Re: [guide-user] Re: Delta-T

Paul Schlyter Sep 19, 2005

Andis Kaulins wrote:
> --- In guide-user@yahoogroups.com, Bill J Gray <pluto@p...> wrote:
>
>>Hi Larry, all,
>>
>> As Denis points out, one can (in theory) go to the Web site and
>>dig through the source code (delta_t.cpp, in this case) and see
>>exactly how Delta-T is computed. As source code goes, this is
>>(in my humble opinion as its author!) reasonably clear and easy
>>to understand... _if_ you happen to be a C programmer. It's
>>probably rather opaque to the rest of the world, I'm afraid.
>>
>> Anyway. 'delta_t.cpp' has a table of values for Delta-T from
>>1618 to 2004, at two-year intervals, and interpolates within
>>that table. After 2002, it just does a linear extrapolation.
>>That is, for 1 January 2002, it has Delta-T = 64.30 seconds;
>>for 1 January 2004, it has Delta-T = 64.57 seconds, i.e.,
>>Delta-T increased by .17 seconds over those two years. So,
>>for a given time t (expressed in years),
>>
>>Delta-T = 64.57 + (t - 2004) * .17 / 2
>>
>> That rate of increase corresponds to 8.5 seconds/century, and
>>to Delta-T = 64.13 seconds on 1 January 2000. So in the more
>>conventional system where t_cen = centuries from J2000,
>>
>>Delta-T = 64.13 + 8.5 * t_cen
>>
>> Usual warning: Delta-T becomes increasingly ill-defined as
>>you extrapolate it. For example, a decade or so ago, it
>>looked as if Delta-T was going to keep increasing by about a
>>second or so each year, requiring a new "leap second" each
>>December. Then it stopped increasing so briskly, and we've
>>not had a new leap second since 1999. The above formula is
>>there simply because Guide has to say _something_ about what
>>Delta-T is apt to be, even if that something isn't very
>>meaningful.
>>
>>-- Bill
>
>
> One way to understand Delta-T better is to spot the cycles which may
> be incorporated within it. One of these may be solar luminosity -
> which may have a ca. 190-year cycle, as manifested in the delta-T
> values evidenced between ca. 1700 and ca. 1890.
>
> As written at
> http://www2.nature.nps.gov/geology/caves/newsletters/ie7_1/ie7_1.pdf
> "A Master's thesis on a broken stalagmite in the main cave
> indicates a temperature cycle of 190 years between ~13,500 and 9,500
> years ago, most likely a solar luminosity cycle."
>
> This in turn may relate to the cycles in sun spots
> http://personal.inet.fi/tiede/tilmari/sunspot5.html
> which in turn are related to geomagnetic activity
> http://www.sec.noaa.gov/info/SumSept.html.
>
> In my opinion, these variations are caused by planetary perturbations
> viz. planetary positions varying between perihelion and aphelion. See
> http://www.stjarnhimlen.se/comp/tutorial.html
>
> If that were true, then primarily responsible for the ca. 190-year
> cycle would be Pluto (actually, the orbit here is 248 years as such),
> which was at perihelion until 1999, when it was still within
> Neptune's orbit. See
> http://science.nasa.gov/headlines/y2001/ast04jan_1.htm
> Now it is headed back out to be the 9th planet again.
>
> Accordingly, if the above theory be true, Delta T should now slow
> down as it has, stay constant at ca. +65 and then diminish, rather
> than increase. Of course even if we were right on this prediction, we
> could be wrong, since current theory is that the planets can not
> exert this kind of influence, but I am not so sure.

If the planets had any noticeable influence on the Earth's rotation, it
must be through gravitational forces, right? And what matters here is
the tidal forces (which are nothing but the gradient of the gravitational
force).

Now, the tidal force is proportional to the mass of the gravitating body,
and inversely proportional to the third power of the distance to the body.
This is well-known.

You assume Pluto influences Delta-T merely because of a (very) approximate
coincidence in the period. Now, the tidal force on the Earth due to Jupiter
is some 100 million times stronger than the tidal force on the Earth due to
Pluto.

If Pluto noticeably influences the Earth's rotation, how come we don't see
a vastly stronger variation on Delta-T due to Jupiter? Such an influence
could be expected to have a period of some 12 years, right?

The answer is that even the tidal force from Jupiter upon the Earth is
far too weak to have any noticeable influence on the Earth. The tidal
force from the Moon (which is quite noticeable) is some 300.000 times
stronger than the tidal force from Jupiter --- and some 30 trillion
times stronger than the tidal force from Pluto.


I hope these numbers make you realize why planets cannot have this influence
on the Earth's rotation. In principle the planets do have an influence of
course, but it is far too small to be detectable.


> Andis Kaulins
> The LexiLine Group at Yahoo
> http://groups.yahoo.com/group/LexiLine/ with a posting relating to
> Delta-T at http://groups.yahoo.com/group/LexiLine/message/1340
>
>
>
>
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