Asteroid Impact

I’ve for some time wondering how often space debris impacts on the earth. We have a problem that the earth is constantly wearing down the evidence through weathering, so that even massive impacts are concealed by nature. We only have a very limited history of recorded impacts and observation, most being in the last 200 years. Before then there were very few recorded events unless they were pretty remarkable. Even in the past 200 years they have been sketchy. Add weathering and they soon disappear.

The Chicxulub impact that is supposed to have caused a mass extinction of the dinosaurs, an impact that seems to be seen in the K-P boundary (K-Pg, Cretaceous-Paleogene), formerly known as the artist K-T boundary (Cretaceous-Tertiary), was only discovered by chance by petrochemical geophysicists Glen Penfield and Antonio Camargo in 1978, looking for new resources with an airborne magnetic survey. The formation was noticed by Robert Baltosser 10 years earlier, but the disclosure was denied publicity by the firm paying for it. The KP boundary is of course all nuts to some people, as chance doesn’t always happen by chance, even if you see the discarded wrapper, and wasn’t really accepted to consensus until about 1990.

It’s said that the universe started about 13.8 billion years ago, but that is now under review due to recent evidence, and the earth was formed about 4.54 billion years ago. During this time the main view is that there were periods of intense bombardment that has since long disappeared, or have they?

4.54 billion years is a long time and nobody is sure of the concentration of bombardments, as there is no real evidence apart from the view of bodies like the moon. With the moon we have an advantage, as it’s a pretty airless and relatively undisturbed environment, all we need to do is to investigate its characteristics and scale it to earthly standards.

We are constantly being bombarded by space dust and junk mail, most of it not reaching the ground before disappearing completely, but some of it does manage to pass through the atmospheric filter and reach the ground if it has enough mass. It’s said that the earth can get hit by as much as 50,000 tonnes a year of the stuff, but there is no decent record of the amounts, so to give an idea of impacts we need to turn to a body that has little atmosphere such as the moon. Mars has an atmosphere closer to the moon’s, at 1/100th that of earth’s, and is mainly carbon dioxide, but that still causes a massive amount of friction at the speeds these fly at; 25,000 to 160,000 miles an hour.

When things are travelling 25,000-160,000 miles an hour it takes a lot to change their minds and go in another direction. In the case of the moon there is a real chance that some useless object such as a big planet gets in the way of a truly spectacular impact, and it gets the benefit instead, so we have a problem with moon nearside line of flight, but a more tragic trajectory.

On the earth we have a much bigger cross section to aim at to the moon. The diameter of the moon is only 1737km in diameter, has a surface area of 3.8 x 10^7 km2 and a volume of about 2.2 x 10^10 km3, coming in at 3.34gm/cm3, so has an approximate mass of 7.3 x 10^22kg and is closer to an average asteroid or meteorite density of 3.5gm/cm3, compared to the earth’s 6,371km diameter, 5.1 x 10^8 km2 area, 1.08 x 10^12 km3 volume and density of 5.52gm/cm3. So, the difference in half sphere cross section or target is 13.45 times as large for the earth. We can probably ignore the gravitational influence at distance as there is not really a relevant vector change unless the object is quite close and will probably hit the earth or moon anyway, it’s just a matter of where, by a matter of miles. The corridor for the difference between a close miss and a hit is very small, that’s why returning spacecraft need to be exact, as a fraction of a degree off can cause completely different outcomes. With the earth’s 300km effective atmosphere, it can cause things to bounce off it, but usually the difference is within a 20-mile band, so you could say that earth’s capture area is half of 5.1 x 10^8 km2, the extra atmosphere would add maybe 1% to this target.

The other problem is that there may be a difference between the early stages of the solar system and now, with various periods of bombardment taking place early on. These bombardments are likely to have taken place, but there is always the possibility that they did not, and there was a gradual bombardment that is higher at some stages than others. We are not sure that the earth is subject to a specific and unique kind of formation, the earth and moon being an almost unique situation. Other possibilities is concentric fields of debris and others giving figure 8 capture and transfers between boundaries in our solar systems rotation around the galaxy.

So, onto the moon. What you notice when you look at the moon is that it’s really just a big rock in the sky that floats there in the way that earth rocks don’t. The reason is inertia. The mass of the moon is travelling fast, in distant freefall around the earth, or a point that is in the earth, but off centre by the difference in mass ratios, travelling at a speed so that it keeps on missing the earth as it changes its angle, and having very little stuff in front to slow it down, but still showing some attraction after all these years, even if it is waning a bit. Orbits and free-fall are worse than watching two drunks fighting, spending most of the time missing each other in very wide swings. The moon is slowly moving onto new pastures at about 1.5 inches a year, and it’s only a matter of time before it’s attracted to some other body. It keeps the same face to the earth, and this slowing down of body mass to body mass and more brilliant neighbours’ attraction, it may be another 140,000 miles farther out or more in double the earth’s age, if earth makes it off the solar toasting fork.

So, the moon is more pockmarked than many bad guys in the movies. But if you look at them closely they don’t like it. So, studying the moon instead, you find that there are really big craters and smaller ones within each crater. Look closer and you find craters, within craters, within craters. It must be all done with mirrors and goes on endlessly. You have some fresh ones, and are mostly flat, but if you count the consistency of each size you find there is a relationship in the diameters that seems to fit a general curve.

This is where the mundane spending hours looking at black and white pictures of the moon’s surface and drawing endless circles around the curves takes off. A poor man’s spirograph. You could use a computer to do it, but most computers are too intelligent to take the job on. Complicated and important stuff they do; looking at stuff, guessing and estimating, that’s human work; and beneath them. If you get hold of photographs of untrod and undisturbed moon surface that the astronauts took, you can see the scale of tiny craters with microcraters inside that continues to a microscopic level.

The moon takes 27.3 days to travel around the earth, and probably formed about 4.5 billion years ago, maybe 400 million years after the earth, and it’s guessed that it was probably due to and early one of the sorts of collisions we are talking about. But most of the surface is probably around 3.3 billion years old, so we can do a count of each type and estimate its bombardment over a 3.3 billion year period. A useful calculation is the difference between the far side of the moon and the near side, as the near side receives a very small amount of protection when shielded by its bigger brother, but the far side doesn’t receive any. An estimate would be in the region of 5% difference between sides.

The astronauts discovered smaller craters fill with the dust that is constantly falling on its surface at a rate of about 1mm every 1,000 years, so we can assume that about 3km of dust has fallen in that time, so anything under about 3km difference in base to top elevation may have disappeared if it was from right at the start. 1.5km if it was about 1.5 billion years ago, a 1 metre crater a million years ago, down to a 1mm mark if it was within the last 1,000 years, so we need to factor in a certain amount of evidence concealment for every size crater. For every large crater that has smaller craters within it we can of course rely on the largest crater being there first.

The identification is possible by using a computer to do this, but in a lot of cases it is beyond the capabilities of one currently to recognise the shapes at the moment without a lot of processing, training, and reinforcement time for a neural net. But, we are trying to get a rough estimate of the occurrence, so it needs to be done by hand.

If you look at the large craters, most of them have sub craters within their confines, and some of those have sub-sub craters and so on. If you look at the patterns there are on average about 5 times the number of small craters as larger ones, and within their surfaces each one has about 5 sub-sub craters.

Looking at photographs of undisturbed terrain, you find that it generally conforms to this similar pattern, a pock hole having about 5 smaller pock holes on average. The figure ranges from about 4-6, so it may be a lower or higher figure. Obtaining data is the problem, and low res photos and charts.

Since the figures are reasonably consistent I would put forward a hypothesis:

The likelihood of an impact on any area is in the ratio of for every doubling of the diameter of the object; the number reduces by a factor of five.

This I have included it in a theory that the likelihood of an impact is based on the area of maximum cross section of a body or silhouette. So, the moon will have a maximum cross section of its Pi x Radius Squared, approximately 3.14 x 1737 x 1737 = 9,478,715 square kilometres, so call it 10 million km2 as a target. You will have a fractionally larger target as gravity will bend an object towards it, but it is a rough measure and compensated for by atmospheric drag and bounce. But asteroids or meteorites are travelling at a fair lick, usually between 25,000 and 60,000 miles an hour, insterstellar ones being a bit faster, so it needs quite a strong influence to change the direction by a considerable amount, there being no atmosphere to slow or deflect them, and not running parallel to the surface like with a snipers bullet. So mostly they will go in the direction they originally run in, only with numerous revolutions or collisions changing this in any considerable way.

The earth has a maximum cross section of 3.14 x 6371 x 6371 = 127,516,117 square kilometres, so say 130,000 km2. Bending trajectory by gravity will give a larger figure than the moon, but atmospheric bounce will deflect a lot of casual passers, so the rough comparison of about 13 times as likely to be hit as the moon is somewhere in the ballpark. So that you include in the probability of object strike.

If you take an area of the moon, count the number of craters and sub craters and fit it into the format of the 5x as many smaller craters, for the approximate life of the moon, you get a figure for an approximate hit rate for an approximately centimetre diameter of about a hit every 4.7 minutes. This would translate into earth terms somewhere near the table below:

Diameter in Cm Diameter in miles Volume Cu Cent. Vol Cu Miles Average period  
1.10 6.8266E-06 0.65 1.56086E-16 20.00 Seconds
2.20 1.36532E-05 5.20 1.24869E-15 1.67 Minutes
4.39 2.73064E-05 41.64 9.9895E-15 8.33  
8.79 5.46128E-05 333.10 7.9916E-14 41.67  
17.58 0.00011 2664.82 6.39328E-13 3.47 Hours
35.16 0.00022 21318.53 5.11463E-12 17.36  
70.31 0.00044 170548.26 4.0917E-11 3.62 Days
140.63 0.00087 1364386.08 3.27336E-10 18.08  
281.25 0.00175 1.09E+07 2.61869E-09 90.42  
562.50 0.00350 8.73E+07 2.09495E-08 1.24 Years
1125.00 0.00699 6.99E+08 1.67596E-07 6.19  
2250.00 0.01398 5.59E+09 1.34077E-06 30.95  
4500.00 0.02796 4.47E+10 1.07261E-05 154.73  
9000.00 0.05592 3.58E+11 0.0001 773.63  
18000.00 0.11 2.86E+12 0.0007 3868.17  
36000.00 0.22 2.29E+13 0.0055 19340.87  
72000.00 0.45 1.83E+14 0.0439 96704.37  
144000.00 0.89 1.46E+15 0.35 483521.85  
288000.00 1.79 1.17E+16 2.81 2.42 Million years
576000.00 3.58 9.38E+16 22.49 12.09  
1152000.00 7.16 7.50E+17 179.95 60.44  
2304000.00 14.32 6.00E+18 1439.64 302.20  
4608000.00 28.63 4.80E+19 11517.11 1.51 Billion years
9216000.00 57.27 3.84E+20 92136.91 7.56  

A lot of this is just rough and ready figures, suggesting the chance of a ½ mile object hitting the earth in a particular year around 150,000:1 and a 1 mile object hitting the earth in any particular year around 750,000:1. Also it may be that there is a belt of debris that intersects with the sun orbit, and therefore the earths, so it may be like buses of drinkers, all coming at once and getting plastered. Also, it take no account of the density of objects, so mass is undetermined. Meteorites tend to have a 4:1 ratio for stony to metallic, so you’re probably looking at an average density of somewhere near 5g/cm3.

The risk of a major event is highly unlikely, a 50m asteroid occurring something like every 170 years, but we must take into account that we are in a shooting gallery, and such an asteroid could weigh 300,000 tonnes running at 50,000mph.

What can we do?

The biggest drawback to understanding the problem is one of understanding the scale of it. A typical worrying asteroid is one of 100m across weighing 31 million tonnes flying at 35,000mph until it gets closer to a gravitational field, then speeding up. To destroy it is impractical, but you might deflect it to a non-earth intersecting course.

We have a large arsenal of nuclear weapons on this planet totalling about 26,000 warheads, but most are short range and not capable of being used against a far target not on this planet.

For an asteroid say about 5 miles across, 26,000 nuclear weapons might not be enough. If one of those managed to go into a deep cavern maybe, otherwise you might only get a small ditch for each one. For explosives to work, even nuclear ones, you need energy and compression. In space there is next to none, and energy will not necessarily give enough power to fragment it unless it was just a weak conglomerate held together by its gravity. The best way to hit an asteroid is by using a mass that is propelled directly in opposition to it trajectory to try and destroy it, but you would need time to manage it and it would be better just deflecting it, as large chunks could fly off anywhere, and there would be a lot of them. We don’t know the constituency of the asteroid, but they ten to have a 4:1 ratio of stony to metallic, so an average density to work on would be around 5gm/cm3, so if the asteroid is 100m diameter that would work out to 21 million tonnes flying at say 50,000 miles an hour. Compare that to a 10 gram 357 magnum bullet travelling at 850 miles per hour and you see the problem.

It’s a question of time. Asteroids travel at a velocity of around 35-50,000mph, so just over 300-400 million miles a year. If we knew about it 5 years in advance we would have half that time to try and alter the course, so an intercept something like a billion miles away, somewhere near the orbit of Saturn at its closest. The earth is around 8,000 miles in diameter, so that’s the absolute minimum course change, being easier to deflect behind and inside the orbit rather than in front of it. But it is possible it will need at least 3 times that. Then it’s a question of moving the mass. A 100m asteroid is probably around 21 million tonnes, a 1 mile asteroid around 85 billion tonnes, over 10 miles forget it and devote your time to leaving, probably to the moon until it’s over.

There have been attempts at deflection plans, using things like lasers or attaching motors, but the Saturn 5 was about 3,000 tonnes moved by about 60 miles or 180,000 ton miles, so on a 50k 100m asteroid you would need to mount 2 of them, twice the size 16 of them. Using a laser wouldn’t produce anything near what is required and spread would mean it would need to be close by. The only other options I can see would be to slow it down by friction to miss, so constantly exploding heavy masses in its path or diverting smaller asteroids to hit it.

Recently there was an impact on a relatively small asteroid called Scheila that is about 110 kilometres in diameter. The hit was from an asteroid probably in the 100 metre diameter range, travelling at about 11,000 miles an hour, so a hit on earth in comparison would be about 4 times as bad for that size of asteroid.

On Scheila it created a crater 300 yards across and 100 feet deep, with negligible damage outside that crater. It’s estimated that about 600,000 tonnes of material was displaced.

With an atmosphere on earth to allow for compression, you would need around 50 million tonnes of TNT to do that, so equivalent of a 50 megaton device planted on the surface. So far there hasn’t been any evidence at all that it changed Scheila’s trajectory at all other than producing a relatively small crater.

The biggest warhead that was supposed to have been created called the Tsar Bomba is supposed to be 50MT, and the average warhead is probably 250kilotons for most of the worlds 26,000 nuclear weapons, totalling somewhere near 6.500MT, so you would probably give the asteroid with all of them a bad case of acne, with little effect.

It would be better relying on one scifi film I saw, where an expert sent up what is now little more than hobby rocket to destroy a massive asteroid, using a discovered material that was unknown to science and could be put in a test-tube in their top pocket. It worked out to about the equivalent of 242kg of antimatter, and antimatter is supposed to cost about $60 trillion a gram, so about 300 years of world GDP.

What we have at the moment are rockets. Rockets use the same principle as most things of chucking out stuff behind you to push you forward. The velocity you get forward relative to the speed at which you chuck out a mass behind. Rockets fuel is mainly explosive stuff that uses chemical reactions to cause the explosions. But consider that the most powerful boosters of the Saturn V has a boost for about 3 minutes that propelled 3,000 tonnes 100 kilometres, the effect on 21 million tonnes would be about 14 metres if you could get that whole fuel filled mass up there. But to get that sort of mass to the asteroid though would probably take at 10 tonnes per mission, about 300 trips at best before setting up.

Another alternative is to use solar reflectors to burn part of the asteroid producing a jet to push the asteroid out of the way using it’s own fuel, but the concentration an accuracy of using the expelled matter at the right angle is probably a tiny fraction of the rocket method. If you had a diameter of something like a mile across that would at best probably acquire a maximum of 500 watts per square metre, so about 4 gigawatt concentrated at one small point, say a metre across. So if we take water as the easier material to work with, as burning rock would take a lot more, we have a watt is 1 C per second needing 4,186 joules to raise it by about 500 C past vapourisation at a suitable velocity. It’s no good if it just drifts away like an evaporating comet, and comet paths have show that losing a few tonnes doesn’t seem to make much impression on it’s orbit. So that could expel about 2 tonnes of water per hour, but with albedo and power loss I would expect to eject more than 200kg per hour. If it was rock then it might be as low as 40kg per hour. It’s a combination of explosive loss against heat transfer and dissipation. Would it be enough to change its direction?

So a 100m asteroid, weighing 31 million tonnes at 35,000 mph would have a force of about 1.7 x 109 giganewtons covering an orbit of something like 250 million miles for intercept. To miss we probably need to alter the course by 50,000 miles outward or inward at earth intercept, inward or behind the earth being better. It’s easier if you just use straight-line trajectory as view of what’s needed. Most asteroids are turning, but if the force isn’t constantly directed all you impart is an increased or decreased spin, not a change in trajectory, the spin only taking effect when there is friction present.

You only need to alter the course by 20,000/250,000,000 or 2 seconds of arc, but you’re still trying to shift 31 million tonnes in space, when the average spacecraft is in the order of 2 tonnes, and that’s for just a 100m one. For every doubling in diameter the weight goes up by about 8 times, so is 8 times the problem. An example,

Apophis a recurrent earth crossing asteroid that is supposed to go past the earth on Friday 13th April 2029 and again in on Thursday 12th April, 2068, is 185m on average across and should just miss just on the edge of safe limits suggested above, so we’re told it has a mass of about 61,00,0000 tonnes, but I would have probably put it nearer to 100 million tonnes. There are 3 known recurrent asteroids that are similar, but the underlying link to our calendar is worrying for a recurrent object.