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Text File | 1994-04-15 | 8KB | 135 lines

6. The Final Orbit of Shoemaker-Levy 9

        The motion of Comet Shoemaker-Levy 9 can technically be
described as chaotic, which means that calculations based upon the
input of comet positions having very tiny differences (small input
errors) causes large differences in the results of calculations of
the subsequent motion and the apparent prior motion. Large
perturbations caused by successive close approaches to Jupiter
have resulted in each orbit being different in size, shape, and
orientation. The orbits have not been the simple result of a small
body in orbit around a large one but rather the product of a "tug
of war" between Jupiter and the Sun, a classic "three-body
problem". Near to Jupiter the planet's gravity has dominated the
motion, but far from Jupiter the Sun is more important. On
July 16, 1993, at apojove (the point farthest from Jupiter) in the
current orbit, Shoemaker-Levy 9 was almost 1,200 times as far from
Jupiter as at the time of breakup, a distance of 50 million km,
equal to a third of the distance of Earth from the Sun. The comet
has been in a closed orbit around Jupiter for many decades, but
that orbit is far from stable. Figure 8 by Chodas shows what this
orbit will look like as viewed from the Sun at the time of impact.
It is tipped (inclined) 53 deg. to Jupiter's equator as measured at
apojove and is bent about 20 deg. more near to Jupiter. (A three-body
orbit rarely lies in one plane like the simple two-body orbit.)

During this final orbit, after breakup in July 1992, Shoemaker-
Levy 9 was followed carefully from discovery in March 1993 until
the time the cometUs angular distance from the Sun became too
small to permit observations. The last useful astrometric
(positional) observations reported before the fragments were lost
in the glare of the Sun were made on July 11. The comet was
recovered (found again after almost five months without
observations) by Scotti and Tom Gehrels on December 9, with the
comet rising above the horizon a bit more than three hours before
the Sun in the morning sky. (The comet is so faint that it cannot
be observed in twilight or too low on the horizon.) The quality of
the predictions for the time of impact of the individual fragments
on Jupiter will depend upon the number of high-quality astrometric
observations of each comet fragment made between December 1993 and
the time of impact. A week before the impacts the times should be
known at least to 110 minutes (with 50% confidence), improving to
perhaps 15 minutes a half day before impact.

At a fall planetary astronomy meeting (DPS) Jewitt, Luu, and Chen
exhibited an image showing 21 distinct fragments in the Shoemaker-
Levy 9 nucleus train. At discovery in March, this train was about
50 arc seconds or 162,000 km in length as projected on the sky.
This angular distance had increased by about 40% (and the true
linear distance by about 50%, since Jupiter was then farther from
Earth) by the time the comet was lost in the glare of the Sun in
July. The spreading is caused mainly by the fact that the piece
closest to Jupiter at breakup was some 9 km closer than the
farthest piece (the diameter of the comet) and therefore entered a
faster orbit. The orbits are all so elongated that from Earth they
appear to be nearly a straight line with the fragments strung out
along it. The fragment nearest to Jupiter at breakup remains
nearest to it and will be the first to impact. At this writing,
Chodas and Yeomans predict that the train will reach an apparent
length of some 1,286 arc seconds at the time the first of the
fragments enters Jupiter's atmosphere. The true length of the
train will be 4,900,000 km at that time, and it will require
5.5 days for all of the major fragments to impact.

The new data taken following solar conjunction (the closest
apparent approach to the Sun as projected against the sky) more
than doubled the length of time since discovery for which cometary
positions were available. With this new data, it appears that the
impacts will be centered on about July 19.5, a day and a half
earlier than the first predictions. The approach to Jupiter that
shattered the comet appears to have been even closer than first
thought, about 96,000 km from the planet's center and only
25,000 km above the clouds. The revised orbit has also moved the
impact points closer to the visible hemisphere, but unfortunately
still on the back side as seen from Earth. The brightest fragment,
of which there is some indication that it itself is fragmented,
will impact on about July 20.78 and contains about 10% of the
total mass of the comet. The other 20 observed fragments contain
more than 80% of the mass. The remaining mass is contained in all
of the dust and small pieces in the train, the trails, and the
tails. Most of this mass also will hit Jupiter over a period of
several months beginning about July 10, but it probably will cause
few or no detectable effects.

Meanwhile, the dust trails of small debris will continue to
spread, as will the major fragments. The east-northeast trail is
expected to reach a maximum apparent length of some 70 arc minutes
in late June of 1994 and then decrease again in apparent length
with the tip turning around into a "V" shape. The west-southwest
trail may reach a length of almost 100 arc minutes before impacts
begin. Only the larger trail material will actually impact
Jupiter. The earliest dust will begin to hit about July 10, and
impacts will continue into October. The smaller dust will be moved
into the tail by solar radiation pressure and will miss the planet
completely.

If upon further study it is found that the pieces of Shoemaker-
Levy 9 have continued to fragment, then predicting impact times
will be much more difficult and the predictions less reliable.
Such continued fragmentation of pieces already badly fractured is
very possible, but fragmentation in the last day or two, when it
is most likely to occur, will have no significant effect on the
predicted times of impact. The pieces typically separate with a
velocity of less than a meter per second. There are 86,400 seconds
in a day, so even pieces separating at a full meter per second
would be only 86.4 km apart after one day. Moving jointly at a
velocity which reaches 60 km/s at impact, the pieces would hit
within a few seconds of each other. The effect of further
splitting upon the impact phenomena would be far greater and is
discussed in the next section.

Figure 9 by David Seal shows the final segment of the comet
fragment's trajectories. They will impact near a latitude of 44 deg. S
and a longitude 70 deg. past the midnight meridian, still 10 deg. beyond
the limb of Jupiter as seen from Earth, impacting the atmosphere
at an angle of about 42 deg. from vertical.

Observing conditions from Earth will not be ideal at the time of
the impacts, since there will be only about two deg. hours of good
observing time for large telescopes at any given site after the
sky gets good and dark and before Jupiter comes too close to the
horizon to observe. At least it will be summer in the northern
hemisphere, and there will be a better chance for good weather
where many observatories are located. With 21 pieces hitting over
a 5.5-day period, there will be an impact on average about every
6 hours, so any given site should have about one chance in three
of observing at the actual time of an impact each night. Since the
impacts will be on the back side of Jupiter, light from the
impacts can only be observed by reflection from Jupiter's moons or
perhaps from the rings or the dust comae of the comet fragments.
Those attempting observations of the effects of the impacts on
Jupiter can begin about 20 minutes after the impacts, when the
impact area rotates into view from Earth.