 ly = 9.460730472 * 10^15 m".

* B.W. Carroll & D.A. Ostlie. An introduction to modern astrophysics. 2nd ed. 2007. Pearson. ISBN 0-8053-0402-9. p. 58. (It's considered by many to be the standard textbook in astrophysics.)

[PakledHostage]

It is an interesting question... One that I'd never really thought about until you mentioned it. I guess I always regarded the "light year" as a somewhat inexact number. But standards are standards and there should be a standard conversion for light years into metres. I pulled out my trusty HP48 to see what unit conversions are stored in it. It gives 1 light year = 9.46052840488x10^15 metres. Comfortingly, the HP48's value for c is 299742458 m/s.

I also had a look at the Wikipedia entry for Light year. It says that the IAU has defined a light year as exactly 9460730472580800 metres. The article says that definition of the light year has been in use since 1984. I wonder, then, why a calculator designed in the early '90s and modern Google still give a value that is different than the IAU definition? Who's definition are they quoting and why is it still in use? Is it maybe a derived SI unit, as well?

[PTNLemay]

@ christok

Thanks. Dividing that value of a LY with SoL does indeed give me the proper length of a Julian year. I'll have to check out that book.

Edit:

Thinking about it though... does anyone have a value of C beyond 9 digits in accuracy? something that goes into decimals of meter per second?

Edited June 30, 2014 by PTNLemay

[Mr Shifty]

It is an interesting question... One that I'd never really thought about until you mentioned it. I guess I always regarded the "light year" as a somewhat inexact number. But standards are standards and there should be a standard conversion for light years into metres. I pulled out my trusty HP48 to see what unit conversions are stored in it. It gives 1 light year = 9.46052840488x10^15 metres. Comfortingly, the HP48's value for c is 299742458 m/s.

I also had a look at the Wikipedia entry for Light year. It says that the IAU has defined a light year as exactly 9460730472580800 metres. The article says that definition of the light year has been in use since 1984. I wonder, then, why a calculator designed in the early '90s and modern Google still give a value that is different than the IAU definition? Who's definition are they quoting and why is it still in use? Is it maybe a derived SI unit, as well?

Wikipedia shows that the Google number has something to do with the "J1900 tropical year" (whatever that is) and a measured (not defined) quantity for the speed of light. It seems to be the pre-1984 IAU definition.

Edited June 30, 2014 by Mr Shifty

[RenevB]

Edit:

Thinking about it though... does anyone have a value of C beyond 9 digits in accuracy? something that goes into decimals of meter per second?

Take a look at this part of christoks post:

299 792 458 metres = distance light travels in 1 second, by definition.

That's the exact and precise definition. Should you want more numbers, any behind the comma (or period, depending on your location) are zeros.

[PTNLemay]

@Renev

I doubt that the universe would be so considerate as to base one of its most important constants around our humble metric. I'm sure the speed of light in a vacuum is something other than the value we've given it here, if only varying by tiny increments beyond the decimal places. If we don't have any more precise measure for it it would have to be because of limitations on our instruments.

edit:

Or... are you saying we defined the meter as being exactly that based on the constant of the speed of light... in which case... yeah it could be followed by infinite zeros.

Edited June 30, 2014 by PTNLemay

[Kryten]

@Renev

I doubt that the universe would be so considerate as to base one of its most important constants around our humble metric. I'm sure the speed of light in a vacuum is something other than the value we've given it here, if only varying by tiny increments beyond the decimal places.

The speed of light isn't that many metres a second because we've measured it to be so; it's that many because that's part of the definition of what a metre actually is. Any error in the measurement results in errors in the length of the metre, not the value in m/s of the spped of light,

[PTNLemay]

@kryten

mmhmm, I realize that now. I should have thought more before posting.

Edited June 30, 2014 by PTNLemay

[WinkAllKerb'']

in, just to say that a human lifespan can't by definition give us the measurement opportunity to appreciate those infinitesimal variation for what they really worth.

larger time scaled measurement process approach and still approximative process required imho, yup yup think out of your own flesh bottle and apply to whatever it might be interesting too.

Edited June 30, 2014 by WinkAllKerb''
oh and regardless of current tools relative accuracy to do so ;) have fun

[Ralathon]

in' date=' just to say that a human lifespan can't by definition give us the measurement opportunity to appreciate those infinitesimal variation for what they really worth.

larger time scaled measurement process approach and still approximative process required imho, yup yup think out of your own flesh bottle and apply to whatever it might be interesting too.[/quote']

How do you know that as one of those 'flesh bottles'?

The human brain hasn't evolved to deal with timescales and distances that are commonplace in the universe. But that same human brain was used to travel to the moon, crack the atom and drastically alter the planet to make us the dominant species.

Just because we aren't made to deal with these things doesn't mean we can't appreciate them.

[WinkAllKerb'']

That's the point evolutions use many branchs, paths and nodals.

Regarding a single flesh bottle lifespan, even if a brain may have the ability to attract all thoose knowledges with it's links like a black hole, main matter after extracting this knowledge back will remain to revive the links scheme and get enough time to explore it.

problematic around "exact values of a lightyear and the speed of light" illustrate this approximative limitation pretty well.

Simple version: if you missed/occulted some links with other related things evolutions, for example due to an egotic dominative perceptive approach of a supposed already solved problem at a certain scale, you'll never get the exact value you seek.

that's one thing i know if it was unclear.

Edited July 1, 2014 by WinkAllKerb''