[LEAPSECS] the big artillery

[Warner Losh]

On Nov 6, 2014, at 4:40 AM, michael.deckers via LEAPSECS <leapsecs at leapsecond.com> wrote:

> 
>  On 2014-11-05 15:30, Warner Losh wrote on the
>  determination of TAI - UT1:
> 
>> Now, back to the SI second vs the UT1 second. The UT1 second is 1E-8 or 1E-9 different
>> from the SI second. Unless they are computing the results to 7 or more digits, the answers
>> will be identical, no matter which definition of second you use.
> 
>  I don't understand. Measuring (mean solar day)/(1 d) is equivalent to
>  measuring d(TAI - UT1)/d(UT1); if you assume the first quantity is 1,
>  then the second becomes 0. Looking at a recent Bulletin B, the uncertainty
>  for measurements of the rate d(UT1)/d(TAI) is of the order 1₁₀-9 (the IERS
>  give 13 digits!), and typical uncertainty for LOD is around 10 µs/d.
>  The IERS certainly won't fudge on their units.

I’m not assuming the first quantity is 1. I’m saying that when you need a low-precision answer
the calculation is simple. Way 1 I describe below. When you need higher precision, you
need to do the complicated thing I described before and summarize below. Way 1 below is
different than assuming they are the same, it just assumes that a delta time in the arrival
of PPS pulses is sufficient to make a statement about the phase difference in seconds.

There are two ways to obtain numbers for a difference in time scales. One is to have
each one produce a PPS. Then a time interval counter can easily measure the differences
in PPS. That’s one definition of phase difference. For the UT1 case, you steer an atomic
clock or other device that can create a PPS to celestial observations and you compare
that PPS to the PPS of a clock that’s steered to UTC with a TIC. TICs can do remote
data collection, but that’s a pain and likely not what’s done. Especially since the data for
UT1 doesn’t come from some reference oscillator, but from celestial observations and
transit times.

Way two is to convert the measurements to cycles or some other measure of the angle
of the phase. You can then subtract the angle / cycle of the phase from each other after
interpolating them to a common time. Once you have  a phase difference in cycles / radians,
you can convert that to a time difference using whatever definition of the ‘second’ that
is appropriate. For UT1, this almost has to be the way things are computed since
you have a bunch of points in time that correspond to celestial events which are then
translated to an angular position / UT1 time which can be correlated to UTC which gives
you the phase and frequency evolution of UT1 relative to UTC.

Warner
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