By the end of 1990, 65 Venus-crossing asteroids were recognized; these represent 59 percent of the known Earth-crossing asteroids. Further studies, chiefly numerical integrations of orbit evolution, may reveal one or two more Venus crossers among the set of discovered asteroids. A Venus crosser was defined as an asteroid whose orbit can intersect the orbit of Venus as a result of secular (long range) perturbations. Venus crossers revolving on orbits that currently overlap the orbit of Venus are called Venapol asteroids, and those on orbit that don't overlap are called Venamor asteroids; 42 Venapols and 23 Venamors were recognized. Collision probabilities with Venus for 60 of the known Venus crossers were determined

Shoemaker, C. S.

Shoemaker, E. M.

Wolfe, R. F.

English

NASA Technical Reports Server

N92-10880
ASTEROID FLUX AND IMPACT CRATERING RATE ON VENUS. E.M. Shoemaker, R.F. Wolfe,
and C.S. Shoemaker, U.S. Geological Survey, Flagstaff, AZ 86001.
By the end of 1990, 65 Venus-crossing asteroids had been recognized (Table 1); these represent 59%
of the known Earth-crossing asteroids. Further studies, chiefly numerical integrations o[ oro, evolution, may
reveal one or two more Venus crossers among the set of discovered asteroids. We defne a Venus crosser as
an asteroid whose orbit can intersect the orbit of Venus as a result of secular (long range) perturbations. Venus
crossers revolving on orbits that currently overlap the orbit of Venus are here called Venapol asteroids, and those
on orbits that don't overlap are called Venamor asteroids; we recognize 42 Venapols and 23 Venamors.
Collision probabilities with Venus for 60 of the known Venus crossers have been determined by the
methods described in [1]. The mean collision probability with Venus is 6.2 x 109 y/l, which is 1.45 times the
mean collision probability of Earth-crossing asteroids with Earth [1]. Hence, the collision rate of asteroids on
Venus is 0.59 x 1.45 = 0.86 times the collision rate on Earth. The collision rate per unit area on Venus is
0.86 x 0.509 x 100 km2/0.460 x 10_ km 2 = 0.95 times the rate per unit area on Earth.
The cratering efficiency (for sufficiently large asteroids) is somewhat higher on Venus than on Earth,
owing partly to the higher rms impact speed of the asteroids and partly to the slightly lower surface gravity on
Venus. If we neglect atmospheric retardation, the average cratering efficiency is 1.14 times higher on Venus
than on Earth (as measured by relative crater diameters). This is equivalent to a correction to the cratering rate
of (1.14) 2"2r = 1.34 relative to the cratering rate on Earth. Hence, the nominal asteroid impact cratering rate
on Venus is 0.95 x 1.34 = 1.27 times the asteroid cratering rate on Earth. Before accounting for losses, we add
about 10% to the total asteroid cratering rate for the undiscovered Venus-crossing asteroids whose orbits lie
entirely inside the orbit of Earth and remain undetected in the conventional search programs. Thus, the total
(uncorrected) asteroid cratering rate on Venus is 1.1 x 1.29 = 1.4 times the rate on Earth.
Two corrections should be considered for asteroids impacting on Venus. First, extinct comets probably
should be eliminated. The ratio of extinct comets among Earth-crossing asteroids is very uncertain. No known
Earth crossers are D-type objects, but there is good presumptive evidence that a few dark asteroids (F-type and
C-type) are extinct comets (e.g., Phaethon, the source of the Geminid meteors, and 1986 JK, which appears
cometary from its radar properties). We estimate that about 10% of the Venus-crossing asteroids are extinct
comets that won't survive atmospheric passage (unless they are very large--10 km diameter or greater). This
reduces the cratering rate relative to Earth to about 1.27.
Secondly, a rough correction for atmospheric deceleration of projectiles can be made as follows.
Nominally, a 20-km-diameter crater on Venus is produced by an S-type asteroid 1.71 km in diameter. At an
average entrY2angle of 45', this body sweeps out a mass of atmosphere equivalent to about 92 kg cm 2/sin 45°
-- 130 kg cm" . The longitudinal mass at the stagnation point of a nominal S-type asteroid is 1.71 x 105 cmx
4 gm cm 3 = 410 kg crn "2. From conservation of momentum, the impact speed v_ will be v i = Yo x 410/
-" _ -, _.,, u.l 7 • 134f ! be onl 0 6 n 8'i times the efficmncv for the(410 + 1._0) = 0.,6v o, and the cratcring e ficien,._ ,_i, y ( .. _ • = .... i " ,
uncorrected velocity. The cratering rate will be reduced by the factor (0.85) 2"2r = 0.69. About 40% of the
craters are produced by S-type asteroids and the other 60% produced by C-type asteroids, which are larger but
have lower density than S-type [1]. At the same kinetic energy, the longitudinal mass of C-types is the same as
S-types and the correction for momentum transfer is the same. For crater production at 20-km diameter, the
asteroid cratering rate on Venus is 0.69 x 1.27 = 0.88 times the rate on Earth. With increasing crater diameter,
the relative rate increases; at 50-km crater diameter, the relative rate on Venus is 0.84 x 1.27 = 1.06 times the
rate on Earth. For craters >__20 km diameter, our best estimate of the asteroid impact cratering rate is
(3.7+_2.0) x l(115 km 2 yfl on Earth [1] and (3.3- + 1.8) x 10is km 2 yfl on Venus.
All except a few of the largest impact craters on Venus probably have been produced by asteroids, as
the atmosphere tends to shield the surface from impact of comets. Applying our estimate of the crater
production rate, we find an average crater retention age at 20 km crater diameter of 260 + 310, - 90 million years
for the Venusian surface imaged by the Venera spacecraft [2] and 240 + 290, - 85 million years for the portion
of the surface imaged by the Magellan spacecraft [3].
References: [1] Shoemaker, E.M., Wolfe, R.F., and Shoemaker, C.S., 1990, in Sharpton, V.L., and Ward, P.D.,
eds., Geol. Soc. America Spec. Paper 247, p. 155-170. [2] Schaber, G.G., Shoemaker, E.M., and Kozak, R.C.,
1987, Solar System Research, v. 21, p. 89-93. [3] Schaber, and 7 others, 1991, this volume. [4] Veeder amd 5
others, 1989, Astron. Jour., v. 97, p. 1211-1219. [5] Williams, J.G., 1969, Ph.D. Thesis, Univ. Calif. at Los Angeles,
270 p. [6] Shoemaker, E.M., Williams, J.G., Helin, E.F., and Wolfe, R.F., 1979, in Gehrels, T., ed. Asteroids:
Tucson, Univ. Ariz. Press, p. 253-282. [7] Opik, EJ., 1951, Proc. Roy. Irish Acad., v. 54A, p. 168-199.
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TABLE 1. VENUS-CROSSING ASTEROIDS:
N DLau q
kn AU
VNNAPOL ASTEROIDS
3200 Phiethon 14.65 4.9
1966 Icarus 16.45 0.9
2212 Nephalstol 14.0 "5
1990 UO 20.5 "0.2
1989 VA 27.0 "1
3830 1986 WA 15.5 "3
1990 SN 14.5 "2
2100 Re-Shalom 18.12 2.4
2340 Rather 20.2 (0.2)
3753 1986 TO 15.0 "3
1974 NA 14.0 "5
1984 KB 16.4 1.4
5025 P-L 15.9 "2
1854 Daedalus 15.02 (3.1)
1954 XA 10.9 "0.5
3362 Khufu 10.15 0.7
2201 OlJato 15.56 1.4
2101 Adonis 18.2 "1
1065 Cerberus 14.91 1.0
1990 NU 15.0 "3
4450 1987 ST 17.20 "1
1989 PB 17.2 "1
1979 XS 19.0 "0.5
4183 1959 LN 14.60 -4
4341 1987 NF 15.70 "3
1983 TF2 17.5 -1
4034 1986 PA 18.20 1
1981 NLdxs 16.9 "1
1937 UN 17.0 "1
1990 NO 14.0 "5
1989 QF 17.0 -1
1989 Ug 19.0 -0.5
1862 Apollo 10.23 1.4
1987 OA 10.5 "1
1988 EG 10.0 -1
3554 Anun 15.94 2.0
1990 VA 20.0 "0.3
1990 TG1 15.0 "3
4581 1989 PC 20.60 -0.2
3360 1981 VA 16.55 1.0
1989 UR 18.0 "1
2063 Nacchus 17.6 °1
VNNANOR ASTEROIDS
1990 NA 17.0 "1
1909 DA 18.0 "1
4197 1982 TA 15.40 1.8
3288 Seloucus 15.34 2.8
1990 UA 19.5 "0.4
1990 UQ 17.5 "1
1990 UR 23.5 "0.05
1988 VP4 15.5 "3
1983 LC 19.0 "0iS
1980 Xa 17.5 -1
1988 TA 21.0 "0.2
1980 WF 18.5 0.6
2329 Grebes 15.1 "3
1978 CA 17.8 1.9
2062 Aten 10.94 0.9
6743 P-L 17.3 "1
1950 DA 15.0 -2
1983 VA 14.5 "2
1973 NA 13.5 -3
1986 3K 19.0 "1
3752 Cxmillo 15.6 "2
2408 Seneca 17.57 0.9
1915 Quotaalcoatl 18.97 0.3
Note:
NAGNXTUDES, DXA/4ETERS CROSSING DEPTHS, AND COLLISION PARARNTERE
Depth • i dr/dt Tc P8 Po vi
AU IU dog &U 10qyr _ _ kn/s
10qyr 10Vyr
(0.24) ..... 1.271 (0.89) (22) ............... (2.2) (41)
0.1g| 0.596 1.078 0.818 15.0 1.9 5.32 2.3 3.9 38.0
0.139 0.653 2.143 0.890 8.74 25 0.83 0.82 2.1 18.3
0.285 0.485 1.134 0.785 21.0 2.1 4.73 1.2 2.4 34.9
(0.29) ..... 0.728 (0.60) (29) ............... (4.0) (29)
0.381 0.302 1.505 0.747 24.7 1.9 4.11 0.77 1.8 31.4
0.393 0.452 2.157 0.810 10.7 11 1.04 0.62 1.9 31.4
0.402 0.448 0.832 0.510 8.76 0.38 9.20 8.6 11 22.3
0.003 0.387 0.844 0.523 5.19 0.42 8.48 13 16 22.1
0.412 0.374 0.998 0.587 15.8 0.57 7.53 3.2 4.7 25.6
(0.42) ..... 1.775 (0.78) (30) ............... 11.03 (38)
0.429 0.485 2.221 0.807 3.27 14 0.76 1.7 8.2 29.2
(0.44) ..... (4.2) (0.90) 16.23 ............... (1.13 1313
0.451 0.218 1.461 0.691 20.1 1.3 3.91 1.2 2.1 28.6
0.471 0.308 0.777 0.394 4.41 0.21 10.0 23 23 27.8
0.479 0.302 0.990 0.518 7.76 0.44 7.36 7.1 9.3 21.4
0.511 0.302 2.174 0.765 1.38 7.4 0.09 3.8 8.0 15.4
0.513 0.345 1.875 0.727 2.09 3.4 1.58 4.8 8.9 34.4
0.522 0.216 1.080 0.517 14.4 0.40 6.81 4.0 5.1 22.0
0.543 0.202 1.622 0.665 29.4 ............... 2.4 2g.2
0.555 0.247 1.442 0.615 1.97 0.94 3.35 11 11 11.1
0.567 0.201 1.063 0.467 9.62 0.31 6.81 7.0 8.1 19,0
0.586 0.286 2.244 0.741 12.0 3.27 0.99 1.2 2.0 23.4
0.594 0.152 1.981 0.700 10.2 ............... 1.8 32.2
0.597 0.237 1.837 0.675 8.80 1.4 1.84 3.3 4.0 21,0
0.605 0.140 2.439 0.752 16.4 ............... 0.60 24,1
0.800 0.100 1.060 0.424 10.3 0.22 7.10 8.4 8.0 17.4
(0.42) ..... 1.778 (0.85) (40) ............... (1.5) (31)
0.627 0.185 1.639 0.617 6.87 0.70 2.58 5.4 4.0 19.1
0.638 0.126 1.806 0.573 32.2 0.11 4.81 6.2 2.4 27.$
0.640 0.142 1.255 0.445 5.73 0.22 5.88 14 14 18.1
0.443 0.132 0.915 0.297 1.94 0.12 8.97 59 42 13.7
0.052 0.147 1.471 0.557 7.30 0.36 3.44 8.0 7.5 17.9
0.458 0.140 1.490 0.558 13.5 0.26 3.50 4.2 0.7 10.0
0.445 0.124 1.270 0.474 3.14 0.22 4.81 24 lg 15,4
0.672 0.074 0.974 0.310 22.7 ............... 3.7 19.4
0.679 0.0g0 0.984 0.310 14.2 0.07 8.56 18 13 15.8
0.681 0.204 2.486 0.728 8.63 1.4 0.55 4.0 3.5 18.5
0.681 0.095 1.023 0,334 4.79 0.10 7.16 35 30 13.5
0.684 0.061 2.462 0.722 24.7 ............... 1.7 24.3
0.688 0.085 1.080 0.363 12.8 0.08 7.22 • 18 13 15.4
0.694 0.032 1.078 0.354 10.1 ............... 13 14.7
0.426 0.320 2.567 0.834 4.10 ............... 1.5 30.1
0.427 0.320 2.166 0.803 8.12 ............... 1.6 29.4
0.450 0.296 2.297 0.E04 13.7 ............... 0.80 29.5
0.685 0.081 2.032 0.843 4.73 ............... 0.68 17.0
0.088 0.058 1.721 0,400 1.30 ............... 8.1 15.5
0.491 0.054 1.571 0.540 4.51 ............... 4.0 15.6
0.492 0.034 1.709 0.Sg5 3.00 .............. 3.2 15.7
0.892 0.054 2.263 0.694 12.9 ............... 0.77 18.9
0.094 0.053 2.829 0,734 1.11 ............... 1.2 17.0
0.717 0.029 2.467 0,511 5.32 ............... 4.0 18.1
0.717 0.030 1.541 0.535 4.83 ............. 3.5 14.2
0.721 0.026 2.231 0.477 5.07 ............... 0.43 15.4
0.726 0.019 2.404 0,498 20.1 ............... 0.52 21.2
0.727 0.019 1.125 0.354 28.6 ............... 0.45 21.5
0.739 0.007 0.948 0.235 19.2 ............... 0.71 16.0
0.740 0.007 1.881 0.580 0.09 ............... 0.18 15.3
0.742 0.003 1.883 0.559 13.4 ............... 0.07 14.7
10.813 .................... Chxotlc orblt ..........
(0.88) .............................. * ..............
(0.90} .................... 5:2 ConmenaurabLlity ..........
(0.983 .............................................
(1.03) .................... 3:1 Commensurability ..........
(1.083 .................... 3:1 Connonsurshlltty .........
within each class (Vsnxpols end Venanors), asteroids ere listed in order of Increasing perihelion
distance: estimated perihelion st the time of Venus crossing 1s used to order *11 asteroids vith fornxlly
derived crossing depths. Other asteroids ere listed Jn order of current perihelion d/sisera.
H is absolute magnitude in the V band, as determined from observation by internationally adopted
formulae.
The colunn headed Dixn gives tha estimated disaster in k/IGniters. Accurately dsterntnod diameters,
based on infrared observations, have been taken chiefly from [d].Dixneters estimated from accurate
magnitudes, vhsre albedoa have been assumed on the basis Of epectrophotonetric classification, ore shorn In
parentheses. Approximate dioneters, vhere nxgnitude8 ere based on photographic observations xnd
spectrophotonitric class is unknovn, xre preceded by symbol ".
Perihelion distance, q, is et the ring of Venns crossing, except for vxl_es in parentheses,
vhich are osculating perihelion distances.
Depth As the creasing depth (the maximum overlap of the orbit of the asteroid vith the orbit
of Venus along the radius to the node) deternined from the theory of WLllions {5J.
The orbital elements s (soninsJor axis), • (eccentricity), sad i (inclination ulth respect tO
the invariable plane) and the derivative of the radius to the node, dr/dt, are eat/noted representative
vxlues at the tins of Venus crossing. Tc is the period of precasilon of the major axis vith respect to
the 11no of the nodes in the invariable plane. Ps is the pcobabllity of oo1115ion vLth Venus
calculated from thn aquation8 of Shoemaker *t el. |4|, xnd 9o is probability of collision vith Venus
calculated from the equations Of Opik (7|. Uncertain vo2ue8 ore ahovn In parentheses.
The colunn heeded vi glues the lnpact speed in kilometers per second, ¢otrespondln 9 to the
orbital elements 8horn for the tang of collision vith Venus. Collision 13 assumed to occnr et 0.723
AU for venxpo18 and at 0*744 AU for Vonenors.
39O


Asteroid flux and impact cratering rate on Venus

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