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On 2020-01-04 15:01, Robin Stuart wrote:
> When I came to think things through starting from first principles recently 
I was operating under the assumption you couldn’t possibly create an almanac 
based on a time scale that is not known in advance.

To some extent the Nautical Almanac really is constructed from a time
scale not known in advance. GHA is affected by the revolution of solar
system bodies in their orbits, which is calculated from TT (Terrestrial
Time). Since the almanac time argument is UT1, that's a problem. For
each line in the daily pages, the tabulated UT1 must be converted to TT
via the application of ∆T (= TT - UT1, currently about 69 seconds).

The true ∆T is only known after the fact, so the Almanac must be based
on a prediction. Fortunately the GHA of a body is mainly affected by
Earth rotation angle, which is a function of UT1 and therefore can be
calculated from the tabulated time with utmost exactness. The orbital
motion contribution is greatest for the Moon: 0.5″ per second, or 1/30
the 15″ per second due to Earth rotation. For other bodies the ratio is
even more favorable.

In other words, a 1 second error in ∆T affects Moon GHA only .008′.

But if leap seconds are discontinued, change will be forced on celestial
navigation. One option is to retain UT1 as the NA time basis. Without
leap seconds, UT1 and UTC will diverge, eventually reaching the point
where longitude error becomes intolerable without a DUT1 correction.
With the correction, celestial navigation will be as accurate as before.

Another option is to tabulate the NA in UTC, which has the advantage
that users need not change their procedures. But it does put the
computers of the Almanac in the wrong side of the 30:1 ratio. That is,
the 0.5″ per second (maximum) GHA contribution from TT will be precisely
known, while the 15″ per second from UT1 will depend on the ∆T estimate.
A few years ago a paper by a USNO astronomer said it would be no small
challenge to maintain the present day NA accuracy with our current
modeling of ∆T.

   

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