Re: What to do if International Time hits the International Date Line?

From: Markus Kuhn <>
Date: Tue, 01 Jul 2003 21:51:09 +0100

Steve Allen wrote on 2003-07-01 19:52 UTC:
> On Tue 2003-07-01T20:34:58 +0100, Markus Kuhn hath writ:
> > Newcomb's formula for the geometric mean longitude of the Sun is
> >
> > L = 279 41' 48".04 + 129602768".13 C + 1".089 C^2
> not really valid more than 200 years into the future.
> Please don't use Newcomb for that.
> You want to use something intended to match integrations that have
> moved much farther into the future.
> For a start, see Simon et al., Astron. Astrophys 282, 663-683 (1994)

Thanks. If I understood it correctly, section 5.8.3 gives me with

  L = 100.46645683 + 1295977422".83429*t - 2".04411*t^2 + 0".00523*t^3

the mean longitude of the sun, where t is kiloyears from the year 2000.

Oops, I am mildly shocked to see that the sign of the t^2 term has
changed its sign compared to how Newcomb's formula is printed on page
4(512) of

while the magnitude changed by a factor of 2 whereas the scale of t has
changed by a factor of 0.1.

The large number of decimal digits provided for the Newcomb formula in
the Metrologia leapsecond paper had suggested to me that all this is
rather exact science and that these digit are actually significant ... :-(

Given the new formula, unless I made a silly mistake with my pocket
calculator, the second term in the mean longitude of the sun will have
grown to 0.5 days by

  (360/(2 * 365.25) * 60*60" / 2".044)^1/2 = 29 kiloyears from now

whereas the third term will have accomplished the same (with opposite
sign) by

  (360/(2 * 365.25) * 60*60" / 0".00523)^1/3 = 70 kiloyears from now

Sounds much better! If the annual oscillation of the earth does really
not diverge from atomic time by more than one day for the next 30
kiloyears, then adjusting the leap year rules for civilian time zones
might really help to keep the

  a) civilian time zones
  b) international (atomic) time
  c) the date of the spring equinox

synchronized more or less for the next few ten thousand years. So there
might be hope not to mess up everything completely by dropping leap
seconds. Perhaps this idea is not that crazy after all and deserves
being scrutinized by professional astronomers. Comments welcome.

Is the Simon et al. formula considered good enough to predict the mean
longitude of the sun within half a day for the next few tenthousand
years? The authors make only a statement on the quality of ephimerides
derived for the years 1000-3000.


Markus Kuhn, Computer Lab, Univ of Cambridge, GB | __oo_O..O_oo__
Received on Tue Jul 01 2003 - 13:54:05 PDT

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