DATING LUNAR SURFACE FEATURES BY USING CRATER FREQUENCIES* T. J. Kreiter

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1 DATING LUNAR SURFACE FEATURES BY USING CRATER FREQUENCIES* T. J. Kreiter Divisin f Space Sciences Jet Prpulsin Labratry Califrnia Institute f Technlgy INTRODUCTION Several theries have been advanced relating t the mdes f frmatin and the ages f lunar surface features. Baldwin has prpsed that the maria were frmed s early in lunar histry that nly a small fractin f the Archezic age had passed. 1 Accrding t Kuiper, Mare Imbrium resulted frm a majr impact ccurring nearly a billin years after the frmatin f the mn, 2 while Urey believes that the bmbardment causing Mare Imbrium ccurred between 3 and 4.5 billin years ag, 3 and Gld attributes the present surface f Mare Imbrium t erded materials that have accumulated ver the entire lunar histry. 4 The ages f certain lunar features have recently been estimated by Lyubarski, wh cmputed the number f meteritic bdies falling n the mn per year per square km under certain assumptins cncerning the velcity and mass distributins f the meterites. 5 In his investigatin, Lyubarski fund an age fr Mare Tranquilitatis f between 2 and 46 millin years and an age fr Mare Humrum f between 4 and 94 millin years. These estimates crrespnd t upper Cretaceus and early Tertiary perids. We have fllwed a smewhat different methd by which large craters and maria are dated by cmparing the number f craters f a given diameter per square km in these areas with the crrespnding number f craters in the cntinental areas. We have als assumed a cnstant and istrpic meteric influx n the mn. * This paper presents the results f ne phase f research carried ut at the Jet Prpulsin Labratry, Califrnia Institute f Technlgy, under cntract NASw-6, spnsred by the Natinal Aernautics and Space Administratin. 393

2 394 T. J. KREITER DATING METHOD Brwn has cllected extensive data n the recvered meteritic falls in such heavily ppulated areas as Japan, India, and western Eurpe. 6 He has determined the mass distributin fr bth stny and irn meterites, and cmputed the maximum and minimum number f falls per year fr the earth. These values have then been translated int lunar cllisin frequencies: Brwn s estimate fr the number f meterites f mass m (in grams) hitting the mn per year is 6.7 X 10 3 ^ 20 X IQ 3 m.8 m 0.S Use f this relatinship fr age determinatin, hwever, requires knwledge f the crrelatin between meteritic mass and crater diameter. Baldwin s crater diameter-energy relatinship 1 was derived frm subsurface bmb explsins : e = d d , where e is lg energy, expressed in small calries, and d is lg diameter, expressed in feet. In defining the upper and lwer limits fr the number f crater-prducing falls, meteritic velcities f 70 km/sec (velcity f impact fr mtin retrgrade t that f the earth-mn system) and 2.4 km/sec (lunar escape velcity) were used tgether with Brwn s relatinship. We thus btain Upper limit : n = d d 2, Lwer limit : n = d d 2, where n is the lgarithm f the number f craters per km 2 f diameter greater than r equal t a given value and d is the lgarithm f the crater diameter in feet. Wilkins has recrded innumerable craters n his 300-inch mn map, ne-tenth reductins f which appear in the bk by himself and Mre, The Mn. 1 In the present study, Plate XXIII f that vlume was used in the derivatin f the cntinental, r undisturbed, crater frequencies. This illustratin cvers abut 3 % f the mn s surface area and prtrays mre than 3000 craters. The Munt Wilsn 100-inch phtgraph f the suthern

3 DATING LUNAR SURFACE FEATURES 395 sectr f the mn, frm Ptlemaeus t the rim, was used as a qualitative check n the crater frequencies inferred frm Wilkins drawing. A study f the zne cvering 30 t 60 suth latitude and 0 t 20 east lngitude revealed clse t 900 craters. This area, which appears within Plate XXIII, is apprximately 1.02% f the mn s ttal surface area. The phtgraph was als f value in discriminating between debris, craters, and muntains n the drawing. Mare Imbrium appears in Plates IV, V, XV, and XVI f The Mn. Mre than 1000 craters were cunted within this circular area f abut 2.6% f the lunar surface. We have derived rim-t-rim diameters f the craters by scaling them frm the diameters f nearby craters given by Baldwin. 1 In Figure 1 we have pltted the bserved cumulative frequencies per km 2 f craters f diameter greater than r equal t a given value fr bth the cntinental and Mare Imbrium areas. The least-squares curves shwn were calculated using nly craters f diameter less than 30 km. Hwever, the smallest crater size measured n Wilkins mn map fr the cntinental and maria cunt Fig. 1. Observed impact frequencies.

4 I x IO' 1 p 1 IXIO CL < X Ql < tr e> si c CO L. n 5 r i j Il I I I I. I I I 11 I I I I I I I 11 I I I I.1 I L I I I I II I I L O x x <9 x x x z-uj> SU31VU0 - O TJ" _ O t 04 O CRATER DIAMETER, km CRATER DIAMETER, km Fig. 2. Crater cunts: left, cntinental regin; right, Mare Imbrium regin. 396

5 DATING LUNAR SURFACE FEATURES 397 was mitted because f uncertainty as t scaling. The expressins derived were : Cntinental : n = ^ d 2, Mare Imbrium : n = d d 2, where d is nw the lgarithm f the crater diameter expressed in kilmeters. If cntemprary meterite frequencies are greater than the minimum values prpsed by Brwn, the cntinental area crater frequency appears cnsistent with a unifrm rate f meteric bmbardment fr all f gelgical and selenlgical time (4.5 X 10 9 years). Öpik has recrded the diameters f mre than 800 craters ccurring in the western prtin f Mare Imbrium, using a 1919 Munt Wilsn phtgraph fr his study which cvered 1.2% f the lunar surface. 8 Integrated frequency curves (Fig. 1) and histgrams (Fig. 2) indicate that cunts made frm drawings agree fairly well with thse made frm phtgraphs. This is especially true fr craters between 5 and 25 km in diameter. We may calculate the age f Mare Imbrium frm the integrated frequency curves fr the cntinental and Mare Imbrium areas by the expressin : Age f Mare Imbrium = 4.5 X 10 9 Imbrmm. years. N Cntinental Frm the freging, it wuld appear that the age f Mare Imbrium is between ne and five hundred millin years. Un- dubtedly, many ther factrs culd have been cnsidered in this wrk : e.g., the variatin f crater frequencies with latitude and lngitude, a crrectin t the bserved crater cunts t take int accunt the fact that craters will be destryed by subsequent im- pacts, and a study f the statistical significance f fluctuatins in the small sample regin f the size-frequency curve. Such prb- lems will be investigated in the near future with the help f the lunar atlas recently published by Kuiper. 9 The writer is indebted t Mrs. Judith A. Sidwell, wh meas- ured and recrded the diameters f apprximately 5000 lunar craters.

6 398 T. J. KREIT ER 1 R. B. Baldwin, The Face f the Mn (Chicag: University f Chicag Press, 1949). 2 G. P. Kuiper, /. Gephys. Research, 64,1713, H. C. Urey, Sky and Tel., 15,108, T. Gld, in Vistas in Astrnautics, Vl. II, M. Alperin and H. F. Gregry, eds. (New Yrk: Pergamn Press, 1959), p K. A. Lyubarski, Missiles and Rckets, 6, N. 9, p. 30, H. Brwn, /. Gephys. Research, 65, 1679, H. P. Wilkins and P. Mre, The Mn (Lndn: Faber and Faber, 1955). 3 E. J. öpik, M.N.R.A.S., 120, 404, G. P. Kuiper, Phtgraphic Lunar Atlas (Chicag: University f Chicag Press, 1960).

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