How many milliseconds in a year?

Originally posted by sonhouse
The seconds in a year are usually this: 86,400 (seconds in one day)
times 365.26 and that gives 31558464 seconds in a year. But is that the actual #? Can you get it down to milli or microseconds? I think it has been proven the earth speeds down and slows up a bit but how many days in a year? I can't believe its known only to 5 digit accuracy.

Prior to 1956 the second was indeed defined in terms of the rotation of the Earth: it was 1/86,400 th of a mean solar day. Now, not every solar day is 86400 seconds long (they can be as short as 86378s or as long as 86429s), but the mean was calculated from nearly 150 years' data.

By 1956 it was recognised that the Earth's rotation was not a constant enough clock and so the second was re-defined in terms of the earth's rotation around the Sun:

1 second = 1/31,556,925.9747th of the tropical year for 1900 January 0 at 12 hours ephemeris time.

By 1967, however, the invention of the atomic clock meant that even this value was not accurate enough and the second was redfined to be:

1 second = the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

At this point the connection between time and astronomical events was broken. It is no longer meaningful to ask exactly how many seconds in a year, because each year will be different. There is no longer an exact ratio between seconds and days or seconds and years - the current mean solar day is 86,400.002 s for instance and increasing at 1.7 ms/century.

If you wanted to "time" a year say then the accuracy would not be limited by the clock used but rather the accuracy of your atronomical observation. If for instance you use "noon" as a datum; how accurately can you determine the time at which the Sun is at its highest elevation? I doubt that an accuracy better than 1/100th is possible.

Originally posted by howardbradley
Prior to 1956 the second was indeed defined in terms of the rotation of the Earth: it was 1/86,400 th of a mean solar day. Now, not every solar day is 86400 seconds long (they can be as short as 86378s or as long as 86429s), but the mean was calculated from nearly 150 years' data.

By 1956 it was recognised that the Earth's rotation was not ...[text shortened]... n is at its highest elevation? I doubt that an accuracy better than 1/100th is possible.

Well the answer to that one is the sun is much too large and amorphous to use as a measuring tool so it would be much better in that regard to use telescopes at night to measure the position of some agreed upon star which is for all intents and purposes, a point source and therefore much more definable in azimuth and altitude.
Then the limiting factor is the rotation period of the earth itself which because of tides and such, varies from year to year. Even the orbit of the earth has a certain precession, such as the famous one explained by Einstein, the 43 arc seconds per century, earth has the same thing but its around 8 arc seconds per century if I remember my calculations, did that a long time ago. So the second has to be defined by something more stable than any of earth's orbital/rotation geometries. Therefore the cesium fine line 9 Ghz thing and others even more accurate. So the best you can hope for is a definition of how many milliseconds there were in LAST year but you probably could not predict how many milliseconds are going to be in NEXT year.

Originally posted by sonhouse
Well the answer to that one is the sun is much too large and amorphous to use as a measuring tool so it would be much better in that regard to use telescopes at night to measure the position of some agreed upon star which is for all intents and purposes, a point source and therefore much more definable in azimuth and altitude.
Then the limiting factor is t ...[text shortened]... AST year but you probably could not predict how many milliseconds are going to be in NEXT year.

The stars are certainly a lot more accurate for timing the rotation of the Earth - whence the Sidereal day (23h 56min ish). However, the most natural definition of a year is the time taken for the Earth to make one orbit of the Sun, and here the background stars don't help much - the parallax would not be enough. For instance in order to measure length of a year accurate to 1 whole second you would need to know the Earth's position in space accurate to 30km. Tricky when the nearest star is over 4LY away.

Originally posted by howardbradley
The stars are certainly a lot more accurate for timing the rotation of the Earth - whence the Sidereal day (23h 56min ish). However, the most natural definition of a year is the time taken for the Earth to make one orbit of the Sun, and here the background stars don't help much - the parallax would not be enough. For instance in order to measure len ...[text shortened]... e Earth's position in space accurate to 30km. Tricky when the nearest star is over 4LY away.

I see what you mean there, 30 Km is about how fast the earth is swinging around the sun. 30 * 31E6 =~934E6Km circumferance of earths orbit. You would have to have a really good handle on the parallax of a star to get that accurate. I guess impossible at this point but maybe with the hiparcos probe you could get close and there are newer probes that will go a hundred times more accurate still but thats a few years off. Can you figure out exactly how, well approximately how close you have to know the parallax figure to peg the earth's orbit within one second? Ah, I guess it would have to be that parallax represented by a 30 KM change in the earth's orbit as seen from AC.
Ok, lets see. Wow, works out to be about 150 nanoarcseconds of parallax. Do we know any parallax number that well?

Originally posted by howardbradley
The stars are certainly a lot more accurate for timing the rotation of the Earth - whence the Sidereal day (23h 56min ish). However, the most natural definition of a year is the time taken for the Earth to make one orbit of the Sun, and here the background stars don't help much - the parallax would not be enough. For instance in order to measure len ...[text shortened]... e Earth's position in space accurate to 30km. Tricky when the nearest star is over 4LY away.

OK so AC at 4.3 Ly away represents a circle of 2.5E14 Km/30Km which works out to about 155 Nanoarcseconds of parallax. I guess not even hiparcos knows the parallax that well not even the next generation after that, eh. 155 nanoarcseconds of parallax represents 30 Km of change of the earths orbit as seen from AC.
Would that mean conversely if you knew the parallax to AC that well you could define the distance to AC within 30 Km as well? Sorry, thought my last post didn't make it in.