[LEAPSECS] the big artillery

[Michael Deckers]

    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.