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From: Michael Deckers <Michael.Deckers_at_fujitsu-siemens.com>

Date: Fri, 13 Jan 2006 11:17:52 +0000

On 2006-01-13, Mark Calabretta wrote:

*> I have two time scales, TAI and UT1, that tick at very slightly
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*> different rates. I want to make TAI the basis for civil time keeping
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*> but I need to make adjustments occasionally to keep it in step with
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*> UT1. How do I do it?
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*>
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*> The answer provided by CCIR was to represent TAI in a variable-radix
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*> notation that matches (or appears to match), to within 0.9s, that of
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*> UT1 expressed in the usual calendar/clock format. This is done by
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*> varying the radix of the seconds field in a pseudo-sexagesimal clock
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*> format from 60 to 61 (or in principle 59) on occasions announced 6
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*> months in advance.
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*>
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*> So if asked for a definition I would say that "UTC (post 1972) is a
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*> representation of TAI such that ... (you know the rest)".
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*>
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*> The point is that UTC is simply a representation of TAI. "Writing UTC
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*> as a real" reveals it to be TAI.
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I believe I'm now grasping what you mean: the rate of UTC is the same

as the rate of TAI (since 1972), that is, the derivative

d( UTC )/d( TAI ) = 1. Hence, when I integrate the "ticks" of UTC

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.

Astronomers who "write UTC as a real" (eg, in JD or MJD notation)

want an approximation of UT1 to point their telescopes, they do

_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.

Michael Deckers

Received on Fri Jan 13 2006 - 03:18:15 PST

Date: Fri, 13 Jan 2006 11:17:52 +0000

On 2006-01-13, Mark Calabretta wrote:

I believe I'm now grasping what you mean: the rate of UTC is the same

as the rate of TAI (since 1972), that is, the derivative

d( UTC )/d( TAI ) = 1. Hence, when I integrate the "ticks" of UTC

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.

Astronomers who "write UTC as a real" (eg, in JD or MJD notation)

want an approximation of UT1 to point their telescopes, they do

_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.

Michael Deckers

Received on Fri Jan 13 2006 - 03:18:15 PST

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