Fifteen new EA's (Earth approachers) have been discovered since September, among them the smallest asteroids on record: 1990 UN, 1991 BA, and 1991 JR, which are in the 10 to 100 m size range (Scotti et al. 1991b). For the first time, we can make estimates of the fluxes near the Earth of these small objects, thought to be the immediate parents of meteorites, from direct observation. In this paper, I show that for EA's larger than a few 100 m, the magnitude-frequency dependence we observe is consistent with the cumulative magnitude-frequency relation, m(H), established for the main belt asteroids. Assuming this relation extends to smaller sizes, however, the probability for discovering both 1990 UN and 1991 JR was 15 percent, and for discovering 1991 BA only 1 percent. Objects smaller than approx. 100 m are therefore increasingly overabundant compared to an extrapolation from larger objects, with the excess increasing with decreasing size. Near 10 m, the most probable flux near the Earth is two orders of magnitude higher. This is in agreement with the flux extrapolated from observations of bright meteors and fireballs. It is thus likely that processes other than collisional breakup of asteroidal material begin to supply the population of small objects near the Earth at sizes near 100 m. Tantalizing clues from spectral measurements and orbital associations suggest that these objects may be the debris from extinct, short-period comets

Rabinowitz, David L.

English

NASA Technical Reports Server

Asteroids, Comets, Meteors 1991, pp. 481-485 "_///o_ _- _ ¢_
Lunar and Planetary Institute, Houston, 1992 481
THE FLUX OF SMALL ASTEROIDS NEAR THE EARTH ,_
A__] D. L. Rabinowitz, Lunar and Planetary Laboratory /,_ ,,_
A-_:_.'_ _ "_. The University of Arizona, Tucson AZ 85721
Tom Gehrels, Jim Scotti, and I have been scanning for Earth approachers since
September of 1990. By Earth approacher (EA), I mean any object that approaches the sun to
within 1.3 astronomical units (AU). Information about our scanning technique has been
presented elsewhere in these proceedings (Sc otti et al. 1991a) and in other publications
(Rabinowitz 1991, Gehrels et al 1990).:We have discovered fifteen new EAs since
September, among them the smallest asteroicls on record: 1990 UN, 1991 BA, and 1991 JR,
which are in the 10 to 100m size range (Scotti et al. 1991b). For the first time, we can
make estimates of the fluxes near the Earth of these small objects, thought to be the
immediate parents of meteorites, from direct observation. In this paper, I show that for
EAs larger than a few 100m, the magnitude-frequency dependence we observe is
consistent with the cumulative magnitude-frequency relation, re(H), established for the
main belt asteroids. Assuming this relation extends to smaller sizes, however, the
probability for discovering both 1990 UN and 1991 JR was 15%, and for discovering 1991
BA only 1%. Objects smaller than -100m are therefore increasingly overabundant
compared to an extrapolation from larger objects, with this excess increasing with
decreasing size. Near 10m, the most probable flux near the Earth is two orders of
magnitude higher. This is in agreement with the flux extrapolated from observations of
bright meteors and fireballs. It is thus likely that processes other than collisional
breakup of asteroidal material begin to supply the population of small objects near the
Earth at sizes near 100m. Tantalizing clues from spectral measurements and orbital
associations suggest that these objects may be the debris from extinct, short-period
comets. ,'
_.._1.0 AU _ 2.0 AU
earthsun
III I I t
• • 3 km
Fig. 1. Opposition geometry at discovery for Earth approachers discovered with the
Spacewatch Telescope.
Discovery Geometry
A quick inspection of Fig.1 reveals that the larger EAs observed with the Spacewatch
telescope have an incremental size distribution that is nearly proportional d"3, where d is
diameter. The figure is to scale, and shows the position in the ecliptic plane relative to the
sun-earth line at the time of discovery for nearly all the EAs we have detected since
September of 1990. The circles representing each object scale linearly with the estimated
sizes. Notice that the the number of objects we find does not depend strongly on object
size. We have found EAs larger than 3 km as far as 2 AU from the earth, kin-sized objects
~1 AU away, objects of ~200m diameter -0.5 AU away, and smaller objects at nearer
distances. Since the maximum geocentric distance, A L, at which we can detect one of these
objects is nearly proportional to d, and the number we detect of a given size goes as AL3
https://ntrs.nasa.gov/search.jsp?R=19930010036 2020-03-17T07:29:16+00:00Z
482 Asteroids, Comets, Meteors 1991
(the search volume), the flatness of the spectrum we observe implies that the true
incremental size distribution is proportional to d -3. This same size distribution has been
determined for the main-belt population (van Houten et al. 1970).
Detailed Analysis
The size distribution revealed by Fig_l can be tested by a more rigorous analysis of
the EAs discovered with the Spacewatch Telescope. I use a computer to simulate an
arbitrarily large population of EAs with the same-distribution o_biial-elements, a, e,
and i, as the population of known EAs, but random arguments of perihelion and ascending
nodes. For each simulated EA, the computer assigns a random mean anomaly, solves for
position and velocity, and evaluates the offset from apparent to abs6lute magnitude, V-H.
Given an assumed form for re(H), it can then predict the incremental number of simulated
EAs, An(H), that would be observed with the Spacewatch Telescope as a function of H. I
then use the ratio of the actual number detected, AN(H), to the predicted number to
correct re(H) and arrive at the true magnitude-frequency for the Earth approachers, m*(H):
_ aN_E_
m*(H) - An(H) m(H) ( 1 )
This method of determining m*(H) is reliable to the extent that the orbits fo-r the known
EAs faithfully represent the true population. For example, an over-representation of
orbits which are near to the orbit of the Earth, such as Arch-type orbits with low
inclinations, would cause An(H) to be over-estimated for large H values; hence, an under-
estimate for m*(H). This is because the smallest objects are only observable near the
Earth.
In order to determine the cumulative impact rate at the Earth, F(H), I must normalize
the above expression for m*(H) by an independent estimate for the impact rate, F(Ho), at
some fixed absolute magnitude, Ho:
m*(H) F(no)
F(H)= m,(Ho) (2)
I can estimate F(Ho) from the discoveries of the Spacewatch Telescope with d > 1.0km
(H o < 20.0). Assuming the EAs have a constant velocity relative to the Earth, v, their
incremental impact rate at the Earth, 6F(I-I), is given by:
2
AF(I-I)= _(H) 4rip Kv (3)
where fl(H) is the volume of space searched in order to find the asteroids of magnitude H, p
is the radius of the Earth, and K is the flux enhancement due to gravitational attraction.
As discussed above, _(H),,AL3, and is the volume of a sphere with radius A L scaled by the
fraction of the sky Scanned by the Spacewatch Telescope. For the larger EAs observed near
opposition and far from the Earth, it is straight forward to calculate A L for the Spacewatch
Telescope as a function of H and the limiting magnitude,V L. Evaluating AFOT) for
magnitude intervals H-AH/2 to H+AH/2 and summing over the range spanned by the
observations represented =in Fig. i with H<H o yields F(Ho).
Asteroids, Comets, Meteors 1991 483
Results
Fig. 2 shows F, as determined by equations (1) - (3) with p=6400km, K=l.8 (Kres_k
1978), v= 20km/s (Shoemaker 1983), VL=20.5, and AH=2.5, plotted as a function of the
impacting mass, m (black squares). The vertical error bars show the uncertainty owing to
counting statistics. There is an additional systematic uncertainty of a factor of 2 owing to
the uncertainty in the calculated normalization, F(Ho)=4.6xl0"6y'l at Ho=18.8. I have
converted from F(H) to F(m) assuming uniform spheres with density 3500 kg/m 3 and
geometric albedo 0.12:1:0.07. The horizontal error bars show the uncertainty in this
transformation. Also shown in Fig. 2 are the "impact rates determined by other authors
from observations of bright meteors (Ceplecha 1988), photographic surveys for asteroids
(Shoemaker et al. 1990), and the size distribution of craters in lunar maria (Shoemaker
105
,..,
'_._
V
10 °
t"4
.n
10_5
i0 o
=.
1983).
diametei:(km) 0.01 0.03 0.10 0.30 1.0 3.0 10.0
I I I I I I I
l Spacewatch EAs
"'-- (this work)
bright meteors ra photographic ECAs
(Shoemaker et al 1990)
(Ceplecha 1988) _.
\ 4 `¸
_ " \T x"r\ comet fragments
m "065 _ -\_-_ '_ (Kresak 1978) 1
(Shoemaker 1983) "_'_ -1
105 101o 1015
mass (kg)
Fig. 2. The cumulative impact rate at the Earth as a function of impacting mass.
Examination of Fig. 2 shows that the values for F derived in this paper are within a
factor of 2 of the results of photographic surveys (Shoemaker 1990) near m=l.0xl012 and
3.2x1013 kg (d-lkm and d-2km, respectively). These estimates, and the estimates from
this paper for F at m=3.2x10 I0 and 1.0xl015 kg are fit well by a line with slope -0.65
(the solid line labeled "m "0"65" in the figure). This is the same m dependence seen in the
population distribution of the main-belt asteroids, and revealed by Fig. 1. For
m<3.2x1010 kg (d<lS0m), however, it is clear that the fluxes derived in this paper deviate
significantly from the main-belt relation, with values 3 and 100 times larger than an
m "0.65 extrapolation would predict at m=l.0xl09 and 1.0xl0 6 kg, respectively. A similar
deviation is seen in the fluxes derived from the size distribution of lunar craters,
beginning at m=3.2x1010 kg (d-200m) and continuing towards lower masses, but the
deviation is smaller. The greatest deviation from the m "0"65 extrapolation is shown by the
fluxes of bright meteors, which are more than two orders of magnitude higher for m<104
kg. An extrapolation of the meteor curve to larger masses matches the flux reported in
this paper at m=l.0xl06 kg.
484 Asteroids, Comets, Meteors 1991
In addition to the measured flux curves plotted in Fig. 2, there is a curve showing the
flux of cometary fragments predicted by Kresak (1978). As indicated by the vertical
arrows, this curve is an upper limit below 109 kg, and a lower limit above 109 kg. The
fluxes of Spacewatch EAs with masses < 1010 kg approach this upper limit, suggesting
that they are the cometary fragments envisioned by Kres_k. This suggestion is supported
by the orbital characteristics of 1991 BA (Q--3.77, q=0.71 i=2.0 °) and 1991 JR (Q=1.77,
q=l.04, i=10.1°). Though not decisively cometary, the orbit of 1991 BA explores the outer
reaches of the asteroid-belt. In this respect, it is similar to the orbit comet P/Encke. The
orbit of 1991 JR has been found to be clearly associated with the ¢_ Bobtes meteor stream
(J. Drummond, personal communication), wqfiich is a good indicati0n t_t its source is
cometary. 1991 JR also has a featureless C-type spectra (Mueller, 1991; E. Howell,
personal communication), like that of (3200)Phaethon, which has an F-type spectrum
(Tholen 1989) and is strongly associated with the Geminid meteor stream.
Conclusions
The Spacewatch Telescope is finding kilometer-sized Earth-approachers when they are
farther than 1AU from the earth and asteroids with diameters of 10to 100m within 0.1AU
of the Earth. A broad size spectrum has thus been sampled, allowing the first
determination of the magnltude-frequency relation, for the Earth-appr0aCher ::population
from direct observation. This relation is well described by a power law in mass with
exponent -0.65 for the cumulative distribution of asteroids larger than a few hundred
meters. This is the distribution observed for the main-belt asteroids, and it is therefore
likely that the larger Earth-approachers are collisionally derived from this population.
The number of smaller asteroids, however, is significantly enhanced above this power law
spectrum. At 10m they are 100 times more numerous. A possible explanation for this
over-abundance, supported by preliminary spectral measurements and orbital analysis, is
that small asteroids are mostly fragments of decayed comets.
note added in proof: Two more small EAs have recently been discovered with the
Spacewatch Telescope: 1991 _ (~25 to 50m) and 1991 TU (-10m). These discoveries reduce
the statistical uncertainties in the fluxes reported here for masses between 106 and 108
kg to less than a factor of 2.
Credit for the success of tile Spacewatch Telescope goes to T. Gehrels, J. Scotti,
R. McMillan and M. Perry at the Lunar and Planetary Laboratory (LPL). I also thank
B. Marsden at the Minor Planet Center, B. Mueller at Kitt Peak National Observatory,
E. Howell at LPL, and J. Drummond, formerly of LPL, whose efforts strengthened this work
considerably.
References
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Asteroids, Comets, Meteors 1991 485
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The flux of small asteroids near the Earth

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