First published:
TJ
7(1):2–42
April 1993

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Moon dust and the age of the solar system

by Dr Andrew A. Snelling and David E. Rush

Introduction

One of the evidences for a young earth that creationists have been using now for more than two decades is the argument about the influx of meteoritic material from space and the so-called ‘dust on the moon’ problem. The argument goes as follows:

‘It is known that there is essentially a constant rate of cosmic dust particles entering the earth’s atmosphere from space and then gradually settling to the earth’s surface. The best measurements of this influx have been made by Hans Pettersson, who obtained the figure of 14 million tons per year.¹ This amounts to 14 x 10¹⁹ pounds in 5 billion years. If we assume the density of compacted dust is, say, 140 pounds per cubic foot, this corresponds to a volume of 10¹⁸ cubic feet. Since the earth has a surface area of approximately 5.5 x 10¹⁵ square feet, this seems to mean that there should have accumulated during the 5-billion- year age of the earth, a layer of meteoritic dust approximately 182 feet thick all over the world!

There is not the slightest sign of such a dust layer anywhere of course. On the moon’s surface it should be at least as thick, but the astronauts found no sign of it (before the moon landings, there was considerable fear that the men would sink into the dust when they arrived on the moon, but no comment has apparently ever been made by the authorities as to why it wasn’t there as anticipated).

Even if the earth is only 5,000,000 years old, a dust layer of over 2 inches should have accumulated.

Lest anyone say that erosional and mixing processes account for the absence of the 182-foot meteoritic dust layer, it should be noted that the composition of such material is quite distinctive, especially in its content of nickel and iron. Nickel, for example, is a very rare element in the earth’s crust and especially in the ocean. Pettersson estimated the average nickel content of meteoritic dust to be 2.5 per cent, approximately 300 times as great as in the earth’s crust. Thus, if all the meteoritic dust layer had been dispersed by uniform mixing through the earth’s crust, the thickness of crust involved (assuming no original nickel in the crust at all) would be 182 x 300 feet, or about 10 miles!

Since the earth’s crust (down to the mantle) averages only about 12 miles thick, this tells us that practically all the nickel in the crust of the earth would have been derived from meteoritic dust influx in the supposed (5 x 10⁹ year) age of the earth!’²

This is indeed a powerful argument, so powerful that it has upset the evolutionist camp. Consequently, a number of concerted efforts have been recently made to refute this evidence.^3-9 After all, in order to be a credible theory, evolution needs plenty of time (that is, billions of years) to occur because the postulated process of transforming one species into another certainly can’t be observed in the lifetime of a single observer. So no evolutionist could ever be happy with evidence that the earth and the solar system are less than 10,000 years old.

But do evolutionists have any valid criticisms of this argument? And if so, can they be answered?
Criticisms of this argument made by evolutionists fall into three categories:-

1. The question of the rate of meteoritic dust influx to the earth and moon,
2. The question as to whether NASA really expected to find a thick dust layer on the moon when their astronauts, landed, and
3. The question as to what period of time is represented by the actual layer of dust found on the moon.

Dust Influx to the Earth

Petterson’s Estimate

The man whose work is at the centre of this controversy is Hans Pettersson of the Swedish Oceanographic Institute. In 1957, Pettersson (who then held the Chair of Geophysics at the University of Hawaii) set up dust-collecting units at 11,000 feet near the summit of Mauna Loa on the island of Hawaii and at 10,000 feet on Mt Haleakala on the island of Maui. He chose these mountains because

‘occasionally winds stir up lava dust from the slopes of these extinct volcanoes, but normally the air is of an almost ideal transparency, remarkably free of contamination by terrestrial dust.’¹⁰

With his dust-collecting units, Pettersson filtered measured quantities of air and analysed the particles he found. Despite his description of the lack of contamination in the air at his chosen sampling sites, Pettersson was very aware and concerned that terrestrial (atmospheric) dust would still swamp the meteoritic (space) dust he collected, for he says: ‘It was nonetheless apparent that the dust collected in the filters would come preponderantly from terrestrial sources.’¹¹ Consequently he adopted the procedure of having his dust samples analysed for nickel and cobalt, since he reasoned that both nickel and cobalt were rare elements in terrestrial dust compared with the high nickel and cobalt contents of meteorites and therefore by implication of , meteoritic dust also.

Based on the nickel analysis of his collected dust, Pettersson finally estimated that about 14 million tons of dust land on the earth annually. To quote Petterson again:

‘Most of the samples contained small but measurable quantities of nickel along with the large amount of iron. The average for 30 filters was 14.3 micrograms of nickel from each 1,000 cubic metres of air. This would mean that each 1,000 cubic metres of air contains .6 milligram of meteoritic dust. If meteoritic dust descends at the same rate as the dust created by the explosion of the Indonesian volcano Krakatoa in 1883, then my data indicate that the amount of meteoritic dust landing on the earth every year is 14 million tons. From the observed frequency of meteors and from other data Watson (F.G. Watson of Harvard University) calculates the total weight of meteoritic matter reaching the earth to be between 365,000 and 3,650,000 tons a year. His higher estimate is thus about a fourth of my estimate, based upon theHawaiian studies. To be on the safe side, especially in view of the uncertainty as to how long it takes meteoritic dust to descend, I am inclined to find five million tons per year plausible.’¹²

Now several evolutionists have latched onto Pettersson’s conservatism with his suggestion that a figure of 5 million tons per year is more plausible and have thus promulgated the idea that Pettersson’s estimate was ‘high’,¹³ ‘very speculative’,¹⁴ and ‘tentative’.¹⁵ One of these critics has even gone so far as to suggest that ‘Pettersson’s dust- collections were so swamped with atmospheric dust that his estimates were completely wrong’¹⁶ (emphasis mine). Others have said that ‘Pettersson’s samples were apparently contaminated with far more terrestrial dust than he had accounted for.’¹⁷ So what does Pettersson say about his 5 million tons per year figure?:

‘The five-million-ton estimate also squares nicely with the nickel content of deep-ocean sediments. In 1950 Henri Rotschi of Paris and I analysed 77 samples of cores raised from the Pacific during the Swedish expedition. They held an average of. 044 per cent nickel. The highest nickel content in any sample was .07 per cent. This, compared to the average .008- per-cent nickel content of continental igneous rocks, clearly indicates a substantial contribution of nickel from meteoritic dust and spherules.

If five million tons of meteoritic dust fall to the earth each year, of which 2.5 per cent is nickel, the amount of nickel added to each square centimetre of ocean bottom would be .000000025 gram per year, or .017 per cent of the total red-clay sediment deposited in a year. This is well within the .044-per-cent nickel content of the deep-sea sediments and makes the five- million-ton figure seem conservative.’¹⁸

In other words, as a reputable scientist who presented his assumptions and warned of the unknowns, Pettersson was happy with his results.

But what about other scientists who were aware of Pettersson and his work at the time he did it? Dr Isaac Asimov’s comments,¹⁹ for instance, confirm that other scientists of the time were also happy with Pettersson’s results. Of Pettersson’s experiment Asimov wrote:-

‘At a 2-mile height in the middle of the Pacific Ocean one can expect the air to be pretty free of terrestrial dust. Furthermore, Pettersson paid particular attention to the cobalt content of the dust, since meteor dust is high in cobalt whereas earthly dust is low in it.’²⁰

Indeed, Asimov was so confident in Pettersson’s work that he used Pettersson’s figure of 14,300,000 tons of meteoritic dust falling to the earth’s surface each year to do his own calculations. Thus Asimov suggested:

‘Of course, this goes on year after year, and the earth has been in existence as a solid body for a good long time: for perhaps as long as 5 billion years. If, through all that time, meteor dust has settled to the earth at the same rate as it does, today, then by now, if it were undisturbed, it would form a layer 54 feet thick over all of the earth.’²¹

This sounds like very convincing confirmation of the creationist case, but of course, the year that Asimov wrote those words was 1959, and a lot of other meteoritic dust influx measurements have since been made. The critics are also quick to point this out -

‘… we now have access to dust collection techniques using aircraft, high-altitude balloons and spacecraft. These enable researchers to avoid the problems of atmospheric dust which plagued Pettersson.’²²

However, the problem is to decide which technique for estimating the meteoritic dust influx gives the ‘true’ figure. Even Phillips admits this when he says:

‘(Techniques vary from the use of high altitude rockets with collecting grids to deep-sea core samples. Accretion rates obtained by different methods vary from 10² to 10⁹ tons/year. Results from identical methods also differ because of the range of sizes of the measured particles.’²³

One is tempted to ask why it is that Pettersson’s 5-14 billion tons per year figure is slammed as being ‘tentative’, ‘very speculative’ and ‘completely wrong’, when one of the same critics openly admits the results from the different, more modern methods vary from 100 to 1 billion tons per year, and that even results from identical methods differ? Furthermore, it should be noted that Phillips wrote this in 1978, some two decades and many moon landings after Pettersson’s work!

Other Estimates, Particularly by Chemical Methods

In 1968, Parkin and Tilles summarised all the measurement data then available on the question of influx of meteoritic (interplanetary) material (dust) and tabulated it.²⁴ Their table is reproduced here as Table 1, but whereas they quoted influx rates in tons per day, their figures have been converted to tons per year for ease of comparison with Pettersson’s figures.

Even a quick glance at Table 1 confirms that most of these experimentally-derived measurements are well below Pettersson’s 5-14 million tons per year figure, but Phillips’ statement (quoted above) that results vary widely, even from identical methods, is amply verified by noting the range of results listed under some of the techniques. Indeed, it also depends on the experimenter doing the measurements (or estimates, in some cases). For instance, one of the astronomical methods used to estimate the influx rate depends on calculation of the density of the very fine dust in space that causes the zodiacal light. In Table 1, two estimates by different investigators are listed because they differ by 2-3 orders of magnitude.

On the other hand, Parkin and Tilles’ review of influx measurements, while comprehensive, was not exhaustive, there being other estimates that they did not report. For example, Pettersson²⁵ also mentions an influx estimate based on meteorite data of 365,000-3,650,000 tons/year made by F. G. Watson of Harvard University (quoted earlier), an estimate which is also 2-3 orders of magnitude different from the estimate listed by Parkin and Tilles and reproduced in Table 1. So with such a large array of competing data that give such conflicting orders-of-magnitude different estimates, how do we decide which is the best estimate that somehow might approach the ‘true’ value?

Another significant research paper was also published in 1968. Scientists Barker and Anders were reporting on their measurements of iridium and osmium concentration in dated deep-sea sediments (red clays) of the central Pacific Ocean Basin, which they believed set limits to the influx rate of cosmic matter, including dust.²⁶ Like Pettersson before them, Barker and Anders relied upon the observation that whereas iridium and osmium are very rare elements in the earth’s crustal rocks, those same two elements are present in significant amounts in meteorites.

Their results are included in Table 2 (last four estimates), along with earlier reported estimates from other investigators using similar and other chemical methods. They concluded that their analyses, when compared wit iridium concentrations in meteorites (C1 carbonaceous chondrites), corresponded to a meteoritic influx rate forth entire earth of between 30,000 and 90,000 tons per year. Furthermore, they maintained that a firm upper limit on the influx rate could be obtained by assuming that all the iridium and osmium in deep-sea sediments is of cosmic origin. The value thus obtained is between 50,000 and 150,000 tons per year. Notice, however, that these scientists were careful to allow for error margins by using a range of influx values rather than a definitive figure. Some recent authors though have quoted Barker and Anders’ result as 100,000 tons, instead of 100,000 ± 50,000 tons. This may not seem a rather critical distinction, unless we realise that we are talking about a 50% error margin either way, and that’s quite a large error margin in anyone’s language regardless of the magnitude of the result being quoted.

Even though Barker and Anders’ results were published in 1968, most authors, even fifteen years later, still quote their influx figure of 100,000 ± 50,000 tons per year as the most reliable estimate that we have via chemical methods. However, Ganapathy’s research on the iridium content of the ice layers at the South Pole²⁷ suggests that Barker and Anders’ figure underestimates the annual global meteoritic influx.

Ganapathy took ice samples from ice cores recovered by drilling through the ice layers at the US Amundsen-Scott base at the South Pole in 1974, and analysed them for iridium. The rate of ice accumulation at the South Pole over the last century or so is now particularly well established, because two very reliable precision time markers exist in the ice layers for the years 1884 (when debris from the August 26, 1883 Krakatoa volcanic eruption was deposited in the ice) and 1953 (when nuclear explosions began depositing fission products in the ice). With such an accurately known time reference framework to put his iridium results into, Ganapathy came up with a global meteoritic influx figure of 400,000 tons per year, four times higher than Barker and Anders’ estimate from mid-Pacific Ocean sediments.

In support of his estimate, Ganapathy also pointed out that Barker and Anders had suggested that their estimate could be stretched up to three times its value (that is, to 300,000 tons per year) by compounding several unfavorable assumptions. Furthermore, more recent measurements by Kyte and Wasson of iridium in deep-sea sediment samples obtained by drilling have yielded estimates of 330,000-340,000 tons per year.²⁸ So Ganapathy’s influx estimate of 400,000 tons of meteoritic material per year seems to represent a fairly reliable figure, particularly because it is based on an accurately known time reference framework.

Estimates via Aircraft and Spacecraft Methods

So much for chemical methods of determining the rate of annual meteoritic influx to the earth’s surface. But what about the data collected by high-flying aircraft and spacecraft, which some critics^29,30 are adamant give the most reliable influx estimates because of the elimination of a likelihood of terrestriat dust contamination? Indeed, on the basis of the dust collected by the high-flying U-2 aircraft, Bridgstock dogmatically asserts that the influx figure is only 10,000 tonnes per year.^31,32 To justify his claim Bridgstock refers to the reports by Bradley, Brownlee and Veblen,³³ and Dixon, McDonnel1 and Carey³⁴ who state a figure of 10,000 tons for the annual influx of interplanetary dust particles. To be sure, as Bridgstock says,³⁵ Dixon, McDonnell and Carey do report that ‘. ..researchers estimate that some 10,000 tonnes of them fall to Earth every year.’³⁶ However, such is the haste of Bridgstock to prove his point, even if it means quoting out of context, he obviously didn’t carefully read, fully comprehend, and/or deliberately ignored all of Dixon, McDonnell and Carey’s report, otherwise he would have noticed that the figure ‘some 10,000 tonnes of them fall to Earth every year’ refers only to a special type of particle called Brownlee particles, not to all cosmic dust particles. To clarify this, let’s quote Dixon, McDonnell and Carey:

‘Over the past 10 years, this technique has landed a haul of small fluffy cosmic dust grains known as “Brownlee particles” after Don Brownlee, an American researcher who pioneered the routine collection of particles by aircraft, and has led in their classification. Their structure and composition indicate that the Brown lee particles are indeed extra-terrestrial in origin (see Box 2), and researchers estimate that some 10,000 tonnes of them fall to Earth every year. But Brownlee particles represent only part of the total range of cosmic dust particles’³⁷ (emphasis mine).

And further, speaking of these ‘fluffy’ Brownlee particles:

‘The lightest and fluffiest dust grains, however, may enter the atmosphere on a trajectory which subjects them to little or no destructive effects, and they eventually drift to the ground. There these particles are mixed up with greater quantities of debris from the larger bodies that burn up as meteors, and it is very difficult to distinguish the two’³⁸ (emphasis ours).

What Bridgstock has done, of course, is to say that the total quantity of cosmic dust that hits the earth each year according to Dixon, McDonnell and Carey is 10,000 tonnes, when these scientists quite clearly stated they were only referring to a part of the total cosmic dust influx, and a lesser part at that. A number of writers on this topic have unwittingly made similar mistakes.

But this brings us to a very crucial aspect of this whole issue, namely, that there is in fact a complete range of sizes of meteoritic material that reaches the earth, and moon for that matter, all the way from large meteorites metres in diameter that produce large craters upon impact, right down to the microscopic-sized ‘fluffy’ dust known as Brownlee particles, as they are referred to above by Dixon, McDonnell, and Carey. And furthermore, each of the various techniques used to detect this meteoritic material does not necessarily give the complete picture of all the sizes of particles that come to earth, so researchers need to be careful not to equate their influx measurements using a technique to a particular particle size range with the total influx of meteoritic particles. This is of course why the more experienced researchers in this field are always careful in their records to stipulate the particle size range that their measurements were made on.

Figure 1. The mass ranges of interplanetary (meteoritic) dust particles as detected by various techniques (adapted from Millman³⁹). The particle penetration, impact and collection techniques make use of satellites and rockets. The techniques shown in italics are based on lunar surface measurements.

Millman³⁹ discusses this question of the particle size ranges over which the various measurement techniques are operative. Figure 1 is an adaptation of Millman’s diagram. Notice that the chemical techniques, such as analyses for iridium in South Pole ice or Pacific Ocean deep-sea sediments, span nearly the full range of meteoritic particles sizes, leading to the conclusion that these chemical techniques are the most likely to give us an estimate closest to the ‘true’ influx figure. However, Millman⁴⁰ and Dohnanyi⁴¹ adopt a different approach to obtain an influx estimate. Recognising that most of the measurement techniques only measure the influx of particles of particular size ranges, they combine the results of all the techniques so as to get a total influx estimate that represents all the particle size ranges. Because of overlap between techniques, as is obvious from Figure 1, they plot the relation between the cumulative number of particles measured (or cumulative flux) and the mass of the particles being measured, as derived from the various measurement techniques. Such a plot can be seen in Figure 2. The curve in Figure 2 is the weighted mean flux curve obtained by comparing, adding together and taking the mean at anyone mass range of all the results obtained by the various measurement techniques. A total influx estimate is then obtained by integrating mathematically the total mass under the weighted mean flux curve over a given mass range.

Figure 2. The relation between the cumulative number of particles and the lower limit of mass to which they are counted, as derived from various types of recording - rockets, satellites, lunar rocks, lunar seismographs (adapted from Millman³⁹). The crosses represent the Pegasus and Explorer penetration data.

By this means Millman⁴² estimated that in the mass range 10^-12 to 10³g only a mere 30 tons of meteoritic material reach the earth each day, equivalent to an influx of 10,950 tons per year. Not surprisingly, the same critic (Bridgstock) that erroneously latched onto the 10,000 tonnes per year figure of Dixon, McDonnell and Carey to defend his (Bridgstock’s) belief that the moon and the earth are billions of years old, also latched onto Millman’s 10,950 tons per year figure.⁴³ But what Bridgstock has failed to grasp is that Dixon, McDonnell and Carey’s figure refers only to the so-called Brownlee particles in the mass range of 10^-12 to 10^-6g, whereas Millman’s figure, as he stipulates himself, covers the mass range of 10^-12 to 10³g. The two figures can in no way be compared as equals that somehow support each other because they are not in the same ballpark since the two figures are in fact talking about different particle mass ranges.

Furthermore, the close correspondence between these two figures when they refer to different mass ranges, the 10,000 tonnes per year figure of Dixon, McDonnell and Carey representing only 40% of the mass range of Millman’s 10,950 tons per year figure, suggests something has to be wrong with the techniques used to derive these figures. Even from a glance at the curve in Figure 2, it is obvious that the total mass represented by the area under the curve in the mass range 10^-6 to 10³g can hardly be 950 or so tons per year (that is, the difference between Millman’s and Dixon, McDonnell and Carey’s figures and mass ranges), particularly if the total mass represented by the area under the curve in the mass range 10^-12 to 10^-6g is supposed to be 10,000 tonnes per year (Dixon, McDonnell and Carey’s figure and mass range). And Millman even maintains that the evidence indicates that two-thirds of the total mass of the dust complex encountered by the earth is in the form of particles with masses between 10^-6.5 and 10^-3.5g, or in the three orders of magnitude 10^-6, 10^-5 and 10^-4g, respectively,⁴⁴ outside the mass range for the so-called Brownlee particles. So if Dixon, McDonnell and Carey are closer to the truth with their 1985 figure of 10,000 tonnes per year of Brownlee particles (mass range 10^-12 to 10^-6g), and if two-thirds of the total particle influx mass lies outside the Brownlee particle size range, then Millman’s 1975 figure of 10,950 tons per year must be drastically short of the ‘real’ influx figure, which thus has to be at least 30,000 tons per year.

Millman admits that if some of the finer dust partlcles do not register by either penetrating or cratering, satellite or aircraft collection panels, it could well be that we should allow for this by raising the flux estimate. Furthermore, he states that it should also be noted that the Prairie Network fireballs (McCrosky⁴⁵), which are outside his (Millman’s) mathematical integration calculations because they are outside the mass range of his mean weighted influx curve, could add appreciably to his flux estimate.⁴⁶ In other words, Millman is admitting that his influx estimate would be greatly increased if the mass range used in his calculations took into account both particles finer than 10^-12g and particularly particles greater than l0³g.

Figure 3. Cumulative flux of meteoroids and related objects into the earth’s atmosphere having a mass of M(kg) (adapted from Dohnanyi⁴¹). His data sources used to derive this plot are listed in his bibliography.

Unlike Millman, Dohnanyi⁴⁷ did take into account a much wider mass range and smaller cumulative fluxes, as can be seen in his cumulative flux plot in Figure 3, and so he did obtain a much higher total influx estimate of some 20,900 tons of dust per year coming to the earth. Once again, if McCrosky’s data on the Prairie Network fireballs were included by Dohnanyi, then his influx estimate would have been greater. Furthermore, Dohnanyi’s estimate is primarily based on supposedly more reliable direct meas- urements obtained using collection plates and panels on satellites, but Millman maintains that such satellite penetration methods may not be registering the finer dust particles because they neither penetrate nor crater the collection panels, and so any influx estimate based on such data could be underestimating the ‘true’ figure. This is particularly significant since Millman also highlights the evidence that there is another concentration peak in the mass range 10^-13 to 10^-14g at the lower end of the theoretical effectiveness of satellite penetration data collection (see Figure 1 again). Thus even Dohnanyi’s influx estimate is probably well below the ‘true’ figure.

Representativeness and Assumptions

This leads us to a consideration of the representativeness both physically and statistically of each of the influx measurement dust collection techniques and the influx estimates derived from them. For instance, how representitive is a sample of dust collected on the small plates mounted on a small satellite or U-2 aircraft compared with the enormous volume of space that the sample is meant to represent? We have already seen how Millman admits that some dust particles probably do not penetrate or crater the plates as they are expected to and so the final particle count is thereby reduced by an unknown amount. And how representative is a drill core or grab sample from the ocean floor? After all, aren’t we analysing a split from a 1-2 kilogram sample and suggesting this represents the tonnes of sediments draped over thousands of square kilometres of ocean floor to arrive at an influx estimate for the whole earth?! To be sure, careful repeat samplings and analyses over several areas of the ocean floor may have been done, but how representative both physically and statistically are the results and the derived influx estimate?

Of course, Pettersson’s estimate from dust collected atop Mauna Loa also suffers from the same question of representativeness. In many of their reports, the researchers involved have failed to discuss such questions. Admittedly there are so many potential unknowns that any statistical quantification is well-nigh impossible, but some discussion of sample representativeness should be attempted and should translate into some ‘guesstimate’ of error margins in their final reported dust influx estimate. Some like Barker and Anders with their deep-sea sediments⁴⁸ have indicated error margins as high as ±50%, but even then such error margins only refer to the within and between sample variations of element concentrations that they calculated from their data set, and not to any statistical ‘guesstimate’ of the physical representativeness of the samples collected and analysed. Yet the latter is vital if we are trying to determine what the ‘true’ figure might be.
But there is another consideration that can be even more important, namely, any assumptions that were used to derive the dust influx estimate from the raw measurements or analytical data. The most glaring example of this is with respect to the interpretation of deep-sea sediment analyses to derive an influx estimate. In common with all the chemical methods, it is assumed that all the nickel, iridium and osmium in the samples, over and above the average respective contents of appropriate crustal rocks, is present in the cosmic dust in the deep-sea sediment samples. Although this seems to be a reasonable assumption, there is no guarantee that it is completely correct or reliable. Furthermore, in order to calculate how much cosmic dust is represented by the extra nickel, iridium and osmium con- centrations in the deep-sea sediment samples, it is assumed that the cosmic dust has nickel, iridium and osmium concentrations equivalent to the average respective concentrations in Type I carbonaceous chondrites (one of the major types of meteorites). But is that type of meteorite representative of all the cosmic matter arriving at the earth’s surface? Researchers like Barker and Anders assume so because everyone else does! To be sure there are good reasons for making that assumption, but it is by no means certain the Type I carbonaceous chondrites are representative of all the cosmic material arriving at the earth’s surface, since it has been almost impossible so far to exclusively collect such material for analysis. (Some has been collected by spacecraft and U-2 aircraft, but these samples still do not represent that total composition of cosmic material arriving at the earth’s surface since they only represent a specific particle mass range in a particular path in space or the upper atmosphere.)

However, the most significant assumption is yet to come. In order to calculate an influx estimate from the assumed cosmic component of the nickel, iridium and osmium concentrations in the deep-sea sediments it is necessary to determine what time span is represented by the deep-sea sediments analysed. In other words, what is the sedimentation rate in that part of the ocean floor sampled and how old therefore are our sediment samples? Based on the uniformitarian and evolutionary assumptions, isotopic dating and fossil contents are used to assign long time spans and old ages to the sediments. This is seen not only in Barker and Anders’ research, but in the work of Kyte and Wasson who calculated influx estimates from iridium measurements in so-called Pliocene and Eocene-Oligocene deep-sea sediments.⁴⁹ Unfortunately for these researchers, their influx estimates depend absolutely on the validity of their dating and age assumptions. And this is extremely crucial, for if they obtained influx estimates of 100,000 tons per year and 330,000-340,000 tons per year respectively on the basis of uniformitarian and evolutionary assumptions (slow sedimentation and old ages), then what would these influx estimates become if rapid sedimentation has taken place over a radically shorter time span? On that basis, Pettersson’s figure of 5-14 million tons per year is not far-fetched!

On the other hand, however, Ganapathy’s work on ice cores from the South Pole doesn’t suffer from any assumptions as to the age of the analysed Ice samples because he was able to correlate his analytical results with two time-marker events of recent recorded history. Consequently his influx estimate of 400,000 tons per year has to be taken seriously. Furthermore, one of the advantages of the chemical methods of influx estimating, such as Ganapathy’s analyses of iridium in ice cores, is that the technique in theory, and probably in practice, spans the complete mass range of cosmic material (unlike the other techniques - see Figure 1 again) and so should give a better estimate. Of course, in practice this is difficult to verify, statistically the likelihood of sampling a macroscopic cosmic particle in, for example, an ice core is virtually nonexistent. In other words, there is the question’ of representativeness again, since the ice core is taken to represent a much larger area of ice sheet, and it may well be that the cross sectional area intersected by the ice core is an anomalously high or low concentration of cosmic dust particles, or in fact an average concentration -who knows which?

Finally, an added problem not appreciated by many working in the field is that there is an apparent variation in the dust influx rate according to the latitude. Schmidt and Cohen reported⁵⁰ that this apparent variation is most closely related to geomagnetic latitude so that at the poles the resultant influx is higher than in equatorial regions. They suggested that electromagnetic interactions could cause only certain charged particles to impinge preferentially at high latitudes. This may well explain the difference between Ganapathy’s influx estimate of 400,000 tons per year from the study of the dust in Antarctic ice and, for example, Kyte and Wasson s estimate of 330,000-340,000 tons per year based on iridium measurements in deep-sea sediment samples from the mid-Pacific Ocean.

Further Estimates

A number of other workers have made estimates of the meteoritic dust influx to the earth that are often quoted with some finality. Estimates have continued to be made up until the present time, so it is important to contrast these in order to arrive at the general consensus.

In reviewing the various estimates by the different methods up until that time, Singer and Bandermann^5l argued in 1967 that the most accurate method for determining the meteoritic dust influx to the earth was by radiochemical measurements of radioactive Al26 in deep-sea sediments. Their confidence in this method was because it can be shown that the only source of this radioactive nuclide is interplanetary dust and that therefore its presence in deep-sea sediments was a more certain indicator of dust than any other chemical evidence. From measurements made others they concluded that the influx rate is 1250 tons per day, the error margins being such that they indicated the influx rate could be as low as 250 tons per day or as high as 2,500 tons per day. These figures equate to an influx rate of over 450,000 tons per year, ranging from 91,300 tons per year to 913,000 tons per year.

They also defended this estimate via this method as opposed to other methods. For example, satellite experiments, they said, never measured a concentration, nor even a simple flux of particles, but rather a flux of particles having a particular momentum or energy greater than some minimum threshold which depended on the detector being used. Furthermore, they argued that the impact rate near the earth should increase by a factor of about 1,000 compared with the value far away from the earth. And whereas dust influx can also be measured in the upper atmosphere, by then the particles have already begun slowing down so that any vertical mass motions of the atmosphere may result in an increase in concentration of the dust particles thus producing a spurious result. For these and other reasons, therefore, Singer and Bandermann were adamant that their estimate based on radioactive Al²⁶ in ocean sediments is a reliable determination of the mass influx rate to the earth and thus the mass concentration of dust in interplanetary space.

Other investigators continued to rely upon a combination of satellite, radio and visual measurements of the ‘different particle masses to arrive at a cumulative flux rate. Thus in 1974 Hughes reported⁵² that

‘from the latest cumulative influx rate data the influx of interplanetary dust to the earth’s surface in the mass range 10^-13 - 10⁶g is found to be 5.7 x 10⁹ g yr^-1’,

or 5,700 tons per year, drastically lower than the Singer and Bandermann estimate from Al²⁶ in ocean sediments. Yet within a year Hughes had revised his estimate upwards to 1.62 x 10¹⁰ g yr^-1, with error calculations indicating that the upper and lower limits are about 3.0 and 0.8 x 10¹⁰g yr^-1 respectively.⁵³ Again this was for the particle mass range between 10^-13g and 10⁶ g, and this estimate translates to 16,200 tons per year between lower to upper limits of 8,000 - 30,000 tons per year. So confident now was Hughes in the data he had used for his calculations that he submitted an easier-to-read account of his work in the widely-read, popular science magazine, New Scientist.⁵⁴ Here he again argued that

‘as the earth orbits the sun it picks up about 16,000 tonnes of interplanetary material each year. The particles vary in size from huge meteorites weighing tonnes to small microparticles less than 0.2 micron in diameter. The majority originate from decaying comets.’

Figure 4. Plot of thecumulative flux of interplanetary matter (meteorites, meteors, and meteoritic dust, etc.) into the earth’s atmosphere (adapted from Hughes⁵⁴). Note that he has subdivided the debris into two modes of origin - cometary and asteroidal - based on mass, with the former category being further subdivided according to detection techniqes. From this plot Hughes calculated a flux of 16,000 tonnes per year.

Figure 4 shows the cumulative flux curve built from the various sources of data that he used to derive his calculated influx of about 16,000 tons per year. However, it should be noted here that using the same methodology with similar data Millman⁵⁵ had in 1975, and Dohnanyi⁵⁶ in 1972, produced influx estimates of 10,950 tons per year and 20,900 tons per year respectively (Figures 2 and 3 can be compared with Figure 4). Nevertheless, it could be argued that these two estimates still fall within the range of 8,000 -30,000 tons per year suggested by Hughes. In any case, Hughes’ confidence in his estimate is further illustrated by his again quoting the same 16,000 tons per year influx figure in a paper published in an authoritative book on the subject of cosmic dust.⁵⁸

Meanwhile, in a somewhat novel approach to the problem, Wetherill in 1976 derived a meteoritic dust influx estimate by looking at the possible dust production rate at its source.⁵⁹ He argued that whereas the present sources of meteorites are probably multiple, it being plausible that both comets and asteroidal bodies of several kinds contribute to the flux of meteorites on the earth, the immediate source of meteorites is those asteroids, known as Apollo objects, that in their orbits around the sun cross the earth’s orbit. He then went on to calculate the mass yield of meteoritic dust (meteoroids) and meteorites from the fragmentation and cratering of these Apollo asteroids. He found that the combined yield from both crate ring and complete fragmentation to be 7.6 x 10¹⁰g yr^-l, which translates into a figure of 76,000 tonnes per year. Of this figure he calculated that 190 tons per year would represent meteorites in the mass range of 10² - 10⁶g, a figure which compared well with terrestrial meteorite mass impact rates obtained by various other calculation methods, and also with other direct measurement data, including observation of the actual meteorite flux. This figure of 76,000 tons per year is of course much higher than those estimates based on cumulative flux calculations such as those of Hughes,60 but still below the range of results gained from various chemical analyses of deep-sea sediments, such as those of Barker and Anders,61 Kyte and Wasson,⁶² and Singer and Bandermann,⁶³ and of the Antarctic ice by Ganapathy.⁶⁴ No wonder a textbook in astronomy compiled by a worker in the field and published in 1983 gave a figure for the total meteoroid flux of about 10,000 - 1,000,000 tons per year.⁶⁵

In an oft-quoted paper published in 1985, Griin and his colleagues⁶⁶ reported on yet another cumulative flux calculation, but this time based primarily on satellite measurement data. Because these satellite measurements had been made in interplanetary space, the figure derived from them, would be regarded as a measure of the interplanetary dust flux. Consequently, to calculate from that figure the total meteoritic mass influx on the earth both the gravitational increase at the earth and the surface area of the earth had to be taken into account. The result was an influx figure of about 40 tons per day, which translates to approximately 14,600 tons per year. This of course still equates fairly closely to the influx estimate made by Hughes.⁶⁷

As well as satellite measurements, one of the other major sources of data for cumulative flux calculations has been measurements made using ground-based radars. In 1988 Olsson-Steel⁶⁸ reported that previous radar meteor observations made in the VHF band had rendered a flux of particles in the 10^-6 - 10^-2g mass range that was anomalously low when compared to the, fluxes derived from optical meteor observations or satellite measurements. He therefore found that HF radars were necessary in order to detect the total flux into the earth’s atmosphere. Consequently he used radar units near Adelaide and Alice Springs in Australia to make measurements at a number of different frequencies in the HF band. Indeed, Olsson-Steel believed that the radar near Alice Springs was at that time the most powerful device ever used for meteor detection, and be- cause of its sensitivity the meteor count rates were extremely high. From this data he calculated a total influx of particles in the range 10^-6 - 10^-2g of 12,000 tons per year, which as he points out is almost identical to the flux in the same mass range calculated by Hughes.^69,70 He concluded that this implies that, neglecting the occasional asteroid or comet impact, meteoroids in this mass range dominate the total flux to the atmosphere, which he says amounts to about 16,000 tons per year as calculated by Thomas et al.⁷¹

In a different approach to the use of ice as a meteoritic dust collector, in 1987 Maurette and his colleagues⁷² reported on their analyses of meteoritic dust grains extracted from samples of black dust collected from the melt zone of the Greenland ice cap. The reasoning behind this technique was that the ice now melting at the edge of the ice cap had, during the time since it formed inland and flowed outwards to the melt zone, been collecting cosmic dust of all sizes and masses. The quantity thus found by analysis represents the total flux over that time period, which can then be converted into an annual influx rate. While their analyses of the collected dust particles were based on size fractions, they relied on the mass-to-size relationship established by Griin et al.⁷³ to convert their results to flux estimates. They calculated that each kilogram of black dust they collected for extraction and analysis of its contained meteoritic dust corresponded to a collector surface of approximately 0.5 square metres which had been exposed for approximately 3,000 years to meteoritic dust infall. Adding together their tabulated flux estimates for each size fraction below 300 microns yields a total meteoritic dust influx estimate of approximately 4,500 tons per year, well below that calculated from satellite and radar measurements, and drastically lower than that calculated by chemical analyses of ice.

However, in their defense it can at least be said that in comparison to the chemical method this technique is based on actual identification of the meteoritic dust grains, rather than expecting the chemical analyses to represent the meteoritic dust component in the total samples of dust analysed. Nevertheless, an independent study in another polar region at about the same time came up with a higher influx rate more in keeping with that calculated from satellite and radar measurements. In that study, Tuncel and Zoller⁷⁴ measured the iridium content in atmospheric samples collected at the South Pole. During each 10-day sampling period, approximately 20,000-30,000 cubic metres of air was passed through a 25-centimetre-diameter cellulose filter, which was then submitted for a wide range of analyses. Thirty such atmospheric particulate samples were collected over an 11 month period, which ensured that, seasonal variations were accounted for. Based on their analyses they discounted any contribution of iridium to their samples from volcanic emissions, and concluded that iridium concentrations in their samples could be used to estimate both the meteoritic dust component in their atmospheric particulate samples and thus the global meteoritic dust influx rate. Thus they calculated a global flux of 6,000 -11,000 tons per year.

In evaluating their result they tabulated other estimates from the literature via a wide range of methods, including the chemical analyses of ice and sediments. In defending their estimate against the higher estimates produced by those chemical methods, they suggested that samples (particularly sediment samples) that integrate large time intervals include in addition to background dust particles the fragmentation products from large bodies. They reasoned that this meant the chemical methods do not discriminate between background dust particles and fragmentation products from large bodies, and so a significant fraction of the flux estimated from sediment samples may be due to such large body impacts. On the other hand, their estimate of 6,000-11,000 tons per year for particles smaller than 10⁶g they argued is in reasonable agreement with estimates from satellite and radar studies.

Finally, in a follow-up study, Maurette with another group of colleagues⁷⁵ investigated a large sample of micrometeorites collected by the melting and filtering of approximately 100 tons of ice from the Antarctic ice sheet. The grains in the sample were first characterised by visual techniques to sort them into their basic meteoritic types, and then selected particles were submitted for a wide range of chemical and isotopic analyses. Neon isotopic analyses, for example, were used to confirm which particles were of extraterrestrial origin. Drawing also on their previous work they concluded that a rough estimate of the meteoritic dust flux, for particles in the size range 50-300 microns, as recovered from either the Greenland or the Antarctic ice sheets, represents about a third of the total mass influx on the earth at approximately 20,000 tons per year.

Conclusion

Over the last three decades numerous attempts have been made using a variety of methods to estimate the meteoritic dust influx to the earth. Table 3 is the summary of the estimates discussed here, most of which are repeatedly referred to in the literature.

Clearly, there is no consensus in the literature as to what the annual influx rate is. Admittedly, no authority today would agree with Pettersson’s 1960 figure of 14,000,000 tons per year. However, there appear to be two major groupings -those chemical methods which give results in the 100,000-400,000 tons per year range or thereabouts, and those methods, particularly cumulative flux calculations based on satellite and radar data, that give results in the range 10,000-20,000 tons per year or thereabouts. There are those that would claim the satellite measurements give results that are too low because of the sensitivities of the techniques involved, whereas there are those on the other hand who would claim that the chemical methods include background dust particles and fragrnentation products.

Perhaps the ‘safest’ option is to quote the meteoritic dust influx rate as within a range. This is exactly what several authorities on this subject have done when producing textbooks. For example, Dodd⁷⁶ has suggested a daily rate of between 100 and 1,000 tons, which translates into 36,500-365,000 tons per year, while Hartmann,⁷⁷ who refers to Dodd, quotes an influx figure of 10,000-1 million tons per year. Hartmann’s quoted influx range certainly covers the range of estimates in Table 3, but is perhaps a little generous with the upper limit. Probably to avoid this problem and yet still cover the wide range of estimates, Henbest writing in New Scientist in 1991⁷⁸ declares:

‘Even though the grains are individually small, they are so numerous in interplanetary space that the Earth sweeps up some 100,000 tons of cosmic dust every year.’⁷⁹

Perhaps this is a ‘safe’ compromise!

However, on balance we would have to say that the chemical methods when reapplied to polar ice, as they were by Maurette and his colleagues, gave a flux estimate similar to that derived from satellite and radar data, but much lower than Ganapathy’s earlier chemical analysis of polar ice. Thus it would seem more realistic to conclude that the majority of the data points to an influx rate within the range 10,000-20,000 tons per year, with the outside possibility that the figure may reach 100,000 tons per year.

Dust Influx to the Moon

Van Till et al. suggest:

‘To compute a reasonable estimate for the accumulation of meteoritic dust on the moon we divide the earth’s accumulation rate of 16,000 tons per year by 16 for the moon’s smaller surface area, divide again by 2 for the moon’s smaller gravitational force, yielding an accumulation rate of about 500 tons per year on the moon.’⁸⁰

However, Hartmann⁸¹ suggests a figure of 4,000 tons per year from his own published work,⁸² although this estimate is again calculated from the terrestrial influx rate taking into account the smaller surface area of the moon.

These estimates are of course based on the assumption that the density of meteoritic dust in the area of space around the earth-moon system is fairly uniform, an assumption verified by satellite measurements. However, with the US Apollo lunar exploration missions of 1969-1972 came the opportunities to sample the lunar rocks and soils, and to make more direct measurements of the lunar meteoritic dust influx.

Lunar Rocks and Soils

One of the earliest estimates based on actual moon samples was that made by Keays and his colleagues,⁸³ who analysed for trace elements twelve lunar rock and soil samples brought back by the Apollo 11 mission. From their results they concluded that there was a meteoritic or cometary component to the samples, and that component equated to an influx rate of 2.9 x 10^-9g cm^-2 yr^-l of carbonaceous-chondrite-like material. This equates to an influx rate of over 15,200 tons per year. However, it should be kept in mind that this estimate is based on the assumption that the meteoritic component represents an accumulation over a period of more than 1 billion years, the figure given being the anomalous quantity averaged over that time span. These workers also cautioned about making too much of this estimate because the samples were only derived from one lunar location.

Within a matter of weeks, four of the six investigators published a complete review of their earlier work along with some new data.⁸⁴ To obtain their new meteoritic dust influx estimate they compared the trace element contents of their lunar soil and breccia samples with the trace element contents of their lunar rock samples. The assumption then was that the soil and breccia is made up of the broken-down rocks, so that therefore any trace element differences between the rocks and soils/breccias would represent material that had been added to the soils/breccias as the rocks were mechanically broken down. Having determined the trace element content of this ‘extraneous component’ in their soil samples, they sought to identify its source. They then assumed that the exposure time of the region (the Apollo 11 landing site or Tranquillity Base) was 3.65 billion years, so in that time the proton flux from the solar -wind would account for some 2% of this extraneous trace elements component in the soils, leaving the remaining 98% or so to be of meteoritic (to be exact, ‘particulate’) origin. Upon further calculation, this approximate 98% portion of the extraneous component seemed to be due to an approximate 1.9% admixture of carbonaceous-chondrite-like material (in other words, meteoritic dust of a particular type), and the quantity involved thus represented, over a 3.65 billion year history of soil formation, an average influx rate of 3.8 x 10^-9gcm^-2 yr^-l, which translates to over 19,900 tons per year. However, they again added a note of caution because this estimate was only based on a few samples from one location.

Nevertheless, within six months the principal investigators of this group were again in print publishing further results and an updated meteoritic dust influx estimate.⁸⁵ By now they had obtained seven samples from the Apollo 12 landing site, which included two crystalline rock samples, four samples from core ‘drilled’ from the lunar regolith, and a soil sample. Again, all the samples were submitted for analyses of a suite of trace elements, and by again following the procedure outlined above they estimated that for this site the extraneous component represented an admixture of about 1.7% meteoritic dust material, very similar to the soils at the Apollo 11 site. Since the trace element content of the rocks at the Apollo 12 site was similar to that at the Apollo 11 site, even though the two sites are separated by 1,400 kilometres, other considerations aside, they concluded that this

‘spatial constancy of the meteoritic component suggests that the influx rate derived from our Apollo 11 data, 3.8 x 10^-9gcm^-2yr^-l, is a meaningful average for the entire moon.’⁸⁶

So in the abstract to their paper they reported that

‘an average meteoritic influx rate of about 4 x 10^-9 per square centimetre per year thus seems to be valid for the entire moon. ’⁸⁷

This latter figure translates into an influx rate of approximately 20,900 tons per year.

Ironically, this is the same dust influx rate estimate as for the earth made by Dohnanyi using satellite and radar measurement data via a cumulative flux calculation.⁸⁸ As for the moon’s meteoritic dust influx, Dohnanyi estimated that using ‘an appropriate focusing factor of 2,’ it is thus half of the earth’s influx, that is, 10,450 tons per year.⁸⁹ Dohnanyi defended his estimate, even though in his words it ‘is slightly lower than the independent estimates’ of Keays, Ganapathy and their colleagues. He suggested that in view of the uncertainties involved, his estimate and theirs were ‘surprisingly close’.

While to Dohnanyi these meteoritic dust influx estimates based on chemical studies of the lunar rocks seem very close to his estimate based primarily on satellite measurements, in reality the former are between 50% and 100% greater than the latter. This difference is significant, reasons already having been given for the higher influx estimates for the earth based on chemical analyses of deep- sea sediments compared with the same cumulative flux estimates based on satellite and radar measurements. Many of the satellite measurements were in fact made from satellites in earth orbit, and it has consequently been assumed that these measurements are automatically applicable to the moon. Fortunately, this assumption has been verified by measurements made by the Russians from their moon-orbiting satellite Luna 19, as reported by Nazarova and his colleagues.⁹⁰ Those measurements plot within the field of near-earth satellite data as depicted by, for example, Hughes.⁹¹ Thus there seems no reason to doubt that the satellite measurements in general are applicable to the meteoritic dust influx to the moon. And since Nazarova et al.’s Luna 19 measurements are compatible with Hughes’ cumulative flux plot of near-earth satellite data, then Hughes, meteoritic dust influx estimate for the earth is likewise applicable to the moon, except that when the relevant focusing factor, as outlined and used by Dohnanyi,⁹² is taken into account we obtain a meteoritic dust influx to the moon estimate from this satellite data (via the standard cumulative flux calculation method) of half the earth’s figure, that is, about 8,000-9,000 tons per year.

Lunar Microcraters

Apart from satellite measurements using various techniques and detectors to actually measure the meteoritic dust influx to the earth-moon system, the other major direct detection technique used to estimate the meteoritic dust influx to the moon has been the study of the microcraters that are found in the rocks exposed at the lunar surface. It is readily apparent that the moon’s surface has been impacted by large meteorites, given the sizes of the craters that have resulted, but craters of all sizes are found on the lunar surface right down to the micro-scale. The key factors are the impact velocities of the particles, whatever their size, and the lack of an atmosphere on the moon to slow down (or burn up) the meteorites. Consequently, provided their mass is sufficient, even the tiniest dust particles will produce microcraters on exposed rock surfaces upon impact, just as they do when impacting the windows on spacecraft (the study of microcraters on satellite windows being one of the satellite measurement techniques). Additionally, the absence of an atmosphere on the moon, combined with the absence of water on the lunar surface, has meant that chemical weathering as we experience it on the earth just does not happen on the moon. There is of course still physical erosion, again due to impacting meteorites of all sizes and masses, and due to the particles of the solar wind, but these processes have also been studied as a result of the Apollo moon landings. However, it is the microcraters in the lunar rocks that have been used to estimate the dust influx to the moon.

Perhaps one of the first attempts to try and use microcraters on the moon’s surface as a means of determining the meteoritic dust influx to the moon was that of Jaffe,⁹³ who compared pictures of the lunar surface taken by Surveyor 3 and then 31 months later by the Apollo 12 crew. The Surveyor 3 spacecraft sent thousands of television pictures of the lunar surface back to the earth between April 20 and May 3, 1967, and subsequently on November 20, 1969 the Apollo 12 astronauts visited the same site and took pictures with a hand camera. Apart from the obvious signs of disturbance of the surface dust by the astronauts, Jaffe found only one definite change in the surface. On the bottom of an imprint made by one of the Surveyor footpads when it bounced on landing, all of the pertinent Apollo pictures showed a particle about 2mm in diameter that did not appear in any of the Surveyor pictures. After careful analysis he concluded that the particle was in place subsequent to the Surveyor picture-taking. Furthermore, because of the resolution of the pictures any crater as large as 1.5mm in diameter should have been visible in the Apollo pictures. Two pits were noted along with other particles, but as they appeared on both photographs they must have been produced at the time of the Surveyor landing. Thus Jaffe concluded that no meteorite craters as large as 1.5 mm in diameter appeared on the bottom of the imprint, 20cm in diameter, during those 31 months, so therefore the rate of meteorite impact was less than 1 particle per square metre per month. This corresponds to a flux of 4 x 10^-7 particles m^-2sec^-1 of particles with a mass of 3 x 10^-8g, a rate near the lower limit of meteoritic dust influx derived from spacecraft measurements, and many orders of magnitude lower than some previous estimates. He concluded that the absence of detectable craters in the imprint of the Surveyor 3 footpad implied a very low meteoritic dust influx onto the lunar surface.

With the sampling of the lunar surface carried out by the Apollo astronauts and the return of rock samples to the earth, much attention focused on the presence of numerous microcraters on exposed rock surfaces as another means of calculating the meteoritic dust influx. These microcraters range in diameter from less than 1 micron to more than 1 cm, and their ubiquitous presence on exposed lunar rock sur- faces suggests that microcratering has affected literally every square centimetre of the lunar surface. However, in order to translate quantified descriptive data on microcraters into data on interplanetary dust particles and their influx rate, a calibration has to be made between the lunar microcrater diameters and the masses of the particles that must have impacted to form the craters. Hartung et al.⁹⁴ suggest that several approaches using the results of laboratory cratering experiments are possible, but narrowed their choice to two of these approaches based on microparticle accelerator experiments. Because the crater diameter for any given particle diameter increases proportionally with increasing impact velocity, the calibration procedure employs a constant impact velocity which is chosen as 20km/sec. Furthermore, that figure is chosen because the velocity distribution of interplanetary dust or meteoroids based on visual and radar meteors is bounded by the earth and the solar system escape velocities, and has a maximum at about 20km/sec, which thus conventionally is considered to be the mean velocity for meteoroids. Particles impacting the moon may have a minimum velocity of 2.4km/sec, the lunar escape velocity, but the mean is expected to remain near 20km/sec because of the relatively low effective crosssection of the moon for slower particles. Inflight velocity measurements of micron-sized meteoroids are generally consistent with this distribution. So using a constant impact velocity of 20km/sec gives a calibration relationship between the diameters of the impacting particles and the diameters of the microcraters. Assuming a density of 3g/cm³ allows this calibration relationship to be between the diameters of the microcraters and the masses of the impacting particles.

After determining the relative masses of micrometeoroids, their flux on the lunar surface may then be obtained by correlating the areal density of microcraters on rock surfaces with surface exposure times for those sample rocks. In other words, in order to convert crater populations on a given sample into the interplanetary dust flux the sample’s residence time at the lunar surface must be known.⁹⁵ These residence times at the lunar surface, or surface exposure times, have been determined either by Cosmogenic Al²⁶ radioactivity measurements or by cosmic ray track density measurements,⁹⁶ or more often by solar-flare particle track density measurements.⁹⁷

On this basis Hartung et al.⁹⁸ concluded that an average minimum flux of particles 25 micrograms and larger is 2.5 x 10^-6 particles per cm² per year on the lunar surface supposedly over the last 1 million years, and that a minimum cumulative flux curve over the range of masses 10^-12 - 10^-4g based on lunar data alone is about an order of magnitude less than independently derived present-day flux data from satellite-borne detector experiments. Furthermore, they found that particles of masses 10^-7 - 10^-4g are the dominant contributors to the cross-sectional area of interplanetary dust particles, and that these particles are largely responsible for the exposure of fresh lunar rock surfaces by superposition of microcraters. Also, they suggested that the overwhelming majority of all energy deposited at the surface of the moon by impact is delivered by particles 10^-6 - 10^-2g in mass.

A large number of other studies have been done on microcraters on lunar surface rock samples and from them calculations to estimate the meteoritic dust (micrometeoroid) influx to the moon. For example, Fechtig et al. investigated in detail a 2cm² portion of a particular sample using optical and scanning electron microscope (SEM) techniques. Microcraters were measured and counted optically, the results being plotted to show the relationship between microcrater diameters and the cumulative crater frequency. Like other investigators, they found that in all large microcraters 100-200 microns in diameter there were on average one or two ‘small’ microcraters about 1 micron in diameter within them, while in all ‘larger’ microcraters (200-1,000 microns in diameter), of which there are many on almost all lunar rocks, there are large numbers of these ‘smaller’ microcraters. The counting of these ‘small’ microcraters within the ‘larger’ microcraters was found to be statistically significant in estimating the overall microcratering rate and the distribution of particle sizes and masses that have produced the microcraters, because, assuming an unchanging impacting particle size or energy distribution with time, they argued that an equal probability exists for the case when a large crater superimposes itself upon a small crater, thus making its observation impossible, and the case when a small crater superimposes itself upon a larger crater, thus enabling the observation of the small crater. In other words, during the random cratering process, on the average, for each small crater observable within a larger microcrater, there must have existed one small microcrater rendered unobservable by the subsequent formation of the larger microcrater. Thus they reasoned it is necessary to correct the number of observed small craters upwards to account for this effect. Using a correction factor of two they found that their resultant microcrater size distribution plot agreed satisfactorily with that found in another sample by Schneider et al.¹⁰⁰ Their measuring and counting of microcraters on other samples also yielded size distributions similar to those reported by other investigators on other samples.

Fechtig et al. also conducted their own laboratory simulation experiments to calibrate microcrater size with impacting particle size, mass and energy. Once the cumulative microcrater number for a given area was calculated from this information, the cumulative meteoroid flux per second for this given area was easily calculated by again dividing the cumulative microcrater number by the exposure ages of the samples, previously determined by means of solar-flare track density measurements. Thus they calculated a cumulative meteoroid flux on the moon of 4 (±3) x 10^-5 particles m^-2 sec^-1, which they suggested is fairly consistent with in situ satellite measurements. Their plot comparing micrometeoroid fluxes derived from lunar microcrater measurements with those attained from various satellite experiments (that is, the cumulative number of particles per square metre per second across the range of particle masses) is reproduced in Figure 5.

Mandeville¹⁰¹ followed a similar procedure in studying the microcraters in a breccia sample collected at the Apollo 15 landing site. Crater numbers were counted and diameters measured. Calibration curves were experimentally derived to relate impact velocity and microcrater diameter, plus impacting particle mass and microcrater diameter. The low solar-flare track density suggested a short and recent exposure time, as did the low density of microcraters. Consequently, in their calculating of the cumulative micrometeoroid flux they assumed a 3,000-year exposure time because of this measured solar-flare track density and the assumed solar-track production rate. The resultant cumulative particle flux was 1.4 x 10^-5 particles per square metre per second for particles greater than 2.5 x 10^-10g at an impact velocity of 20km/sec, a value which again appears to be in close agreement with flux values obtained by satellite measurements, but at the lower end of the cumulative flux curve calculated from microcraters by Fechtig et al.

Figure 5. Comparison of micrometeoroid fluxes derived from lunar microcrater measurements (cross-hatched and labelled ‘MOON’) with those obtained in various satellite in situ experiments (adapted from Fechtig et al.⁹⁹) The range of masses/sizes has been subdivided into dust and meteors.

Unresolved Problems

Schneider et al.¹⁰² also followed the same procedure in looking at microcraters on Apollo 15 and 16, and Luna 16 samples. After counting and measuring microcraters and calibration experiments, they used both optical and scanning electron microscopy to determine solar-flare track densities and derive solar-flare exposure ages. They plotted their resultant cumulative meteoritic dust flux on a flux versus mass diagram, such as Figure 5, rather than quantifying it. However, their cumulative flux curve is close to the results of other investigators, such as Hartung et al.¹⁰³ Nevertheless, they did raise some serious questions about the microcrater data and the derivation of it, because they found that flux values based on lunar microcrater studies are generally less than those based on direct measurements made by satellite-borne detectors, which is evident on Figure 5 also. They found that this discrepancy is not readily resolved but may be due to one or more factors. First on their list of factors was a possible systematic error existing in the solar-flare track method, perhaps related to our present-day knowledge of the solar-flare particle flux. Indeed, because of uncertainties in applying the solar-flare flux derived from solar-flare track records in time-control led situations such as the Surveyor 3 spacecraft, they concluded that these implied their solar-flare exposure ages were systematically too low by a factor of between two and three. Ironically, this would imply that the calculated cumulative dust flux from the microcraters is systematically too high by the same factor, which would mean that there would then be an even greater discrepancy between flux values from lunar microcrater studies and the direct measurements made by the satellite-borne detectors. However, they suggested that part of this systematic difference may be because the satellite-borne detectors record an enhanced flux due to particles ejected from the lunar surface by impacting meteorites of all sizes. In any case, they argued that some of this systematic difference may be related to the calibration of the lunar microcraters and the satellite-borne detectors. Furthermore, because we can only measure the present flux, for example by satellite detectors, it may in fact be higher than the long-term average, which they suggest is what is being derived from the lunar microcrater data.

Morrison and Zinner¹⁰⁴ also raised questions regarding solar-flare track density measurements and derived exposure ages. They were studying samples from the Apollo 17 landing area and counted and measured microraters on rock sample surfaces whose original orientation on the lunar surface was known, so that their exposure histories could be determined to test any directional variations in both the micrometeoroid flux and solar-flare particles. Once measured, they compared their solar-flare track density versus depth profiles against those determined by other investigators on other samples and found differences in the steepnesses of the curves, as well as their relative positions with respect to the track density and depth values. They found that differences in the steepnesses of the curves did not correlate with differences in supposed exposure ages, and thus although they couldn’t exclude these real differences in slopes reflecting variations in the activity of the sun, it was more probable that these differences arose from variations in observational techniques, uncertainties in depth measurements, erosion, dust cover on the samples, and/or the precise lunar surface exposure geometry of the different samples measured. They then suggested that the weight of the evidence appeared to favour those curves (track density versus depth profiles) with the flatter slopes, although such a conclusion could be seriously questioned as those profiles with the flatter slopes do not match the Surveyor 3 profile data even by their own admission.,

Rather than calculating a single cumulative flux figure, Morrison and Zinner treated the smaller microcraters separately from the larger microcraters, quoting flux rates of approximately 900 0.1 micron diameter craters per square centimetre per year and approximately 10 -15 x 10^-6 500 micron diameter or greater craters per square centimetre per year. They found that these rates were independent of the pointing direction of the exposed rock surface relative to the lunar sky and thus this reflected no variation in the micrometeorite flux directionally. These rates also appeared to be independent of the supposed exposure times of the samples. They also suggested that the ratio of microcrater numbers to solar-flare particle track densities would make a convenient measure for comparing flux results of different laboratories/investigators and varying sampling situations. Comparing such ratios from their data with those of other investigations showed that some other investigators had ratios lower than theirs by a factor of as much as 50, which can only raise serious questions about whether the microcrater data are really an accurate measure of meteoritic dust influx to the moon. However, it can’t be the microcraters themselves that are the problem, but rather the underlying assumptions involved in the determination/estimation of the supposed ages of the rocks and their exposure times.

Another relevant study is that made by Cour-Palais,¹⁰⁵ who examined the heat-shield windows of the command modules of the Apollo 7 - 17 (excluding Apollo 11) spacecrafts for meteoroid impacts as a means of estimating the interplanetary dust flux. As part of the study he also compared his results with data obtained from the Surveyor 3 lunar-lander’s TV shroud. In each case, the length of exposure time was known, which removed the uncertainty and assumptions that are inherent in estimation of exposure times in the study of microcraters on lunar rock samples. Furthermore, results from the Apollo spacecrafts represented planetary space measurements very similar to the satellite-borne detector techniques, whereas the Surveyor 3 TV shroud represented a lunar surface detector. In all, Cour-Palais found a total of 10 micrometeoroid craters of various diameters on the windows of the Apollo spacecrafts. Calibration tests were conducted by impacting these windows with microparticles for various diameters and masses, and the results were used to plot a calibration curve between the diameters of the micrometeoroid craters and the estimated masses of the impacting micrometeoroids. Because the Apollo spacecrafts had variously spent time in earth orbit, and some in lunar orbit also, as well as transit time in interplanetary space between the earth and the moon, correction factors had to be applied so that the Apollo window data could be taken as a whole to represent measurements in interplanetary space. He likewise applied a modification factor to the Surveyor 3 TV shroud results so that with the Apollo data the resultant cumulative mass flux distribution could be compared to results obtained from satellite-borne detector systems, with which they proved to be in good agreement.

He concluded that the results represent an average micrometeoroid flux as it exists at the present time away from the earth’s gravitational sphere of influence for masses < l0^-7g. However, he noted that the satellite-borne detector measurements which represent the current flux of dust are an order of magnitude higher than the flux supposedly recorded by the lunar microcraters, a record which is interpreted as the ‘prehistoric’ flux. On the other hand he, corrected the Surveyor 3 results to discount the moon’s gravitational effect and bring them into line with the interplanetary dust flux measurements made by satellite- borne detectors. But if the Surveyor 3 results are taken to represent the flux at the lunar surface then that flux is currently an order of magnitude lower than the flux recorded by the Apollo spacecrafts in interplanetary space. In any case, the number of impact craters measured on these respective spacecrafts is so small that one wonders how statistically representative these results are. Indeed, given the size of the satellite-borne detector systems, one could argue likewise as to how representative of the vastness of interplanetary space are these detector results.