Low-relative velocity and long-lasting encounters can dramatically change the orbital elements of a comet; the object could be temporarily bound to Jupiter for a period of several years. It is well stated that most of the discoveries of comets occurred just after a close encounter with the planet and a decrease of the perihelion distance of the comet. So, why don't we look for comets during close encounters with Jupiter rather than waiting to find them afterwards? To estimate the feasibility of this proposal, dynamical computations and observational analysis of the Jupiter family of comets were made. A criterion to distinguish comets during an encounter from other moving objects in the field is discussed

Lindgren, Mats

Tancredi, Gonzalo

English

NASA Technical Reports Server

Asteroids, Comets, Meteors 1991,pp. 601 604
Lunar and Planetary Institute, Houston, 1992 _"t-'r"/(_ -" f-_ _) 601
N9 3 ",.,$ : P--iflS "3
The vicinity of Jupiter : a region to look for comets
G. Tancredi 1,2 and M. Lindgren 1 _
It
I Astronomiska Observatoriet, Box 515, S-75120 Uppsala, Sweden
Dept. Astronomia, Fac. de Ciencias, Montevideo, Uruguay
ABSTRACT
Low-relative velocity and long-lasting encounters can dramatically change the orbital elements of a
comet; the object could be temporarily bound to Jupiter for a period of several years.
It is well stated that most of the discoveries of comets ocurred just after a close encounter with the
planet and a decrease of the perihelion distance of the comet. So, why don't we look for comets during
close encounters with Jupiter rather than wait to find them afterwards? To estimate the feasibility of this
proposal we have made dynamical computations and observational analysis of the Jupiter family of comets.
A criterion to distinguish comets during an encounter from other moving objects in the field is discussed.
THE SPACE DISTRIBUTION OF JUPITER-FAMILY COMETS
Kres_k (1979) made a first attemp to look at the space distribution of asteroids and comets and found
a few interesting patterns not observed in the usual orbital elements phase-space where we study these
objects. We made numerical integrations of the whole sample of Jupiter family (hereafter JF) comets (143
short-period comets with P<20 yr) to have a new look into the problem and in particular to analyze the
distribution of objects on different regions of the Solar System. We integrated each comet and the nine
planets at a time, starting at J.D. 2448000.5 for 200 yr into the past (for more details about the integration
method see Tancredi and Rickman 1991, hereafter TR). At every 500 days the heliocentric positions and
velocities of the objects were stored.
We were interested in the positional distribution of comets at any time. As JF comets have low incli-
nations, we took the ecliptic plane as the reference plane and divided the plane into square boxes of 1 AU.
Cubes of 1 AU centered on these boxes were considered to compute the mean number of comets inside each
cube at any time. In Fig. 1 we present a grey-scale picture of the observed distribution, where the darkest
point corresponds to a density of 1 obj/AU 3. The orbit of Jupiter with its perihelia and apsidal lines is
superposed. We can see a "crater-like" structure, with a slight increase of the density of comets towards the
orbit of Jupiter. This is naturally explained considering that JF comets tend to have their aphelia in the
- -.-i".;"-"-.::"-"::-_il_2.-T':-:':.4"-:':..:(-:';-;'::::.";'...-
_--.i::::_;.::"__-<-'- __%-_-._.:...::.:;_i;;-
- - -
i
I llll,liilillir-
-1 0 1
Fig. 2. Grey-scale picture of the positional distri-
b.ution of observed short-period comets at any time
m a rotating-pulsating frame with Jupiter fixed
(unit distance = distance Jupiter-Sun).
https://ntrs.nasa.gov/search.jsp?R=19930010064 2020-03-17T08:18:11+00:00Z
602 Asteroids, Comets, Meteors 1991
As Jupiter is the main body responsible for shaping the distribution of JF comets, we plotted the
distribution of objects in a more appropriate frame : a rotating-pulsating frame, with the instantaneous
distance Jupiter-Sun as unit distance and the instantaneous Jupiter's angular velocity as the rotating velocity.
In this frame the Sun is at the centre and Jupiter is always at z = 1 , y = 0. Fig. 2 shows a grey-scale
picture of the space distribution. The "crater rim" observed in Fig. 1 almost shrinks to a point, i.e. Jupiter's
position; where the density reaches a value ofl.4 obj/AU3_
The importance of this finding is that we do not only constrain the position where comets tend to
concentrate but we also constrain their velocities, because, as we will show later, the relative velocities to
Jupiter are generally low.
The previous density values give only a rough
estimate of the number of comets close to Jupiter
at any time, computed by making an average over
the last 200 yr. Most comets have been discovered
just after a close encounter with Jupiter (Karm and
Rickman 1982, TR), when their perihelion distance
decreased. In addition to this point, when we plot
the distribution of number of encounters at distances
< 0.5 AU from Jupiter during the past and future
1000 yr for the whole sample of observed JF comets
(TR), we see a peak at the present time (Fig. 3).
It is obvious that the_observed_J F comets is a bi-
ased sample of the whole population in the sense that
we have a preponderance of comets that hav_expe-
rienced a close encounter in the near past. Due to
the chaotic behaviour of the majority of short-period
comets orbits, if we integrate the observed popula-
: : : -: ...... :: f
120 __
100
o_ 80
v
60
_ 40
zo
0 -i J i, I _l t Jl Ljj_, I _ 1 , , ,
1000 1500 2000 2500 3000
Time (yr)::
Fig. 3. Distribution of the number of encounters
with ninimum distance D < 0.5 A U for 2000 years
centered in the present epoch.
tion for a long enough period of time, the successive
encounters with Jupiter will randomize the orbital distribution and we would obtain a closer representation
of the whole sample. We will compare the figure s obtained averaging over the last 1000 yr and the ones
obtained for the last 40 yr (when the discovery rate of JF comets has had a dramatic increase, TR):-
In Fig. 4 we plot the number of comets at any time within a certain distance D to Jupiter as a function
of this distance (the full-line corresponds to the average over the last 40 yr, the dashed-line over the last 1000
yr). Mthough at greater minimum distances to the plane _ the number of encounters increases, the duration
of these encounters does not have a steep increase. This fact is shown in Fig. 5, where we plot the time a
comet spends within a certain distance D to Jupiter as a function of this distance (fuli and dashed-lines are
the same as in Fig. 4).
These calculations, using the observed 143 JF comets, then shows that in the near past there was a
density of 1.5 objects at any time at distances less than 0.5 AU from Jupiter (1% of the observed population)
and averaging over the last 1000 yr the density decreases to 0.6 objects (0.4 %) . These comets spend an
average time of 1.1 and 0.7 yr within 0.5 AU from the planet in the last 40 and 1000 yr, respectively. These
agree quite well w_th similar calculations made by Carusi e t al. (1985).numbers
0
0
o
L
5
4
3
2
1
0
0
-I ,..,-£f_ .rl'i ,, l l,i l l,, Ih_
.2 .4 .6 .8 1
Dist. to Jup. D (AU)
Fig. 4. Number of cornets at any time within a
certain distance D to Jupiter as a function of this
distance (full-line : average over the last 40 years,
dashed-line : average over last 1000 years).
_ .5
o f,l,, ,,,I,,,l,,tl,
0 .2 .4 .8 .8 1
Dist. to &up. D (ALl)
Fig. 5. Time spent within acertain distance D
to Jupiter as a function of this distance ( full and
dashed-line same as in Fig. 4).
Asteroids, Comets, Meteors 1991 603
A SEARCH FOR COMETS AT CLOSE ENCOUNTERS
If comets are usually discovered after a close encounter with Jupiter and the actual density of observed
JF comets around Jupiter is greater by a factor of 2 or 3 compared to any other place in the Solar System,
we may ask why we do not look for comets around Jupiter. Below, we will identify the problems and define
an observational strategy to do such a search.
a) The identification problem
At Jupiter's opposition, a distance of 0.5 AU from the planet corresponds to a projected angular distance
in the sky plane of 7 °. A Schmidt telescope with a plate size on the order of 5 ° × 5 ° is the most suitable
instrument to cover such a big region of the sky.
If we take a plate of an ecliptic region we would find from 200 up to 400 asteroids down to 20 mag.
in a 5 ° x 5 ° field (van Houten et al. 1970). We may also find a few comets that are not undergoing a
close encounter with Jupiter. How could we distinguish those objects from comets at close encounters? At
Jupiter's distance to the Sun, we expect that comets would not show any trace of activity, making almost
impossible any observational distinction from asteroids. Therefore, if we do not have clear physical differences
we have to look for a dynamical criterion to separate these two samples.
The distribution of Tisserand parameters (T) for JF comets shows a concentration towards 3, and values
generally greater than 2.5 (TR). Remembering that the encounter velocity with jupiter (expressed in terms
of the planet's orbital velocity) is given by U 2 = 3 - T , we concluded that JF comets tend to have low
velocity encounters with Jupiter and their heliocentric orbital velocity is similar to that of Jupiter at the
time of the encounter. If we make the observations close to Jupiter's opposition, the vast majority of the
field asteroids will move with typical retrograde velocities of main belt objects, while the comets that are
experiencing a close encounter will have a slower motion, similar to that of Jupiter.
Fig. 6shows the hourly motion in a and 6of _7 I ' i i i I i , , , I i , i i 1£
all numbered asteroids with angular separation from 30 -- • --
Jupiter less than 10 ° (small dots) and the planet for _i
the 1992 opposition (29/2/1992). We computed the ,_-
mean relative velocities during the encounters for dif- _ 20
ferent JF comets that experienced encounters in the
last 40 yr. For comets with a minimum distance to
Jupiter < 0.5 AU, we found that the mean relative x_ 10
velocity had a median value of 6 km/s. As the previ-
ous value corresponds to a relative velocity in any di-
rection, we calculated the projected median velocity
on the sky plane averaging over all possible directions
(a factor of _ times the velocity). In Fig. 6 we drew a
full circle with radius corresponding to this projected
median velocity (5"/hr in the sky plane) and dashed
lines corresponding to the upper and lower quartiles.
Tracking the telescope on Jupiter we would find that
asteroids should show a trail on the order of 17" in
one hour exposure (0.25 mm with a plate-scale of 67.5"/mm), while comets should be more like point-sources.
The stars will appear as trails of 19" .7 (0.29 mm with the same scale-plate) but in opposite direction compared
to asteroids. Thereforel if we make the observations close to Jupiter's opposition and track the telescope on
the planet, we would be able to pinpoint very easily comets at close encounters.
...v'_:.:'.:
V. "_.",_. • ,_m..,
• ..":._._, _-'_
-40 -30 -20 -10
da ("/hr)
Fig. 6. Hourly motion in _ and6 ofa/1 numbered
asteroids (small dots) and Jupiter for 28/2/1992.
C-_rdes centered in Jupiter with radius correspond-
ing to different projected relative velocities are su-
perpcr, ed (see text).
b) The magnitude problem
The heliocentric distance of Jupiter ranges between 4.9 and 5.5 AU. The correction that we have to
introduce to the absolute magnitude to obtain the apparent magnitude depends on the particular circum-
stances of the opposition. We make our calculations for the 1992 opposition, when Jupiter wilI have an
heliocentric distance r# = 5.4 AU and geocentric distance pj = 4.4 AU. Assuming that at Jupiter's distance
from the Sun, the comet would look like a bare nucleus, we express the difference between apparent and
absolute nuclear magnitude Am = 5 Iog(rp) . For comets at close encounters we obtain a mean value of
604 Asteroids, Comets, Meteors 1991
Am = 7. If the telescope has a limiting magnitude of 21 - 23 in a 1-2 hours exposure, we could detect comet:
brighter than absolute nuclear H,,(1,0) _ 14 - 16.
Based on nucelar photographic magnitude determinations made by Roemer during 1960's and crater-
ing rates on Galitean satellites, Shoemaker and Wolfe (1982) developed an expression for the power law
distribution of number of comets (N) with brightness (Hn)
N(H, + AH,_) = 100.4AH. (1) .
N(H,_)
The size of the JF population is unknown and in fact, a search like the one proposed here could give a
better estimation of the number of JF comets. Previous estimations of the population size range from one
thousand (Shoemaker and Wolfe 1982) to a few (3-4) thousand objects (Fern£ndez et al. 1991) down to
nuclear magnitude H,_(1,0) = 17.5 and perihelion distance q < 5.5. Using eq. (1), the total number of comets
in the range of detectable nuclear magnitudes (14-16) could then range from 60 to 170 for H,(1,0) < 14 and
360 to 1000 for H,_(1,0) < 16: : =:
If we take plates covering a region out to a distance of 0.7 AU from Jupiter (a field of 20 ° x 20 ° centered
on Jupiter) and consider the values of the density of comets around Jupiter found before, we would expect
to find a comet with a probability of 60 % in the worst case (e.g. density of 0.6 comets at distances less than
0.5 AU, smallest population and observed limiting magnitude 21) up to 20 comets in the best alternative
(e.g density of 1.5, largest population and mag. 23).
The values of the number of comets at close encounters obtained before are only a lower limit to
the values that we would obtain during the observations because we are neglecting two other sources of
encountering objects. When we consider the observed population, we are taking into account very few cases
of comets moving between Jupiter and Saturn. This population of objects couldcontribute a lot to the
number of encounters, and we would expect a large number of objects belonging to this sample if a gradual
transfer of comets from the outer to the inner regions of the Solar System is assumed. Furthermore, there
is another population of objects that could increase the number of objects at close encounters: dormant
comets. As the magnitude distribution and the estimates of the population size were based on the observed
active short-period comets, dormant comets are not included in our estimations, and at Jupiter's distance
to the Sun, active and dormant comets would have a similar appearance.
Finally, we argue that a survey of comets during their close encounters with Jupiter could have important
consequences in several aspects dealing with the evolution of small bodies of the Solar System; e.g.:
* the size of the Jupiter-family population of comets
* the origin of comets and the effects of encounters with Jupiter in the transfer of comets from the outer to
the inner region of the Solar System
* the capture-hypothesis for the origin of the outer satellites of the outer planets.
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The vicinity of Jupiter: A region to look for comets

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