I know that the definition of the second is a precise value based on some natural oscillation of a certain isotope, with a day being exactly 86400 (i.e., 60 x 60 x 24) seconds - whether or not the actual average day is a little different (and hence the leap seconds we've been getting lately.) But I am wondering what is the exact definition of a year as a unit of time, that used for radioactive decay and the light-year. I figure that it is based on a tropical year (i.e., time between a pair of vernal equinoxes) or some epoch, but what exactly is the value in number of days. I can't seem to find this anyone on the 'net. Thanks
I guess there are different definitions. A light year is defined as the distance light travels in a Julian year.
The "precise definition" is not a number but a procedure to calculate/measure it. The numbers changes slightly from year to year. For the tropical year you can read this http://en.wikipedia.org/wiki/Tropical_year for example. It has a table towards the bottom with the actual values for several years.
I think part of the problem is that "year" means two different sorts of thing. One meaning is to do with calendars. That includes the Julian Year used in astronomy (exactly 365.25 days), various calendar years (Western, Islamic, etc), financial years (either exactly 52 or exactly 53 weeks long), etc. These are "defined" rather than "measured". the relevant international standard is ISO 8601. The other meaning is to do with the earth's rotation around the sun, and as another post said that has to be measured,since it is perturbed by the gravitational attraction of the other planets etc. Because of effects like precession (the "wobble" of the earth's axis of rotation, with a period of about 26,000 years) there are several possible ways to define it which give slightly different answers.
I may actually be able to help out some in regards to the traditional duration of a year based on the tropical year. The orbital plane of the earth's yearly rotation around the sun stands tilted at a 23° 26' (though not a constant) degree angle towards the earth's equator. The projection of this plane on to the firmament is known as the ecliptic. The ecliptic intersects the celestial equator (the projection of the equatorial plane onto the firmament) in two places, the vernal equinox (0' Aries) and the autumnal equinox (0' Libra). The sun appears there in the northern hemisphere at the beginning of spring around the 21st of March (vernal equinox) and at the beginning of autumn around the 23rd of September (autumnal equinox). At both equinoxes the sun rises in the east and sets precisely in the west. So, the period of time from one sun's passage of the spring equinox till the next is called the tropical year. But to answer your question; the exact value of duration based on the tropical year is 365.242 198 79 days = 31 556 925.9747 seconds. Hope that helps!
Thanks for the explanation. However, it seems that a year, when used by physicists, is the Julian year, or 365.25 days. One wonders why the more accurate Gregorian year of 365.2425 days was not used instead.
Physicists also use 10m/s^2 for gravity on earth, and 3*10^8m/s for the speed of light in vacuum. A lot of physics is using approximations to get an idea of a problem, and later, if need be, more accurate numbers/assumptions can be used.
"One wonders why the more accurate Gregorian year of 365.2425 days was not used instead." My guess would be that it's taken on average (perhaps so as to have some form of a constant for mathematical calculations). Someone else more knowledgeable than I would likely know.
It's astronomers, not physicists, who use the Julian year. Physicists tend to use seconds. Seconds aren't all that convenient a time scale in planetary astronomy. Years and centuries are much more convenient. Nowadays astronomers use "days" that comprise exactly 86400 seconds and Julian centuries that comprise exactly 36525 of those days. This is a fairly recent development. Prior to the 1960s or so, astronomers used Besselian years. The SOFA still provides functions to convert Besselian epoch to Julian epoch. Astronomy has been moving away from things based on the fictitious mean sun for the last sixty years or so. For example, there is no such thing as GMT anymore, at least not officially. GMT was replaced by UTC in January 1, 1972. The tropical year is inherently based on the concept of a fictitious mean sun. It's a concept that is a bit outdated concept, at least in astronomy. Which tropical year? The mean time between successive summer solstices is slightly different than the mean time between successive spring equinoxes. In what year? The length of the mean tropical year is not constant. The Sun is slowly losing mass and slowly transferring rotational angular momentum to the Earth's orbital angular momentum. The number of seconds in a tropical year is increasing slightly. What unit of time? In terms of number of (solar) days per (tropical) year, the mean tropical year is getting shorter. A solar day is no longer 86,400 seconds long. Outdated or not, it's still a concept of interest in a lay sense because the seasons follow the tropical year.
I've been fooling around with numbers pertaining to the Earth, moon, and the Sun. From going to the bookstore, the used bookstores, and the library, no one can agree on the precise value of the Earthyear_indays. I personally went to a single source for all my numbers and that source was the "World Alamanac 2005" edition. From the imformation therein, i had to do a little math, and i got the value of 365.257 Earthyear_indays. Is it precise? I don't know. Think of it like this. The Earthmoondistance_inmiles is only precise at a specific point in time because it orbits the Earth ellipitically. So it has a minimum and maximum distance from the Earth. When averaged out, the moon is 238,855 miles from the Earth, but then again no x number of sources can even agree on this. So maybe then this pertains to the length of the year also.
I think it's interesting to note that the 365.25 day duration of the julian year is exactly the average between the tropical earth year and the sidereal year. tropical earth year = 365.24219879 sidereal year = 365.25636042 365.249279605 - 365.25636042 = 0.01416163/ 2 = 0.007080815 + 365.24219879 = 365.249279605 or 365.25 The sidereal year is the space of time between the sun's passages of a certain star and is about 20 minutes longer than the tropical year due to the retrograde motion of the point of vernal equinox.
Since you started this, I have a different question which someone suggested as an April fool joke. But it got me thinking. Things would be much simpler if we adapt a different time keeping system. Yes, a decimal or a metric system instead of base-60 time keeping. 100 sec = 1 minute 100 minutes = 1 hour 10 hours = 1 day (12-hour) 10 months = 1 year, months will have more days. Is this idea totally impractical?
Our current time system is really based on angles of sun, which I think makes perfect sense. But, as far as I know, the division of the angles into 12/60/60 is arbitrary. We could potentially change our time system, but I don't really see a reason to. Remember, our base 10 numerical system is pretty arbitrary too (my guess is that it's simply based, pun intended, on our fingers). If I recall correctly, economists have worked the numbers in ways I don't really care much about, and they seem to typically say there isn't much reward in going to different time systems.