Originally Posted by
analog man
The answer you've been looking for can be found here:
Light Years and Julian Years
in particular, this part...
On Rick’s other point about the length of the ‘year’ used in calculating a light year, again as an astronomer perhaps I might make a few comments. I’ll break these up for ease, although there is no great significance or ordering to the points, and this is not meant to be a complete list:
* As Rick notes, the accuracy of determinations of the sorts of distances involved are such that the difference between 365.25 days and the length of a tropical year is inconsequential...
* Let’s say that instead of thinking about relatively nearby stars (like within a few hundred ly), instead you are looking at the far edge of the galaxy, or towards some distant galaxy. Now the relative speeds are high enough such that time dilation is substantial... So which ‘year’ do you use?
* What about the speed of the Earth? At about 30 km/sec there is a significant effect due to that being about 1/10,000 of the speed of light...
* And the Earth changes speed during the year, between about 29.3 & 30.3 km/sec, due to the finite orbital eccentricity, so that time proceeds at different speeds during the year...
* Ah, but also one needs to consider the orbit of the Earth compared to the solar system barycentre, rather than the centre of the Sun...
* In any case there is also a time dilation affect due to the mass of the Sun...
* Come to that, what about the masses of the objects which one is measuring the distances to, in units of ‘light years’? Proximity to those affect the ‘rate of time flow’, but not the speed of light of course...
* Don’t forget that the Sun is also galloping along relative to the centre of our galaxy, a carousel-like ride in which it takes about 250 million years to circuit the centre (with a galactocentric orbital eccentricity of about 0.07) whilst we oscillate up & down through the galactic plane about every 30 million years, our galactocentric speed being variable but of order a couple of hundred km/sec... So our speeds change, and our distances to whatever extra-solar system celestial object you might have in mind - and they’re moving too!
I am just really listing off things which one might need to think about, without any great seriousness. It’s just that in any situation one has to consider what is significant, and what not.
In fact I work on solar system objects, as opposed to more distant things. So let’s leave light years alone and think instead of where one might use the length of a ‘year’ in some solar system dynamics. The speed of an object in heliocentric orbit (like that of the Earth, as I gave above) is given by:
V2 = G Msun [(2/a) - (1/r)]
where:
* G = universal constant of gravitation
* Msun = mass of the Sun
* a = semi-major axis of the orbit (which is NOT the ‘mean distance’ from the Sun, as many books mis-state, at least if by ‘mean’ you imply ‘time-average’);
* r = heliocentric distance of the object for which the speed V is wanted.
Now in evaluating that one could plug in various constants (like the astronomical unit, AU), but generally it’s easiest to use good old Kepler and recall that he told us that the cube of the period in years divided by the square of the semi-major axis in AU is a constant. My point is that when I do that I habitually use ‘1 year = 365.25 days.’ Any ‘better’ value does NOT lead to an improvement, as such, for the sort of simple sums that I’m doing. Of course, if I were doing a proper numerical integration of the solar system then things would be different (all double-precision numbers etc.), but not for a few sums on a pocket calculator. Even if I did diligently type in values of G, Msun, and the AU, still I know that the first two at least are not known to better than about six figures, so what the hell. On the other hand, when I calculate an ephemeris for an asteroid, all these things are significant, else I could miss it. It all depends, doesn’t it? For a ‘light-year’, 365.25 is NEAR enough.
If you guys can find any better explanation than this, then all the better.
-RODION
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