Number of miles in a light year is prime!
 

Did you know that the number of miles in a light-year, rounded to the nearest integer, is prime? Here's the number:

5874601673407

The real value is 5874601673407+2/(11*127) miles. Google doesn't show any results for "5874601673407 prime number", so I guess no one knew.

[QUOTE=Stargate38;285424]Did you know that the number of miles in a light-year, rounded to the nearest integer, is prime? Here's the number:

5874601673407

The real value is 5874601673407+2/(11*127) miles. Google doesn't show any results for "5874601673407 prime number", so I guess no one knew.[/QUOTE]

Is it this year light year? Because this year we have a leap second on June 30th.

It's the definition for a non-leap-year. In other words, it worked for 2009, 2010, and 2011, and it will also work for 2013, 2014, 2015, and every year that isn't of the form 4*x

According to Wikipedia, a [URL="http://en.wikipedia.org/wiki/Light-year"]light year[/URL] is actually defined as the distance light travels in one Julian year, i.e. 365.25 days precisely, (regardless of leap years and leap seconds) which is about 5,878,625,373,183.608 miles. [URL="http://factordb.com/index.php?id=5878625373183"]5878625373184[/URL] = 2[SUP]10[/SUP] * 5107 * 1124113. You've given the distance for [URL="http://www.wolframalpha.com/input/?i=365.0000000000000+light+days+in+miles"]365 light days[/URL]. While still an interesting bit of trivia, that likely explains the lack of others noting it previously (at least, as far as you could find).

[QUOTE=Mini-Geek;285431] [URL="http://factordb.com/index.php?id=5878625373184"]5878625373184[/URL][/QUOTE]

fixd

This thread could be why we don't attract women.

I'm not sure what is the official definition of a lightyear, there are many different values:

Wikipedia: 5,878,625,373,183.608 miles (9,460,730,472,580.8 km)
Online Conversion: [URL="http://www.onlineconversion.com/length_all.htm"]http://www.onlineconversion.com/length_all.htm[/URL]
Light year (Julian): 5,878,625,373,200 miles (9,460,730,472,600 km)
Light year (Tropical): 5,878,499,814,100 miles (9,460,528,404,900 km)
Light year (traditional): 5,874,601,673,400 miles (9,454,254,955,500 km)

My old Texas TI-85 calculator conversion: 5,878,499,814,135.1 miles (9,460,528,404,879.4 km)

[QUOTE=ATH;285452]I'm not sure what is the official definition of a lightyear, there are many different values:

Wikipedia: 5,878,625,373,183.608 miles (9,460,730,472,580.8 km)
Online Conversion: [URL="http://www.onlineconversion.com/length_all.htm"]http://www.onlineconversion.com/length_all.htm[/URL]
Light year (Julian): 5,878,625,373,200 miles (9,460,730,472,600 km)
Light year (Tropical): 5,878,499,814,100 miles (9,460,528,404,900 km)
Light year (traditional): 5,874,601,673,400 miles (9,454,254,955,500 km)

My old Texas TI-85 calculator conversion: 5,878,499,814,135.1 miles (9,460,528,404,879.4 km)[/QUOTE]

[url]http://www.google.ca/search?sourceid=chrome&ie=UTF-8&q=define%3Alight+year#hl=en&q=light+year&tbs=dfn:1&tbo=u&sa=X&ei=MkYKT6HhD8f-ggeSsayhAg&ved=0CDQQkQ4&bav=on.2,or.r_gc.r_pw.,cf.osb&fp=e2d3beeb13884780&biw=1600&bih=775[/url]

[QUOTE=Flatlander;285443]This thread could be why we don't attract women.[/QUOTE]
:ick: 13 points for the joke! (could not give 10, is not prime, and 11 is not an exponent of a mersenne prime...). Nice one! But next time, talk in your name only :yucky::redface:

[QUOTE=ATH;285452]I'm not sure what is the official definition of a lightyear, there are many different values:

Wikipedia: 5,878,625,373,183.608 miles (9,460,730,472,580.8 km)
Online Conversion: [URL="http://www.onlineconversion.com/length_all.htm"]http://www.onlineconversion.com/length_all.htm[/URL]
Light year (Julian): 5,878,625,373,200 miles (9,460,730,472,600 km)
Light year (Tropical): 5,878,499,814,100 miles (9,460,528,404,900 km)
Light year (traditional): 5,874,601,673,400 miles (9,454,254,955,500 km)

My old Texas TI-85 calculator conversion: 5,878,499,814,135.1 miles (9,460,528,404,879.4 km)[/QUOTE]
[url]http://www.iau.org/public/measuring/[/url]
[quote]For studies of the structure of the Milky Way, our local galaxy, the parsec (pc) is the usual choice. This is equivalent to about 30.857×1012 km, or about 206,000 AUs, and is itself defined in terms of the AU – as the distance at which one Astronomical Unit subtends an angle of one arcsecond. Alternatively the light-year (ly) is sometimes used in scientific papers as a distance unit, although its use is mostly confined to popular publications and similar media. The light-year is roughly equivalent to 0.3 parsecs, and [b]is equal to the distance traveled by light in one Julian year in a vacuum, according to the IAU. To think of it in easily accessible terms, the light-year is 9,460,730,472,580.8 km or 63,241 AU.[/b][/quote]

[QUOTE=ATH;285452]I'm not sure what is the official definition of a lightyear...[/QUOTE]

Wikipedia's source is [url]http://www.iau.org/public/measuring/[/url], which looks official enough to me! Besides defining the "year" as 365.25 days, it gives the distance in KM, which converts to the number I gave.
Of course, non-standard usages can be used anyway (and are, given your links; which also show a level of precision too low to give the precise integer), but regardless, an official standard definition exists.

[QUOTE]Besides defining the "year" as 365.25 days…[/QUOTE]
Don't forget the Leap Year every century year that is divisible by 400.

365.2425

[QUOTE=Xyzzy;285460]Don't forget the Leap Year every century year that is divisible by 400.

365.2425[/QUOTE]But the IAU clings to the auld ways.

From [URL]http://www.iau.org/public/measuring/[/URL]
[quote]... the IAU regards [I]a year[/I] as a Julian year of 365.25 days (31.5576 million seconds) unless otherwise specified. The IAU also recognises a Julian century of 36,525 days in the fundamental formulas for precession ...[/quote]

[QUOTE=Xyzzy;285460]Don't forget the Leap Year every century year that is divisible by 400.[/QUOTE]

The honest truth: my wedding to my (ex-)wife was held on 2000.02.29.

The advantage of getting married on a leap day is you only have to remember your anniversary every four years.

In my case, only every 400....

(Maybe that's why she's my ex-wife?)

[QUOTE=chalsall;285504]The honest truth: my wedding to my (ex-)wife was held on 2000.02.29.[/QUOTE]Same as a relative of mine.
[QUOTE=chalsall;285504](Maybe that's why my ex-?)[/QUOTE]Same as a relative of mine.

[QUOTE=chalsall;285504]The advantage of getting married on a leap day is you only have to remember your anniversary every four years.

In my case, only every 400....

(Maybe that's why she's my ex-wife?)[/QUOTE]

No, because anniversaries are typically celebrated every year, not every 100 years. If they were celebrated every 100 years, [I]then [/I]you could wait 400 years on yours. In your case, even though the wedding day was Feb. 29th 2000, you'd still have to celebrate them every 4 years since there is a Feb. 29th every 4 years except the 1 time per centery (actually 3 times per 400 years) that you could wait 8 years between celebrating them. :smile:

[QUOTE=Xyzzy;285460]Don't forget the Leap Year every century year that is divisible by 400.

365.2425[/QUOTE]

[QUOTE=cheesehead;285502]But the IAU clings to the auld ways.

From [URL]http://www.iau.org/public/measuring/[/URL][/QUOTE]

It seems very odd that the IAU doesn't take into account the 3 times every 400 years where years divisible by 4 are not leap years. Since there are 146,097 days in 400 years, as Mike stated a year should be considered 365.2425 days and a century 36524.25 days when calculating precise measurements of the speed of light.

[QUOTE=gd_barnes;285511]It seems very odd that the IAU doesn't take into account the 3 times every 400 years where years divisible by 4 are not leap years. Since there are 146,097 days in 400 years, as Mike stated a year should be considered 365.2425 days and a century 36524.25 days when calculating precise measurements of the speed of light.[/QUOTE]It's not in the least bit odd. Astrometry began long before the invention of the Gregorian calendar and astronomers are still interested in events which occurred millennia ago and which will occur millennia hence, each of which lie outside the period when the Gregorian algorithm gives adequate precision. Sticking to the Julian calendar has the advantage of simplicity and of requiring no adjustments to the timings of two thousand years of observations.

[QUOTE=xilman;285513]It's not in the least bit odd. Astrometry began long before the invention of the Gregorian calendar and astronomers are still interested in events which occurred millennia ago and which will occur millennia hence, each of which lie outside the period when the Gregorian algorithm gives adequate precision. Sticking to the Julian calendar has the advantage of simplicity and of requiring no adjustments to the timings of two thousand years of observations.[/QUOTE]
Yes, clearly there needs to be a pressing need to alter the definition of a standard measurement with all the inconvience and confusion which that would entail, and there is no such necessity regarding the light year. It is a unit of distance and there is no need to tie that to the exact time taken for the earth to orbit the sun.

The Gregorian calendar itself is hardly optimal in terms of being a natural way of recording dates. The lengths of the months are certainly not the most natural way of dividing up the year (why should February be particularly short?). But there's no need to go through all the hassle of changing the calendar: it serves its purpose perfectly adequately.

However: perhaps this inherent inaccuracy of the light year compared with the distance travelled by light in a sidereal year in a vacuum might be an important reason why astronomers in modern times decided to use the parsec instead? Just my guess.

Using a year of 365.2425 days, I got this factorization:

Rounding up: 5878504662190319=179*256499*128034839
Rounding down: 5878504662190318=2*23*2670653*47851061

[QUOTE=Brian-E;285518]
However: perhaps this inherent inaccuracy of the light year compared with the distance travelled by light in a sidereal year in a vacuum might be an important reason why astronomers in modern times decided to use the parsec instead? Just my guess.[/QUOTE]

Is the value of 1 parsec known to this accuracy? It is the distance
subtended by 1 second of arc at opposite points in the Earth's orbit,
but the Earth's orbit is not a perfect circle. And (although the effect is
very small) it precesses in its orbit (like Mercury). So if one says
"one second of arc as measured on the following two dates of the year:...."
its value would change from year to year. Indeed, even though (again)
the effect is small, the Earth's orbit changes slightly from year to year
owing to the (small) influence of other planets.

[QUOTE=R.D. Silverman;285536]Is the value of 1 parsec known to this accuracy? It is the distance
subtended by 1 second of arc at opposite points in the Earth's orbit,
but the Earth's orbit is not a perfect circle. And (although the effect is
very small) it precesses in its orbit (like Mercury). So if one says
"one second of arc as measured on the following two dates of the year:...."
its value would change from year to year. Indeed, even though (again)
the effect is small, the Earth's orbit changes slightly from year to year
owing to the (small) influence of other planets.[/QUOTE]Bob: time for some Socratic questions.

Do you think that astronomers are unaware of the ellipticity of the Earth's orbit? If not, how might they frame the definition of the parsec in order to take ellipticity into account?

If you wish, I could recommend some good books on the subject of astronomical measurement.


Paul

[QUOTE=xilman;285546]Bob: time for some Socratic questions.

Do you think that astronomers are unaware of the ellipticity of the Earth's orbit? If not, how might they frame the definition of the parsec in order to take ellipticity into account?
[/QUOTE]

Of [i]course[/i] they are aware! My questions were intended as rhetorical.
I studied orbital mechanics as part of freshman physics. (A long time ago....)

One would frame the definition in terms of measurement from either the
minor or major axis. But even these change slightly over time. Jupiter
tugs on us and adds/subtracts a miniscule amount of angular momentum....
Venus, although much smaller, tugs from another direction......

The N-body problem is well known to be chaotic.

[QUOTE]
If you wish, I could recommend some good books on the subject of astronomical measurement.
Paul[/QUOTE]

I would ask, but I do not have the time to read them. So much to learn.
So little time.

[QUOTE=R.D. Silverman;285561]One would frame the definition in terms of measurement from either the minor or major axis. But even these change slightly over time. Jupiter tugs on us and adds/subtracts a miniscule amount of angular momentum.... Venus, although much smaller, tugs from another direction...... [/QUOTE]
You might define it in such a way, but the astronomers wouldn't because of the variation in those quantities, some of which you have identified.

AFAIK (meaning it may have changed recently without my becoming aware of it), one first defines a year. The standard year is the time taken for the earth to orbit the sun once with respect to the "fixed" stars. That avoids problems with the proper motions of any particular star. Then you have to specify the epoch when the year is measured, to avoid problems with secular changes of the earth's orbital period due, in part, to planetary perturbations. By convention, this year is that measured in 1900.

Once you have a year defined, you can find out the radius of a circular orbit around a body of one solar mass assuming Newtonian gravity and no perturbations from other material in the solar system. That defines the AU and consequently the parsec.

Paul

From the same page as has been linked by three different people, the parsec is based on the AU, which is (sort of) derived from the Earth's orbit. It is independent of whatever your definition of a year is. The AU is defined as the distance that a point particle of Earth's mass would orbit at, if it's orbit was exactly 365.2568983 days long. Thus the AU is actually slightly shorter than the mean Earth-Sun distance (and the parsec is well defined, independent of the Earth's orbit). Also note that the parsec is generally used in favor of the light year by astronomers.

I suggest everyone actually go read that aforementioned link (reproduced [url=http://www.iau.org/public/measuring/]here[/url]) before more discussion takes place.

[QUOTE=Dubslow;285591]The AU is defined as the distance that a point particle of Earth's mass would orbit at, if it's orbit was exactly 365.2568983 days long. Thus the AU is actually slightly shorter than the mean Earth-Sun distance (and the parsec is well defined, independent of the Earth's orbit[/QUOTE]Ok, one Gaussian year. Thanks for the clarification. Only goes to show how complex this situation has become over the centuries. I was clearly thinking of some other quantity which is/was measured on the basis of the J1900.0 siderial year.

Regardless of this, the definition of the AU is given in terms of the orbital period of a point mass in an unperturbed circular orbit about one solar mass under Newtonian gravity. The latter qualification is important, in principle, because under GR such a system radiates gravitational energy leading to a secular change in the orbit irrespective of other influences.

Paul

[QUOTE=Dubslow;285591]From the same page as has been linked by three different people, the parsec is based on the AU, which is (sort of) derived from the Earth's orbit. It is independent of whatever your definition of a year is. The AU is defined as the distance that a point particle of Earth's mass would orbit at, if it's orbit was exactly 365.2568983 days long. Thus the AU is actually slightly shorter than the mean Earth-Sun distance (and the parsec is well defined, independent of the Earth's orbit). Also note that the parsec is generally used in favor of the light year by astronomers.

I suggest everyone actually go read that aforementioned link (reproduced [url=http://www.iau.org/public/measuring/]here[/url]) before more discussion takes place.[/QUOTE]

Urm, no. One AU is the heliocentric distance at which a massless particle in a circular, unperturbed orbit would have a mean motion of k ( = 0.01720209895) radians/day.

The value of k is that adopted by Gauss, who derived a number of tables needed for orbit computations that depended on k. Rather than having to recompute
these tables each time the value of k was updated (due to better determination of the values involved in its computation), it was decided to keep k fixed
(the so-called Gaussian constant) and dispense with the notion that one AU is exactly the semimajor axis of the earth's orbit.

Gareth

[QUOTE=Graff;285632]Urm, no. One AU is the heliocentric distance at which a massless particle in a circular, unperturbed orbit would have a mean motion of k ( = 0.01720209895) radians/day.

Gareth[/QUOTE]

The IAU either disagrees, or has the same result with a different definition:
[quote]One of the most important of these is the Astronomical Unit, abbreviated AU, which is defined by the IAU as equal to the distance from the centre of the Sun at which a particle of negligible mass, in an unperturbed circular orbit, would have an orbital period of 365.2568983 days.[/quote]Again, the link in that post is suggested reading, and the source for this.

[QUOTE=Dubslow;285636]The IAU either disagrees, or has the same result with a different definition:
Again, the link in that post is suggested reading, and the source for this.[/QUOTE]

if I've got it right from reading the content of the link:

circumference = (3600*360)AU =1296000AU=(2*Pi)Parsec so each parsec is 129600/(2*Pi)AU to be exact. though admittedly I did a Google search for factors of the number claimed by stargate38 that may be a way to come across the statement in the first post of the thread.

[QUOTE=xilman;285618]... under Newtonian gravity. The latter qualification is important, in principle, because under GR such a system radiates gravitational energy leading to a secular change in the orbit irrespective of other influences.

Paul[/QUOTE]Like I said, the IAU clings to the auld ways.

I find it interesting that so many have posted an incorrect value for the length of a year. Even more interesting is that our current calendar is inaccurate by about 26 seconds per year. The Mayan calendar was inaccurate by 10 seconds per year. The difference between us and them is that we know ours is off by 26 seconds/year, they didn't know about theirs. If we wanted to, we could add another leap day about every 3323 years which would correct for the 26 second discrepancy.

Sidereal year = 365.256363004 days
Tropical year = 365.242197 days
Anomalistic year = 365.259636 days

The conventional Julian year is 365.25 days.
With the accuracy of measurement available today, we can measure changes in length of an earth day because the earth is slowing down by about 1 second in 10 years. This causes major headaches for astronomers. It is also a problem with some high tech communications systems that are very time sensitive. I suspect Paul could contribute re some of the effects for astronomy.

DarJones

[QUOTE=Fusion_power;285681]I find it interesting that so many have posted an incorrect value for the length of a year.[/QUOTE]It's so much not that they are incorrect, more that they refer to different things. There are several sensible ways to define a day and a year from astronomical measurements and several other ways from other physical measurements. For the time being, the official definition of a day is 24 * 60 * 60 seconds, the second being defined in terms of the frequency a particular radiation. Under this definition, the astronomical days vary in length over quite short periods.

As for the year, what do you measure? The time between successive perihelia? Between successive northwards passages through the plane of the equator? Between successive passages through the invariant plane of the solar system (roughly speaking, the mass-weighted average plane of the orbits of the planets)? Between the times when the sun appears as close as possible to the same position on the sky? Or do you define the year as a specific number of seconds (as in the Julian and Gregorian calendars)? There are other options, including the Gaussian year which, I've now learned or re-learned, is the basis for the A.U.

Paul

[QUOTE=Dubslow;285636]The IAU either disagrees, or has the same result with a different definition:
Again, the link in that post is suggested reading, and the source for this.[/QUOTE]

It doesn't disagree substantially. The definition on the IAU page is
almost correct. My definition using k is exact. 2 * [TEX]\pi[/TEX] / k = 365.2568983... days.
I'm an IAU member and my primary work is orbits. I will alert the
maintainers of that page to their imprecise definition.

Gareth

[QUOTE=Graff;285819]It doesn't disagree substantially. The definition on the IAU page is
almost correct. My definition using k is exact. 2 * [TEX]\pi[/TEX] / k = 365.2568983... days.
I'm an IAU member and my primary work is orbits. I will alert the
maintainers of that page to their imprecise definition.

Gareth[/QUOTE]
Ooooohhhh, cool. Sorry about that. Any chance they could put the right definition on there, instead of the [strike]less-useful[/strike]... wrong definition? If the page says "define", I'd like it to actually be right.

:P

[URL="http://en.wikipedia.org/wiki/Light_year"]http://en.wikipedia.org/wiki/Light_year[/URL]

[QUOTE]Before 1984, the tropical year (not the Julian year) and a measured (not defined) speed of light were included in the IAU (1964) System of Astronomical Constants, used from 1968 to 1983.[4][/QUOTE]

So my old Texas TI-85 calculator has the exact value for the old tropical light year (although the calculator is newer than 1984) while online conversion rounds it up to the nearest 100 miles/km.

Wikipedia has the exact current Julian lightyear while online conversion again rounds it.

[QUOTE=Dubslow;285822]Ooooohhhh, cool. Sorry about that. Any chance they could put the right definition on there, instead of the [strike]less-useful[/strike]... wrong definition? If the page says "define", I'd like it to actually be right.

:P[/QUOTE]

I contacted the maintainer of that page and the imprecise statement has been replaced.

Gareth

[QUOTE=xilman;285618]Ok, one Gaussian year. Thanks for the clarification. Only goes to show how complex this situation has become over the centuries. I was clearly thinking of some other quantity which is/was measured on the basis of the J1900.0 siderial year.[/QUOTE]And I've now discovered why I though it was the J1900.0 year (though it's the tropical year).

[QUOTE=http://en.wikipedia.org/wiki/Light_year#Other_values]Before 1984, the tropical year (not the Julian year) and a measured (not defined) speed of light were included in the IAU (1964) System of Astronomical Constants, used from 1968 to 1983.[4] The product of Simon Newcomb's J1900.0 mean tropical year of 31,556,925.9747 ephemeris seconds and a speed of light of 299,792.5 km/s produced a light-year of 9.460530×1015 m (rounded to the seven significant digits in the speed of light) found in several modern sources[5][6][7] was probably derived from an old source such as a reputable 1973 reference[8] which was not updated until 2000.[9][/QUOTE]

Ok, so I'm seriously out of date. That's what comes of relying on old memories instead of checking with the definition [i]du jour[/i].

Paul

[QUOTE=Graff;285632]One AU is the heliocentric distance at which a massless particle in a circular, unperturbed orbit would have a mean motion of k ( = 0.01720209895) radians/day.[/QUOTE]Which would imply that the solar mass is constant.

As the mass isn't constant, at which date was the mass measured, or does it have another arbitrary value which may or may not match the true solar mass at least once?

I'm nit-picking, of course, as the mass loss from EM and neutrino radiation and solar wind, offset by the mass gain from infalling matter such as comets is an exceedingly tiny fraction of a solar mass over reasonably short time scales.


Much easier, IMO, would be to define the AU as a particular number of metres.


Paul

[QUOTE=xilman;285919]Which would imply that the solar mass is constant.

As the mass isn't constant, at which date was the mass measured, or does it have another arbitrary value which may or may not match the true solar mass at least once?

I'm nit-picking, of course, as the mass loss from EM and neutrino radiation and solar wind, offset by the mass gain from infalling matter such as comets is an exceedingly tiny fraction of a solar mass over reasonably short time scales.


Much easier, IMO, would be to define the AU as a particular number of metres.


Paul[/QUOTE]

In the 1976 IAU System of Astronomical Constants, the length of the AU
is a derived constant, derived by multiplying one defining constant
(c, the speed of light in a vacuum) by one primary constant ([TEX]$\tau_{A}$[/TEX], the light-time for unit distance).

Gareth

[QUOTE=Graff;285914]I contacted the maintainer of that page and the imprecise statement has been replaced.

Gareth[/QUOTE]

oooooooooooohhh thank you thank you this is so cool :big grin:

[QUOTE=xilman;285919][QUOTE=Graff;285632]Urm, no. One AU is the heliocentric distance at which a massless particle in a circular, unperturbed orbit would have a mean motion of k ( = 0.01720209895) radians/day.
[/QUOTE]Which would imply that the solar mass is constant.[/QUOTE]Since the orbiting particle is massless, wouldn't the solar mass be irrelevant?

The massless particle is not being held in circular orbit by gravity, so we're using a bit of magic rather than Gm[sub]1[/sub]m[sub]2[/sub] here. There may have been a moment when k = 0.01720209895 had a physical meaning, but it's just a defined constant now.

[QUOTE=cheesehead;286127]Since the orbiting particle is massless, wouldn't the solar mass be irrelevant?[/QUOTE]
By "massless" the definition presumably means that the mass of the orbiting body "tends to zero" so that only the sun's gravitational field should be considered. I guess there must be some complicating factor which would affect the orbital speed of a body of significant mass but I am unsure what this factor might be. Perhaps the definition is simply seeking to avoid the hypothetical situation where the body has comparable mass to the sun and then the two bodies are orbiting each other, complicating the measurements of radial speed? Or is there some other more subtle complicating effect if the orbiting body has significant mass?

[QUOTE]There are other options, including the Gaussian year which, I've now learned or re-learned, is the basis for the A.U. - Xilman[/QUOTE]

This was an informative thread. I think we all learned quite a bit from it.

DarJones