# Re: The real problem with leap seconds

```On Fri 2006/01/13 11:17:52 -0000, Michael Deckers wrote
in a message to: LEAPSECS@ROM.USNO.NAVY.MIL```
```
>   I must get TAI, up to an integration constant. This is correct.
>   The integral of d( UTC ) is TAI (up to an integration constant),
>   but this integral is UTC only where UTC is a continuous function
>   of TAI.

You're still not getting the point that UTC is just a representation
of TAI.

>   Astronomers who "write UTC as a real" (eg, in JD or MJD notation)
>   want an approximation of UT1 to point their telescopes, they do

There may be some confusion as to what is meant by "write UTC as a
real".  Astronomers who want UT1 and are prepared to accept an
uncertainty of +/-0.9s can get it from UTC simply by treating it as an
ordinary sexagesimal number, ignoring all leap seconds.  This is "the
trick".

The cost of the trick is that all leap seconds must be accounted for
in computing the precise time difference between two UTC dates.
Effectively you convert TAI from its UTC representation back to a fixed-
radix representation in which subtraction can be performed more easily.
(The same goes for subtracting a UTC from a TAI.)

>   _not_ want TAI. They use UTC as a timescale whose values are
>   close to UT1, but whose rate nevertheless is d( UTC ) = d( TAI )
>   and not d( UT1 ). Such a function cannot be continuous (and it
>   cannot be differentiable everywhere). At the latest discontinuity
>   of UTC, it jumped from a little bit after UT1 to a little bit before
>   UT1.

UT1 derived from UTC does have a discontinuity at the point of leap
second insertion - but that shouldn't bother astronomers who are only
interested in 0.9s accuracy.

Mark Calabretta
ATNF
```