We have considered those comets whose original orbits have been determined to be hyperbolic when only planetary perturbations are accounted for. It is found that formally unbound incident trajectories correlate most confidently with orbits that have small perihelion distances and move in a retrograde sense relative to planetary motion. Arguments are presented that these results are not due to measurement error or to selection effects. We conclude that the phenomenon is attributable to enhanced volatility leading to abnormally large nongravitational forces. Since the effect is absent in the prograde small-perihelia population, increased insolation is not the sole explanation. It is suggested that the significance of the retrograde correlation is connected with a larger energy of relative motion between retrograde comets and a population of prograde ecliptic meteoroids which impact the comet mantle exposing the underlying volatiles. The subsequent enhanced outgassing is the cause of the larger nongravitational forces

Matese, John J.

Whitman, Patrick G.

Whitmire, Daniel P.

English

NASA Technical Reports Server

Asteroids,Comets,Meteors1991,pp. 399402
LunarandPlanetaryInstitute,Houston,1992 399
Ng3?j  o7
COMET NONGRAVITATIONAL FORCES
AND METEORITIC IMPACTS
John J. Matese Patrick G. Whitman Daniel P. Whitmire
Department of Physics, The University of Southwestern Louisiana,
Lafayette, LA 7050_-_210
Abstract
We have considered those comets whose original orbits have been determined to be
hyperbolic when only planetary perturbations are accounted for. It is found that formally
unbound incident trajectories correlate most confidently with orbits that have small perihe-
lion distances and move in a retrograde sense relative to planetary motion. Arguments are
presented that these results are not due to measurement error or to selection effects. We
conclude that the phenomenon is attributable to enhanced volatility leading to abnormally
large nongravitational forces. Since the effect is absent in the prograde small-perihelia
population, increased insolation is not the sole explanation. It is suggested that the sig-
nificance of the retrograde correlation is connected with a larger energy of relative motion
between retrograde comets and a population of prograde ecliptic meteoroids which impact
the comet mantle exposing the underlying volatiles. The subsequent enhanced outgassing
is the cause of the larger nongravitational forces.
INTRODUCTION
The Oort effect [Oort 1950] is the tendency for near-parabolic comet energies to cluster in
a narrow, bound, range of values. When corrected for planetary perturbations, long-period
(> 200 yr) comets have _ 25% of their energies occurring in the upper 0.2% of the bound
range. An additional 10% are found to be unbound. The energy distribution of comets whose
orbit determinations have been designated as highest quality (class I) [Marsden 1989] is shown
in Fig. 1. These results are in reasonable agreement with the idea that the detected Oort
cloud is the external region of a contiguous comet distribution made observable by the actions
of the Galactic tidal torque [Heisler and Tremaine 1986; Duncan, Quinn and Tremaine 1987;
Matese and Whitman 1989]. The tidal torque is capable of explaining that part of the observed
distribution in the range 5 _< 1/a <_ 50 (in units of 10 -6 AU-1). In contrast, energies 1/a <<_0
(and 1/a > 50) require an alternative explanation. Matese et al. [1991] have discussed those
comets which have been determined to be hyperbolic originally. The question of interest is "Are
these comets truly hyperbolic in origen or, if not, what is the explanation for the erroneous
hyperbolic designation?"
POSSIBLE INTERPRETATIONS
• Hyperbolic designations are due to measurement error.
In Table 1 we list those comets for which the osculating value of 1/a is hyperbolic at a level
>_ 5× the formal measured error, $. Maxsden et al. [1978] have noted that the true measured
error may be as much as 3× the formal value. Therefore multiples _< 5 may not be significant
indicators of hyperbolic orbits. Matese et al. [1991] demonstrated that attributing unbound
https://ntrs.nasa.gov/search.jsp?R=19930010018 2020-03-17T07:29:45+00:00Z
400 Asteroids, Comets, Meteors 1991
k_
(1)
,D
(D
k4
,D
O
15
10
Oort Distribution
d
I A
I
"-- I |
_'-x. , I |
_, I
C.)I I
o_ I
OI I
,.Ol I
_I_1
.x=ll t
"_ i / X
_'_I
0 20
Class I
New
Comets
1000 40 x 60 80
1/a
FIG. 1. The observed distribution in reciprocal semimajor axis (units= 10 -_ AU -1) of new class I comets. Also
shown as a dashed curve is the Galactic tidal theory prediction in arbitrary units.
designations to measurement error can be rejected at a confidence level > 95% when "t" and
"F" statistics are considered. This conclusion holds for both class I and class H comets.
• Measurement errors for hyperbolic comets are badly underestimated.
Although true measurement errors _ 3x formal values cannot provide an explanation, the
results shown in Table 1 could be attributed to errors if formal values were underestimated by
factors >_ 10 for small-q retrograde comets. However, there is no reason to expect that this is
the case [Marsden, personal communication].
• The injection mechanism for these comets is distinct from the tidal torque.
One observes that the clearly hyperbolic comets have two distinguishing correlations; they
all have small perihelia and they all move in a retrograde sense relative to the Solar system
• planets. Injection fromthe outer Oort cloud by passing stars or other distant impulses cannot
_ explain the small-q preponderance. Nor can the correlations be explained if the comets were
interstellar in o_rigen. -.... -=-- :: ...............
• These comets are not truly hyperbolic originally but only appear to be because of the
neglect of nongravitational forces due to out-gassing, flaring or splitt(r_yT-== " -_
This has previously been suggested [Maxsden and Sekanina 1978] and is supported by the fact
that six of the seven comets listed in Table 1 have been noted to have physically split or to
have their orbit residuals significantly reduced by the inclusion of modeled nongravitational
forces. The suggestion is consistent with the small-q correlation but requires an explanation
for the correlation with retrograde orbits. Matese et al. [1991] have demonstrated that smaU-q
prograde comets-exlfibit no comparable hyperbolic tendency.
i
Asteroids, Comets, Meteors 1991 401
Table I. Comets That are Most Confidently Hyperbolic
Class Name
I
I
I
I
II
II
II 1960 II
a. known to have s
1895 IV
1953 II
1899 1
1957 III
1955 V
1989 XIX
1/a 4- 6 cos/ q
-172 4- 8 -0.784 0.192
-125 + 9 -0.125 0.778
-i09 4- 9 -0.832 0.327
-98 4- 6 -0.498 0.316
-727 4- 121 -0.301 0.885
-218 4- 34 -0.003 0.642
-135 4- 23 -0.937 0.504
)llt
b. residuals improved by modeling nongravitational forces
c. inconclusive improvement in residuals from modeling
Comment
a
c
a
b
a
b
b
COLLISIONAL SURFACE PROCESSING
We now argue that the distinction between small-q prograde and retrograde Oort cloud
comet energies occurs because in the latter case comet mantle processing will be increased due
to more energetic collisions with ecliptic plane material. In essence, impacts on small-q comets
are most important for their catalytic role in the creation of large nongravitational forces. It
has neen noted that neglecting nongravitational forces will induce a systematic error in the
estimate of the original energy causing it to appear more hyperbolic [Maxsden et al. 1978].
Marsden and Sekanina (1971) have suggested that physical splitting and erratic behavior
of coreless short-period comets could be attributed to the single impacts of an ecliptic plane
population of objects of mass ,,_ l0 s g if their spatial density was -,_ 2 x 10 -18 gcm -3. Such den-
sities are ,,_ 104x larger than is known to exist in the vicinity of the earth. We suggest instead
that at sufficiently high relative velocities the known meteoroidal population can indirectly
expose a significant fraction of the volatiles underlying a cometary mantle.
The relative velocity between a near-parabolic comet and material in a circular ecliptic-
plane orbit of radius r is
U(r)= V_ _3 _ _/8-_cos i
One observes that at r _ q relative velocities in the range 50-150 km s -1 occur for the comets
listed in Table 1. Following Marsden and Sekanina [1971], the meteoroidal mass required to
create a crater of diameter do in loose mantle material is
( U )-2100km s -1ra = 4 × 10-rdo3(cm: g.
The local meteoroidal distribution peaks at a mass ,,_ 10-5g [Griin et al. 1985]. Therefore
the bulk of the meteoroidal mass distribution is capable of exposing the underlying volatiles
in mantles of thickness h ,,_ do < 3cm if the impact velocity is comparable to that obtained for
the retrograde small-q hyperbolic comets that are listed in Table 1.
The impact flux (energy/area/time) on a comet surface due to meteoroids is _pmU 3 where
P,n is the spatial mass density of all objects > m. Leinert et hi. [1983] adopted a spatial dis-
tribution 0c r -1-3 exp(-2.11z/rl) , 0.1AU< r < 3AU. We have integrated the orbits to estimate
402 Asteroids, Comets, Meteors 1991
the impact energy per unit area inside 1 AU. For the four class I comets that are listed in
Table 1 the estimated values are (1.6, 0.04, 0.9, 0.5)×105 erg cm -2. At values ,,_ 105 erg cm -2
we see that a typical meteoroid of 10-Sg at a speed ,,_100 km s-1 will yield ,,_ one 3 cm diameter
crater per m 2 of comet surface. Thus _< one part in 10 3 of the underlying volatile surface can
be expected to be directly exposed (if the mantle thickness h _< 3 cm). Activity from such a
small fraction of the surface cannot, in itself, cause a large nongravitational force.
The nature of comet mantles is insumciently understood to allow a definitive analysis of the
growth (or healing) of impact-produced volatile crater areas. However a dimensional argument
suggests that if a crater of initial diameter do _ h does grow to diameter d >> h, the linear
growth time scale will be r _ pm_mled/_ where (_ is the time averaged mass flux from the
outgassing crater. For small-q, crater growth to d _ 100cm is suggested over time scales on
the order of days since ¢ is an extremely sensitive function of r. We emphasize that a number
of small craters would have their net area grow faster than a single crater with the same initial
area. Marsden [1989] has listed 17 class I new comets whose perihelia are inside 1 AU. Of this
number 8 are retrograde and half of these are clearly hyperbolic. We infer that the probability
that a retrograde small-q Oort cloud comet will have its surface processed sufficiently to induce
1detectable nongravitational effects is _ 1 while that of a prograde smaU-q comet is < 6.
The authors would like to acknowledge the support of a NASA/Ames University Consortium
Grant and a grant from the Louisiana Education Quality Support Fund.
!
|
References
[1] Duncan M., Quinn T. and Tremaine S. (1987) The formation and extent of the Solar
System comet cloud. Astron. J., 94, 1330_1338.
[2] Heisler J. and Tremaine S. (1986) Influence of the Galactic tidal field on the Oort cloud.
icarus, 6_,13-26. _
_[3] Marsden B:CI: (1989) Catalogue of Cometary Orbits 6th edn/Smithsonian Astrophysical
Observat0ry, Cambridge,
[4] Marsden B.G. and Sekanina Z. (1971) Comets and nongravitational forces. IV. Astron. J.,
76, 1135:1151.
[5] Marsden B.G., Sekanina Z. andEverhart E. (1978) New osculating orbits for 110 comets
and analysis of original orbits for 200 comets. _stron. J., 83, 64-71.
[6] Matese J.J. and Whitman P.G. (1989)The Galactic disk tidal field and the nonrandom
distribution 0f observed oort _cl0ud comets. Icarus_, 82, 380-40i.
[7] Matese J.J., Whitman P.G. and Whitmire D.P. (1991) Gravitationally unbound comets
move in predominantly retrograde orbits. Nature, 352, 506'508.
[8] Oort J'H._(i_50) The structure of the cloua of comets surrounding the solar system, and
a hypothesis concerning its structure. Bull. Astron. Inst. Neth., 1__!,91-110. L.
[9] Griin E., Zook H-A.I Fechtig H. and Giese R]H. (1985) Comsional balance of the meteoritic
complex. _, 62, 244-272.
[10] Leinert C., RSser S. and 8uitriagoJ. (1983)rlow to maintain the spatial distribution of
interplanetary dust. Astron. Astrophys., 118, 3452357. _ z_-
r


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