On 2014-11-04 12:34, Zefram wrote:
UT1 always ticks a second for that ERA increase, but Warner's point is that the second of UT1 isn't an *SI* second. The time taken for that ERA increase, and hence the duration of a UT1 second, very rarely exactly matches an SI second. The second of UT1 is an angular unit, defined as 1/86400 circle (= 15 arcseconds), not a unit of physical time.
Then which unit would that be? When the IERS compute a difference TAI - UT1, how do they do it? Do they convert the UT1 reading in any way before they subtract? Or, if they don't, what is the unit of the difference, SI seconds or "second of UT1"? The IERS Conventions certainly do not mention any of this. How could they if the units would really differ?
Of course, due to the history, we alias angular seconds to physical seconds all over the place, especially in the mathematical expressions that we use to describe relationships between time scales. Usually we gloss over that by just calling them both "second". But if you're going to specify which type of second you mean, better pick the right one for the time scale.
I am puzzled by the fact that some people do not seem to accept with time what they easily accept with other quantities. For instance in geodesy, normal height is expressed in meters (or feet) even though it is actually a difference in geopotential observed by leveling. The expression in meters is derived from some conventional "normal" gravity potential model; comparison with orthonormal height thus gives an intuitive notion of its deviation from the real gravity field. But nobody calls for different units for orthometric and normal heights, on the grounds that a meter of normal height would not be an "SI meter" of "real length" while a meter of orthometric height would be. On the contrary, everybody agrees that normal and orthometric height must use the same unit so as to make them comparable. (And, as with time scales, there is a bunch of other important notions of height to which they need to be compared!) The mean solar day on the rotating surface of the Earth is given by the comparison of UT1 with TAI (or TT). Its value, d(TAI)/d(UT1)·(86 400 SI seconds) would be a bad unit of time because it varies remarkably with time. And the mean solar day in a geocentric "inertial" system (as used in satellite dynamics) is a different value altogether, namely d(TCG)/d(UT1)·(86 400 SI seconds) at the geocenter. Neither quantity is used as a unit to express UT1; instead, both are derived from expressions of UT1, TAI, and TCG in SI units. Michael Deckers. _______________________________________________ LEAPSECS mailing list [email protected] https://pairlist6.pair.net/mailman/listinfo/leapsecs
