# [time-nuts] Re: UTC - A Cautionary Tale

Chris O'Byrne obyrne at iol.ie
Wed Jul 20 12:32:26 EDT 2005

```Mike wrote

> Assume someone chasing eclipses in the middle of the desert is an
> "average person," as you have. Exact same scenario, but the program
> was created 7 years prior to show all such events during the next
> century. Because of the unreliable nature of the quadratic equations
> which attempt to predict DUTC, the difference between UTC and UT1 is
> now 7 seconds (completely realistic, based on historical leap
> seconds).
>
> They missed the event by 7 seconds instead of under 1.

A one second difference in UT1 does not correspond to a one second
difference in the observed time of the eclipse in an atomic timescale
(or even in a timescale linked to atomic time by a fixed quadratic
equation). I said in a previous email that a 0.9 second difference in
UT1 corresponds to a 0.1 second difference in the observed time of the
eclipse. I now think that is wrong - I now think the ratio is more like
2:1. I might run a monte-carlo simulation to see exactly what the ratio
is.

Why is there a 2:1 ratio? Well - let me give you a back-of-the-envelope
calculation. A one second difference in UT1 corresponds to a "shift" of
15 arcseconds in longitude. That 15 arcseconds corresponds to
approximately 465 metres on the Earth's surface at the equator (the
worst-case scenario). The lunar shadow typically moves at 1 km/sec.
Viola - the time of the eclipse has been shifted by less than 1/2
second.

The fact of the matter is that there is no way for me to correct for
DUT1 except by using lookup tables. I accept that. What I don't accept
is that, having a value for DUT1 that is "good enough" maybe a year or
more before the eclipse (depending on how good "good enough" is), I then
have to wait for possibly as little as 5 months before the eclipse
before I can finally tie things down to the time that people have on
their watches.

> Had leap seconds continued as currently defined, UTC would still be
> sync'd to celestial events within 0.9 seconds.

Most celestial events are not tied to UT1 - most celestial events are
tied to TDT, which is TAI + 32.184s. The only thing that is tied to UT1
is the rotation of the earth. In other words, the spatial location of
the Sun, the Moon and the planets do not alter in sympathy with the
vagaries of the Earth's rotation.

> If the program's author
> used correct calculations and adequate precision, they could specify
> the accuracy of the results to within 1 second and that accuracy would
> continue for the lifetime of the program.

Or until the next leap second.

I can guarantee you that my calculations and precision are correct -
I've checked them against a NASA reference and, when I use the same
parameters as them, I get precisely the same answers.

> If this same person, who has spent many thousands of dollars in travel
> and equipment costs, had simply used a GPS (at minimal to no
> incremental cost) which gives the choice of presenting GPS time (which
> is parallel to TAI, and unaffected by leap seconds) and a program
> based on that, he would be even closer in time to that event which is
> 6 months away, but off considerably more in the longer term.

Unfortunately, with most reasonably-priced GPS receivers I've seen, it
is very difficult to get GPS time out of them. They all "helpfully"
correct for leap seconds before they display the time.

> (And as long as contrived scenarios are allowed, the friend in _my_
> hotel room is a savant who can do UTC time intervals w/leap seconds in