Re: Precession in Guide

paul_schlyter Nov 4, 2002

--- In guide-user@y..., "Chris Marriott" <chris@c...> wrote:
>
> ----- Original Message -----
> From: "Richard Mallett" <100114.573@c...>
> To: <Blind.Copy.Receiver@c...>
> Sent: Friday, November 01, 2002 8:39 PM
> Subject: [guide-user] Precession in Guide
>
>> Given the above, and on a different, but related, matter, how
>> certain can we be that, as has been stated, the next opposition
>> of Mars will be the closest for 100,000 years ?
>
> Very sure. Don't confuse the approximations to such things as
> precession, planetary motion, etc, used by star charting programs
> such as Guide, SkyMap, etc, with the numerical integrations they
> are derived from.
>
> The IAU precession formula is a polynomial approximation which is
> highly accurate for a few millennia either side of its "origin" of
> J2000.0, but which very quickly degenerates into random numbers
> once you go outside its range of validity. The numerical
> integration models of the solar system which these approximations
> are derived from are a completely different matter; they can be
> run forwards and backwards in time almost arbitrarily and are
> certainly good for millions of years.
>
> Regards,
>
> Chris

Precession could be numerically integrated too, getting rid of the
problem with polynomial approximations.

Even though numerical integrations can be run forwards and backwards
in time for any amount of time we'd like, taht doesn't mean their
accuracy is sufficient forever. You say these integrations are "good
for millions of years"; now "good for" is a quite vague term. Good
for what?

During those millions of years, there'll be hundreds of thousands of
close oppositions of Mars (there's one every 15-17 years). And those
close oppositions when Mars gets the very closest will have
geocentric distances which differ by very small amounts. I
positively don't think that our best current numerical integrations
with certainty can tell that this coming Mars opposition is the
closest for 100,000 years. Even if our current integrations would
say so, their error in some distant epoch, say some 90,000 years from
now, can be large enough to invalidate our claim of the 2003
opposition being THE closest during this time interval.

Yep, we're able to predict planetary positions with an amazing
accuracy, at least in the short term, i.e. during the next centuries
or millennia. But hundreds of millennia or millions of years is a
different matter! Remember that once the error starts to grow at
distant epochs, it can easily grow as the square or the cube, or
faster (depending on the method of integration) of the time from the
present!