NavList:

   

Reply

Alex wrote-

>I think this statement needs some comments/corrections.
>
>On Thu, 2 Dec 2004, George Huxtable wrote:
>
>> Not everything in astronomy is deterministic. Even in a system, such as the
>> solar system, in which more than two bodies have a mutual gravitational
>> interaction, there's a limit to the long-term predictability of it all.
>> This is the famous "three-body problem".
>
>This is not a problem for modern astronomy.
>If we are talking of "predictions" (forward or backward)
>for the period of few thousand years, this will cause no problems
>(in principle). As I understand you were talking of Tycho Brahe
>observations.
>
>The algorithm of such calculations is contained in the book
>of Meeus "Astronomical Algorithms". I doubt that these calculations
>can be easily done by hand, but they can be done with a computer
>and I suppose that Frank Reed's program can do this.
>
>The "long term" prediction is indeed impossible, (because the
>many-body problem of celestial mechanics has no simple solution)
>but "long term" in this sentence refers to billions years.
>For all "practical purposes" such prediction can be done.

=====================

Alex has got my meaning quite wrong, so perhaps I didn't explain it well.

He writes-

"As I understand you were talking of Tycho Brahe
>observations.",

but I wasn't. Not at all. That was the original threadname, but the
discussion had moved on to the question of the unpredictability of Delta-T;
which is why I had changed the threadname.

For the purposes of our own period on the Earth, and for hundreds, perhaps
a few thousands, of years in the future and the past, solar system motions
are indeed predictable to adequate accuracy, based on our own recent
observations of the system dynamics. Alex and I agree about that, when he
states-

>This is not a problem for modern astronomy.
>If we are talking of "predictions" (forward or backward)
>for the period of few thousand years, this will cause no problems
>(in principle)

except that I would describe it as sufficient predicability "in practice",
rather than "in principle"

But the further you get from the present-day, error in these predictions
increases. It's not, simply, that we haven't measured the present positions
and velocities accurately enough, though that plays a part. But you can get
to a point when infinitesimal changes in those initial conditions lead to a
divergence in the predicted results. It's comparable to the "beating of a
butterfly's wing" effect that causes meteorology to be so unpredictable;
but over a MUCH longer timescale.

Alex writes-

>The algorithm of such calculations is contained in the book
>of Meeus "Astronomical Algorithms". I doubt that these calculations
>can be easily done by hand, but they can be done with a computer
>and I suppose that Frank Reed's program can do this.

Well, yes and no. Yes, the JPL, and also Bretagnon of the Bureau des
Longitudes in Paris, have made very accurate predictions available. What
Meeus has published is a cut-down subset of the Bretagnon theory. I have
implemented a cut-down version of that, on my pocket calculator, to quite
sufficient accuracy for any navigation over my own lifetime and even
Alex's.

I'm not familiar with the JPL or Bretagnon originals, but presumably it's
stated somewhere that they will apply only over a stated period of
validity, and can't be extrapolated "for ever" either way. Meeus is careful
to emphasise in his book the limited period of validity of cerain
expressions.

Where Alex says-

>The "long term" prediction is indeed impossible, (because the
>many-body problem of celestial mechanics has no simple solution)...

We agree: that's the topic I was writing about, and said so.

but then he goes on to say-

>...but "long term" in this sentence refers to billions years.


Here we disagree, and strongly. Unpredictable divergences show up over a
MUCH shorter period, tens or perhaps hundreds of thousands of years
(depending on what accuracy is being called for).

>For all "practical purposes" such prediction can be done.

No argument over that.

George.


================================================================
contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
================================================================

   

Reply