On Mar 20, 2013, at 6:02 PM, Joseph M Gwinn <gw...@raytheon.com> wrote: > I would propose that ITU is using continuity and uniformity in their > mathematical definitions, implying that the intent is that at least in > definitional theory, UTC be mathematically continuous with all its > derivatives (noise being ignored). This would exclude step discontinuities > (leap seconds) and piecewise linearity (like UT1). Given that the length of > a SI second is constant, what's left is a UTC that is a constant offset from > TAI, where the offset changes only if so ordered. >
Relative to what? If UT1 is an angle, then derivatives with respect to "angular time" are stationary, and derivatives with respect to atomic time vary. At any rate, continuous is still the wrong word. All the derivatives of sin(t) are continuous, but the function itself is non-monotonic. Leap seconds are a means to an end. Earth does not exist in a vacuum (well, it does :-) but Earth is not the only example we have. There are 25 terrestrial worlds in the solar system - 4 planets, 2 dwarf planets interior to Pluto, 19 large moons - and on each "day" means synodic day. This includes fast and slow, prograde and retrograde and synchronous rotators. Io and Europa actually move non-monotonically (making little backward loops) in their shared orbit with Jupiter. And on each there is one fewer solar day per year than sidereal rotations. It's disingenuous to argue that the functional form of civil time - calendar and clock time - doesn't follow mean solar time, angle or not, varying or not. By all means we can discuss alternative ways to solve the problem. But this will only be successful if the problem is cast in a coherent fashion. Rob
_______________________________________________ LEAPSECS mailing list LEAPSECS@leapsecond.com http://six.pairlist.net/mailman/listinfo/leapsecs
