New calculations of the collision probabilities of asteroids and comets with Venus were carried out based on the orbits of the known Venus-crossing asteroids and comets. For comparison, asteroid and comet collision probabilities and cratering rates on the Earth and Moon were recalculated and the estimated cratering rates on Venus were normalized to those of the Earth

Shoemaker, Eugene M.

Wolfe, Ruth F.

English

NASA Technical Reports Server

CRATER PRODUCTION ON VENUS AND EARTH BY ASTEROID AND COMET IMPACT 
Eugene M, Shoemaker and R u t h  F, Wolfe, U.S, Geological Survey, 
Flagstaff ,  AZ 86001 
Observations of t he  impact-crater record on t he  surface of Venus 
obtained by means of t he  Venera 15 and 16 spacecraft  (Ivanov e t  a1 ,, 
1986; Basilevsky e t  a l e ,  i n  press)  have stimulated renewed i n t e r e s t  i n  
the  cra ter ing r a t e  on Venus (e.g., Schaber e t  a1 . , i n  press) .  
Accordingly, we have carr ied out new calcula t ions  of the  co l l i s i on  
probabi l i t i e s  of as teroids  and comets w i t h  Venus based on the  o rb i t s  of 
t he  known Venus-crossing as teroids  and comets. For comparison, we 
recal cul ated as teroid  and comet col 1 i si on probabi 1 i t i e s  and c ra te r ing  
ra tes  on t h e  Earth and Moon and normalized t he  estimated c ra te r ing  r a t e s  
on Venus t o  those of t he  Earth. 
Of 71 Earth-crossing as teroids  discovered through October 1986 (one 
more than reported by Shoemaker and Shoemaker, this volume), 48 
current ly  pass peri he1 ion ins ide  Ear th 's  o rb i t  and 24 pass peri he1 ion 
ins ide  t h e  o rb i t  of Venus. For these objects ,  approximate co l l i s i on  
probabi l i t i e s  w i t h  Earth and Venus can be calculated by means of Opik's 
(1951) equations, Because we use the  mean orb i ta l  elements of t he  Earth 
and Venus i n  these  equations, co l l i s i on  probabi l i t i e s  w i t h  t he  Earth can 
a1 so be cal cul ated f o r  th ree  addi t i  onal as teroids  t h a t  pass peri he1 ion 
ins ide  t h e  mean aphelion of Earth 's  orbi t .  
We a r e  primarily concerned here w i t h  ca lcula t ing the  re1 a t i  ve 
coll  i s ion and c ra te r ing  ra tes  on Venus and Earth; use of the  Opi k 
col l  is ion probabi 1 i t i e s  is expected t o  y ie ld  a sa t i s fac tory  prel iminary 
estimate of the  r e l a t i ve  cra ter ing r a t e s  from asteroid  impact on the  two 
pl anets,  A1 though Opi k Is equations 1 ead t o  s i  gni f icant  e r ro rs  f o r  the  
col 1 i s i  on probabi 1 i t  i es  of i ndi  v i  dual as teroids  (Shoemaker e t  a1 . , 
1979), t he  average probabi 1 i t y  of col 1 i si on with Earth cal cul ated from 
Opik's equations f o r  22 as teroids  is only 13% greater  than the  average 
obtained by much more rigorous methods. We have neglected the  
contribution t o  t h e  t o t a l  impact r a t e  on Earth of Earth-crossing Arnors 
and the  contribution t o  the  impact r a t e  on Venus of an analogous s e t  of 
as teroids  t ha t  have part-time overlap w i t h  the  o rb i t  of Venus. 
Coll i s ion probabi 1 i t i e s  f o r  these objects  can only be obtained by 
methods based on secular  perturbation theory; these  much more d i f f i c u l t  
cal cul a t i  ons have been deferred f o r  fu tu re  study. The part-time 
overlapping objects contr ibute  only about 25% of t he  t o t a l  impact ra te ;  
f o r  purposes of t h i s  prel imi nary invest igat ion,  we have assumed tha t  t h e  
proportion of t h e i r  contribution t o  t he  t o t a l  impact r a t e  i s  t h e  same on 
Earth and Venus. 
Cratering r a t e s  (number of c r a t e r s  per unit area per u n i t  time) 
have been deri  ved from col 1 i s i  on probabi 1 i t i  es  by methods described by 
Shoemaker and Wolfe (1982). Uncertainties about t he  t o t a l  popul at ion of 
impactors and t h e i r  physical propert ies do not a f f ec t  our r e su l t s ,  as  we 
report  only re1 a t  i ve c r a t e r i  ng e f f i c ienc ies  and re1 a t  i ve c r a t e r i  ng r a t e s  
(Tab1 e 1). We have assumed t h a t  the  d i s t r ibu t ion  of physical propert ies 
i s  the  same f o r  Venus- and Earth-crossing impactors. 
The new mean co l l  i s i  on probabi 1 i t y  w i t h  Earth calculated from 48 
Apollo and Aten as teroids  i s  80% higher than the  mean co l l i s ion  
probabi 1 i t y  found by Shoemaker e t  a l e  (1979) f o r  22 Apoll os and Atens. 
This increase is due chief ly  t o  the  discovery of several as teroids  
having unusually high col l  isi on probabi 1 i t i e s  w i t h  Earth, Half of t he  
https://ntrs.nasa.gov/search.jsp?R=19870014067 2020-03-20T10:30:45+00:00Z
t o t a l  probabil i ty of co l l i s i on  w i t h  Earth is  contributed by 12% of t he  
as teroids  in the  observed sample of Earth crossers.  Because t he  
d i s t r ibu t ion  of co l l i s ion  probabi l i t i e s  is strongly skewed, i t  is 
c r i t i c a l  l y  important t o  cont i nue surveys f o r  pl anet-crossi ng as teroids  
i n  order t o  obtain re1 i ab l e  estimates of both absolute and r e l a t i ve  
cra ter ing ra tes  on the  t e r r e s t r i a l  planets. 
The r e l a t i ve  as teroid  cra ter ing r a t e  shown i n  Table 1 f o r  Venus 
( ~ 0 . 9  times t he  c ra te r ing  r a t e  on Earth) is s t r i c t l y  applicable only t o  
c r a t e r s  large enough f o r  t he  shielding e f f ec t  of the  Venusian atmosphere 
t o  be considered negligible.  A correction should be appl ied t o  account 
f o r  an undiscovered c l a s s  of Venus-crossi ng as teroids  whose o rb i t s  a r e  
en t i r e ly  ins ide  the  o rb i t  of the  Earth. These as teroids  a re  expected t o  
have been captured by repeated encounters w i t h  Venus, just as Aten 
as teroids  have been captured i n  small o r b i t s  by combined encounters w i t h  
Earth and Venus. In t he  case of Earth, Atens account f o r  27% of t he  
t o t a l  estimated as teroid  impact-crateri ng ra te .  A simi 1 a r  but probably 
somewhat smaller contribution t o  t he  c ra te r ing  r a t e  on Venus can be 
expected from the  undiscovered c l a s s  of Venus-crossing as teroids .  We 
ten ta t ive ly  est imate t h e  t o t a l  as teroid  impact-crateri ng r a t e  on Venus 
a t  1.0 t o  1.1 times the  r a t e  on Earth. 
The re1 a t i  ve r a t e s  of c r a t e r  production by comet impact were 
evaluated from the  o rb i t s  of long period comets l i s t e d  by Marsden 
(1986). Calculations were made f o r  a1 1 Earth- and Venus-crossi ng comets 
having periods greater  than 20 years.  The c r a t e r  production on Earth 
and on Venus by impact of comets having shor te r  periods i s  su f f i c i en t l y  
small t o  be neglected, Orbits are  avai lable  from Marsden's catalog f o r  
a t o t a l  of 400 long period Earth-crossing comets; 255 of these comets 
a re  a l so  Venus crossers.  The r e l a t i ve  comet impact-cratering ra te  on 
Venus, calculated by the  methods described by Shoemaker and Wolfe 
(1982), is 1.14 times the  r a t e  on Earth (Table 1).  Again, th is  r a t e  
applies only t o  c r a t e r s  large  enough tha t  t he  shielding e f f ec t  of the  
Venusian atmosphere can be considered negl i gi bl e. Probably few, i f  any, 
c r a t e r s  smaller than about 100 km i n  diameter have been formed by comet 
impact on Venus (cf .  Melosh, 1981; Ivanov e t  a l . ,  1986; Basilevsky 
e t  a l . ,  i n  press). 
References 
Basilevsky, A.T., Ivanov, B.A., Burba, G.A., Chernaya, I.M., Kryuchkov, 
V.P., Nikolaeva, O.V., Campbell, D.B., and Ronca, L.B., i n  press:  
Proc. 17th Lunar and Planet. Sci. Conf., Jour. Geophys. Res. 
Ivanov, B,A., Basilevsky, A.T., Kryuchkov, V.P., and Chernaya, I,M,, 
1986: Proc. Lunar and Planet. Sci . Conf., Jour. Gephys, Res., 
V. 91, p. D413-430. 
Marsden, B.G.? 1986, Catalogue of cometary o rb i t s :  International  
Astronom~ cal Union, Cambridge, Massachusetts, 102 p. 
Melosh, H.J,, 1981: - i n  Multi-ring basins (P.H. Schultz and R.B. 
Merrill , Eds.) : Proc. Lunar Planet. Sci., 12A, p. 29-35. 
o p i k ,  E.J., 1951: Proc. Roy. I r i sh  Academy, Sect. A, v. 54, p. 165-199. 
Schaber, G.G., Shoemaker, E.M., and Kozak, R,C., i n  press: 
Ast ronomi chesky Vestni k and Sol a r  System Research. 
Shoemaker, E.Me, and Shoemaker, C,S. : Reports of the  NASA Planetary 
Geol ogy Program, 1986, Nat i onal Aeronautics and Space 
Administration Tech. Memo., t h i s  vol ume. 
Shoemaker, E.M., Williams, J.G., Helin, E.F., and Wolfe, R.F., 1979: i n  
Asteroids (T. Gehrel s,  Ed. ) : Uni v. Arizona Press, Tucson, ~ r i  z o n x  
p, 253-282. 
Shoemaker, E.M., and Wolfe, R.F., 1982: in  The s a t e l l i t e s  of Jup i t e r  
(D, Morrison, Ed.) :: Univ.  Arizona ~ E s s ,  Tucson, Arizona, p. 277- 
339 e 
Table 1. Crater production on Earth, Venus, and t h e  Moon by impact of 
as teroids  and long period comets 
N P V D R 
*2 km km/sec - 
Asteroid Impact 
Craters 
Earth 
Venus 
Moon 
Comet Impact 
Craters 
Earth 1.000 0.308X10-88 0 . 5 0 9 X 1 0 ~  57.7 1.00 1.00 
Venus 0.638 0.414 X 10" 0.460 X 10 64.3 1.09 1.14 
Moon 
N = Number of impactors overl apping o rb i t  of planet normalized t o  number 
overl appi ng o rb i t  of Earth. 
P = Mean probabil i ty of coll  i s i  on per year  per as teroid  o r  mean probabi 1 i t y  of 
col l  i si on per peri he1 ion passage per comet. 
A = Surface area of planet or t he  Moon. 
V = Root mean square impact velocity weighted according t o  probabil i t y  of 
col 1 i s i  on (atmospheric re tardat ion neglected) . 
D = Weighted mean diameter of c r a t e r  produced by impactor of a given mass 
normalized t o  diameter of c r a t e r  produced on Earth. D i s  applicable only 
a t  diameters g rea te r  than t he  threshold below which the  planetary 
atmospheres shie ld  t he  surfaces from c r a t e r  production. 
R = Crater-production r a t e  per unit  surface area normalized t o  c r a t e r  
production r a t e  on Earth. R is applicable only a t  diameters greater  than 
the  threshold below which the  planetary atmospheres shie ld  the  surfaces 
from c r a t e r  production. 
* Values of D and R calculated f o r  lunar c r a t e r s  smaller than threshold 
diameter f o r  c r a t e r  col l  apse (generally l e s s  than 20 km). 
+ Values of D and R calculated f o r  1 unar c r a t e r s  l a rger  than threshold 
diameter f o r  c r a t e r  collapse (generally greater  than 20 km). 


Crater production on Venus and Earth by asteroid and comet impact

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