[LEAPSECS] When will UT1 definition require replacement?

[Gerard Ashton]

The current relationship that UT1 must satisfy is given on page 78 of the
3rd ed. of the Explanatory Supplement to the Astronomical Almanac (among
other places). I've modified it to live with the typesetting limitation of a
mail list:

ERA(t) = 2 pi (0.7790572732640 + 1.00273781191135448 t)

Where t is the Julian UT1 date - 2451545.0. In other words, the number of
UT1 days since noon, January 1, 2000.

There has much discussion on the list about when the current definition of
UTC will become unworkable, and when a UTC would become unworkable if leap
seconds are discontinued, but I don't think there has been anything more
than hand waving about when UT1 would need to change.

The above equation implicitly defines a fictitious mean sun (FMS for short,
which would differ from Newcomb's fictitious mean sun). We would like
difference in position of the real sun and FMS to be close to 0 when
averaged over the course of a year. But it is difficult to evaluate this,
because accurate estimates for the future position of the sun are only
available in terms of uniform time scales such as TT, and the expression for
the FMS would be in terms of the non-uniform UT1.

So does anyone know of any evaluation of the longevity of the expression for
UT1?

Gerry Ashton