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(meteorobs) Comet nodes and shower maxima (long)



Additional to my earlier message (that stated the time the Earth passes
the node of 55P/Tempel-Tuttle is around 1998 Nov 17 19.2h UT, not 19.7h UT)
I feel I should give a clearer explanation, as I have come across some
incorrect suggestions on the web regarding the comet's node.

Firstly, a heliocentric orbit is constantly changing.  It is not
just a fixed ellipse, but changes its size and orientation depending
on factors additional to the Sun's gravity.  For comets, this includes
the perturbations (gravitational attractions) of the planets (particularly
the gas giants) and effects of material leaving its surface.  The
perturbations by the giant planets dominate, but a close approach to
any planet has an effect.

When an orbit is published, it includes an epoch and equinox.  The current
equinox used for the angular elements is the year 2000.  This basically
relates to the orientation of the Earth's rotation axis in the year 2000
and is a current standard used in coordinate systems.  However the epoch
of an orbit is quite different.  It states the point in time that the
orbital paramaters are calculated for.  At that time, you could calculate
the precise position and velocity of the comet, but for other times,
especially times much distant from the epoch, it is necessary to calculate
the perturbations by the planets (and any other minor effects) to obtain
a precise position and motion.

A number of web pages state that the node of the comet changes from
epoch to epoch, and thus that the time the Earth crosses the comet's node
also changes.  This however has NO PHYSICAL MEANING.  If you look at
the time of perihelion in these orbits with different epochs, you will
notice that these are ALSO different.  How could this be possible if the
comet is only closest to the Sun once in each orbit?  The reason is that
the time of perihelion has NO PHYSICAL MEANING for epochs away from the
actual time of perihelion.  These "other" times of perihelion would be
correct if the comet's orbit were a fixed ellipse based on the actual
position and velocity of the comet at that epoch.  But as stated, the
perturbations continuously change the values of the orbital elements;
drastically so during a close planetary encounter.

Looking at the node of the comet, the exact same principle applies.  The
longitude of the node only has PHYSICAL MEANING when the comet is
actually at the node.  For 55P/Tempel-Tuttle this occurs close to
1998 March 7, so the only relevant value of the node to use is for an
orbit with an epoch close to that date.  As it happens, this is very close
to the perihelion time of the comet, and a standard published epoch for
the comet's orbit just happens to be 1998 March 8.  The predicted node at
this epoch as calculated by Yeomans before the comet's recovery
(Omega=235.25808) and the node calculated by Nakano using 1998 data
(Omega=235.2583, both in equinox 2000) are effectively identical.
Converting this to a solar longitude to find the time the Earth would be
at this point gives 1998 Nov 19.2h UT, but again, this has NO PHYSICAL
MEANING!  The Earth is not at that point at that time and with regard to
meteors, the comet's orbit does not directly intersect the Earth's anyway.

The utility of the comet's node is that dust tends to distribute
predominantly WITHIN the plane of the comet's orbit (ie, the nodes of the
individual dust particles are initially closely similar to the comet)
and it is well known that the peak of meteor storms occurs within a few
hours of the Earth crossing the comet's node.  But the dust distant from
the comet has different (but similar) orbits and DIFFERENT PERTURBATION
HISTORY.  At the time the peak occurs in 1998 November, the comet has
gone out past Mars.  If it were to have had a close encounter with Mars
on the way out (it can't, but just assume it could), the orbit of the comet
would have been dramatically changed, and the value of the node on
1998 Nov 17 could have suggested a nodal crossing time several days
different or worse.  But this has no bearing on the dust rounding
perihelion on its collision course with the Earth to produce the peak.

This has all been rather long-winded, but I think it is necessary to point
out that the time of the nodal crossing of the comet:
a) is just a first approximation of the peak of a shower
b) must be calculated from the value of the node of an orbit with epoch
   close in time to the comet actually crossing the relevent node.
c) applies to all years either side of the comet's passage through the
   node with the uncertainty increasing the further in time from the
   comet's passage
d) need have no physical meaning.

To get a better understanding of the dust, one must develop realistic
numerical models of the ejection of the dust from the comet and its
subsequent evolution.  As noted, this tends to be similar, but independent
of the parent comet.  An excellent example of this is the debris from
P/Pons-Winnecke which produced an outburst in June this year, when the
comet does not currently get as close to the Sun as the Earth's orbit.
If one were to look at the comet alone, the June outburst would have
been impossible.

SUMMARY
The Earth passes the node of 55P/Tempel-Tuttle on 1998 Nov 17 19.2h UT.
This is just an approximation to when the peak will occur, but experience
suggests it will be within several hours.  One cannot suggest whether the 
peak will occur before or after the nodal crossing without consideration
of the planetary perturbations which independently affect the comet and
the dust.

[Note: My calculations of solar longitude 2000 were based on an update of
an equinox 1950 program to 2000.  The 1998 IMO tables of solar longitude
indicate a nodal crossing some 3 minutes later than I give above.]

Robert H. McNaught
(rmn@aaocbn.aao.gov.au)