Success! Defence Against Asteroids

Most people will know that about 64 million years ago an asteroid with a diameter of about 10 km struck the Yucatán peninsula and exterminated the dinosaurs, or at least did great damage to them from which they never recovered. The shock-wave probably also initiated the formation of the Deccan Traps, and the unpleasant emission of poisonous gases which would finish off any remaining dinosaurs. The crater is 180 km wide and 20 km deep. That was a very sizeable excavation. Rather wisely, we would like to avoid a similar fate, and the question is, can we do anything about it? NASA thinks so, and they carried out an experiment.

I would be extremely surprised if, five years ago, anyone reading this had heard of Dimorphos. Dimorphos is a small asteroid with dimensions about those of the original Colosseum, i.e.  before vandals, like the Catholic Church took stones away to make their own buildings. By now you will be aware that Dimorphos orbits another larger asteroid called Didymos. What NASA has done was to send a metallic object of dimensions 1.8 x 1.9 x 2.6 meters, of mass 570 kg, and velocity 22,530 km/hr to crash into Dimorphos to slightly slow its orbital speed, which would change its orbital parameters. It would also change then orbital characteristics of the two around the sun. Dimorphos has a “diameter” of about 160 m., Didymos about 780 m. Neither are spherical hence the quotation marks.

This explains why NASA selected Dimorphos for the collision. First, it is not that far from Earth, while the two on their current orbits will not collide with Earth on their current orbits. Being close to Earth, at least when their orbits bring them close, lowers the energy requirement to send an object there. It is also easier to observe what happens hence more accurately determine the consequences. The second reason is that Dimorphos is reasonably small and so if a collision changes its dynamics, we shall be able to see by how much. At first sight you might say that conservation of momentum makes that obvious, but it is actually more difficult to know because it depends on what takes the momentum away after the collision. If it is perfectly inelastic, the object gets “absorbed” by the target which stays intact, then we simply add its relative momentum to that of the target. However, real collisions are seldom inelastic, and it would have been considered important to determine how inelastic. A further possibility is that the asteroid could fragment, and send bits in different directions. Think of Newton’s cradle. You hit one end and the ball stops but another flies off from the other end, and the total stationary mass is the same. NASA would wish to know how well the asteroid held together. A final reason for selecting Dimorphos would be that by being tethered gravitationally to Didymos, it could not go flying off is some unfortunate direction, and eventually collide with Earth. It is interesting that the change of momentum is shared between the two bodies through their gravitational interaction.

So, what happened, apart from the collision. There was another space craft trailing behind: the Italian LICIACube (don’t you like these names? It is an acronym for “Light Italian Cubesat for Imaging Asteroids”, and I guess they were so proud of the shape they had to have “cube” twice!). Anyway, this took a photograph before and after impact, and after impact Dimorphos was surrounded by a shower of material flung up from the asteroid. You could no longer see the asteroid for the cloud of debris. Of course Dimorphos survived, and the good news is we now know that the periodic time of Dimorphos around Didymos has been shortened by 32 minutes. That is a genuine success. (Apparently, initially a change  by as little as 73 seconds would have been considered a success!) Also, very importantly, Dimorphos held together. It is not a loosely bound rubble pile, which would be no surprise to anyone who has read my ebook “Planetary Formation and Biogenesis”.

This raises another interesting fact. The impact slowed Dimorphos down relative to Didymos, so Dimorphos fell closer to Didymos, and sped up. That is why the periodic time was shortened. The speeding up is because when you lower the potential energy, you bring the objects closer together and thus lower the total energy, but this equals the kinetic energy except the kinetic energy has the opposite sign, so it increases. (It also shortens the path length, which also lowers the periodic time..)

The reason for all this is to develop a planetary protection system. If you know that an asteroid is going to strike Earth, what do you do? The obvious answer is to divert it, but how? The answer NASA has tested is to strike it with a fast-moving small object. But, you might protest, an object like that would not make much of a change in the orbit of a dinosaur killer. The point is, it doesn’t have to. Take a laser light and point it at a screen. Now, give it a gentle nudge so it changes where it impacts. If the screen as a few centimeters away the lateral shift is trivial, but if the screen is a kilometer away, the lateral shift is now significant, and in fact the lateral shift is proportional to the distance. The idea is that if you can catch the asteroid far enough away, the asteroid won’t strike Earth because the lateral shift will be sufficient.

You might protest that asteroids do not travel in a straight line. No, they don’t, and in fact have trajectories that are part of an ellipse. However, this is still a line, and will still shift laterally. The mathematics are a bit more complicated because the asteroid will return to somewhere fairly close to where it was impacted, but if you can nudge it sufficiently far away from Earth it will miss. How big a nudge? That is the question about which this collision was designed to provide us with clues.

If something like Dimorphos struck Earth it would produce a crater about 1.6 km wide and 370 m deep, while the pressure wave would knock buildings over tens of km away. If it struck the centre of London, windows would break all over South-East England. There would be no survivors in central London, but maybe some on the outskirts. This small asteroid would be the equivalent a good-sized hydrogen bomb, and, as you should realize, a much larger asteroid would do far more damage. If you are interested in further information, I have some data and a discussion of such collisions in my ebook noted above.

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The Space Elevator

One of the problems for humans having settlements off-Earth is the huge cost of getting the supporting materials there, and the great bulk of that cost is actually in getting the stuff out of Earth’s gravitational field. If you look at a chemical rocket, you start with a huge monster, and cart up only trivial amounts, the reason being that the great bulk of the initial mass is the mass of the fuel necessary to get the rockets going, and the mass of the metal needed to contain the fuel.

One proposal to get around this is the space elevator. The idea of this is simple in concept. At about 35,800 km above any point on the equator the orbital angular velocity is the same as that of the Earth, and hence you have a point in space where a satellite is always above the same point. At the risk of annoying some physicists, if we reduce the problem to one dimension, the centrifugal force arising from the orbital motion is exactly the same as the force heading towards the Earth and the angular velocity is the same. Now, suppose we put a cable between Earth and this geostationary point, and make the cable strong enough that we can run an elevator up and down it. Now the work done is the same as using an elevator, and an electric motor can power it. But as it stands, this won’t work because where before the centripetal force was that of earth’s gravity, now it has the force from the weight of the cable added to it. This can be corrected by adding corresponding centrifugal force, achieved by extending the cable further and attaching a massive body to it. As long as it stays put, its centrifugal force will cancel the weight of the cable, so if all this is done carefully, you have an elevator cable that you can run things up and down and transfer everything to a geostationary satellite.

From an economic point of view, the space elevator should lift material up there at least 8 times cheaper than the most favourable prediction from rockets, and its capital cost is estimated to be about $20 billion. So, why do I think this is a non-starter?

First, there is the issue of materials. The cable appears to need to be at least 40,000 km long. Something like titanium is far too weak for the task, but it has been speculated that carbon nanotubes might be satisfactory. However, you are not going to make a 40,000 km long nanotube, so some sort of composite will be required. The strength is that of the weakest part. The composite has to be at least as strong as the nanotube, and adhere as strongly, and also retain that strength indefinitely despite space weathering. I do not believe such a material is possible.

The next problem is, where do you put this cable while you are making it? You have a single length that is 40,000 km or so long. Where do you store it while you are making it? Assuming you make it in sections, how do you know the joins will be strong enough? How do you know there are no weaknesses deep within the cable? Then specifically where do you assemble it? How? A coil? How flexible are such nanotubes, and why is the composite sufficiently elastic? What is the proposed radius of the coil? Since it has to be on the equator, how many notice the equator is basically wet?

Now, suppose this huge cable is coiled up somewhere, how do you get it into position? You cannot really take it up with a rocket because the exhaust will ignite your carbon. Oops! On top of that, the rocket has to go up and counter the Earth’s rotation. But just suppose you get this massive weight up there, how do you hook it to the counterweight? The asteroid, recall, is NOT in geostationary orbit but will have quite a relative velocity. Your propulsion unit has to arrive at exactly the right time, with thrusters supporting the whole weight of the cable, and somehow this has to be joined to the asteroid while still supported by the rocket until the junction is firm. And even if you think you can manage this, how can you be sure that nothing will go wrong? One slip, one miscalculation, and 40,000 km of cable comes hurtling back to Earth. That is enough to wrap itself around the planet, causing serious damage to anything in its path. Then, supposing all this can be done, how do you get it down again safely at the end of its working life? In part because I have designed and overseen the construction of a chemical plant, and have seen what can happen with engineering, and I know one should always start off small, to iron out the bugs. That is not possible here and I just do not have sufficient faith in such a one-off engineering feat.