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bug#21912: TAI<->UTC conversion botches the unknown

From: Mark H Weaver
Subject: bug#21912: TAI<->UTC conversion botches the unknown
Date: Mon, 22 Oct 2018 01:54:11 -0400
User-agent: Gnus/5.13 (Gnus v5.13) Emacs/26.1 (gnu/linux)

Hi John,

John Cowan <address@hidden> writes:

> What is more, there are no TAI<->UTC conversion tables from before
> 1961 (when UTC began) and probably never will be.  There was heated
> debate in the R7RS-small working group, and we finally settled on a
> compromise:
> (current-second) [r]eturns an inexact number representing the current
> time on the International Atomic Time (TAI) scale. The value 0.0
> represents midnight on January 1, 1970 TAI (equivalent to ten seconds
> before midnight Universal Time) and the value 1.0 represents one TAI
> second later. Neither high accuracy nor high precision are required;
> in particular, returning Coordinated Universal Time plus a suitable
> constant might be the best an implementation can do.
> I now see that the "ten seconds" is incorrect, and I am filing an
> erratum: the correct figure is 4.2131700 seconds per
> <http://maia.usno.navy.mil/ser7/tai-utc.dat>.

Actually, the correct TAI-UTC delta on January 1, 1970 TAI is
approximately 8 seconds.  You are misinterpreting the relevant line from
that file:

 1968 FEB  1 =JD 2439887.5  TAI-UTC=   4.2131700 S + (MJD - 39126.) X 0.002592 S

This means that TAI-UTC = 4.2131700 + (MJD - 39126) * 0.002592, where
MJD is the modified julian day of the desired TAI-UTC delta.  In this
case, the MJD (modified julian day) of midnight UTC January 1, 1970 is
40587, and plugging that into the equation above yields TAI-UTC =
8.000082 seconds.

If you are doubtful, see the "Atomic Time and Leap Seconds" graph, which
shows a graph of TAI-UTC over the years 1958 to 2017, on the following page:


Note that between January 1961 and January 1972, the TAI-UTC delta was
not an integer, and instead of the discontinuous leap second jumps that
we've had since 1972, the two clocks ran at different rates in those


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