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# The never-ending story of Apophis - third and final part

Passing through the "keyhole" - the problem gets complicated. By Noah Brosh, Galileo 96

In calculating the chances of injury, the possibility is taken into account that the measurement errors, even though they are tiny, may affect the calculation of the body's future trajectory. Therefore, the future route is not described as a clear and well-defined line, but as a series of possible lines that gives a "thickness" of uncertainty to the route. The thickness refers to the position of the body at a certain moment and has a three-dimensional existence: around the predicted point you can draw a three-dimensional space where the body can be found at that moment, when each point in this volume has a certain chance that the body will be found there. Points located within the Earth's mantle indicate possibilities of injury.

The change in Apophis' orbit as a result of the close transit to Earth in 2029. The uncertainty in the orbit is indicated by the white bar perpendicular to the asteroid's orbit

But the problem gets complicated: when MN4 2004 passes near the Earth in 2029, it will be under strong gravitational forces, both of the Earth and (to a lesser extent) of the Moon. These attractive forces will change both the trajectory and the internal structure of the body, otherwise it is a solid block of rock with great self-strength. The expected change in the trajectory will be drastic: a deviation of about 30 degrees from the trajectory in which the body moved before approaching the earth. Because of the great proximity to the earth, slight changes in the geometry of the transition have a large effect on the future trajectory of the body. In particular, the change in orbit could include a passage through tiny pieces of sky, the length of which is less than 600 meters, but their location in the volume through which Apophis will pass is extremely "strategic". If Apophis passes through these regions, the orbital shift will result in an almost certain collision with Earth in 2034, 2035, 2036 or later, because the duration of Apophis' orbit around the Sun will become a multiple of a simple (rational) fraction of the Earth year (e.g., six orbits of Apophis will last seven years, therefore every seven years the two bodies will be next to each other). Such a tiny piece of sky is called a "keyhole", and there is currently no way to ensure that the near-Earth asteroid Apophis will not pass through it and change its course in such a threatening way.
One of the possibilities for the fate of the asteroid is similar to that observed in the case of comet Shoemaker-Levy 9 (SL9), which passed close to the planet Jupiter: the gravitational force acted more strongly on the side of the comet close to Jupiter than on the far side. This difference in the strength of the gravitational forces acts on the comet's nucleus as if an external factor "stretches" it by pulling on its two ends: the side close to Jupiter and the side far from it. The strong pull, known as the "tidal force", caused Shumker-Levy 9's core to break up into 9 pieces, each several hundred meters to a kilometer in diameter, which later fell into Jupiter's atmosphere.
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Image of the fragments of the nucleus of the comet Shumker-Levy 9, which was torn into 22 subnuclei due to the gravitational pull of the planet Jupiter
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The tidal force of a planet can, under certain conditions, overcome the internal strength of a nearby celestial body. From calculations made to understand the mechanism that broke the core of SL9 into so many fragments, it became clear that it must be assumed that this is a body with little internal strength. The self-strength is the relationship between the smallest parts of the body, grains and dust particles, ice of water and other frozen substances, and more. In a solid earthly body, the self-strength comes from the connections between the particles that make it up, which are close to each other. For it to disintegrate as observed, the intrinsic strength of the nucleus of comet 9SL would have to be only one ten-millionth of the intrinsic strength of normal rock on Earth. The density of the material also had to be low: about a third of a gram per cubic meter. It is, therefore, a material whose strength is similar to cotton wool.
We currently have no evidence that Apophis is similar in terms of internal texture to the nucleus of 9SL, but we also have no real reason to think otherwise. The only direct evidence regarding the internal strength of cometary bodies comes from the collision experiment between the subspacecraft of the "Deep Impact" research operation and the nucleus of the comet Temple-1. The collision occurred on July 4, 2005. From the findings, it became clear that the internal structure of the core of Temple-1 is extremely weak. The material up to a depth of several tens of meters below the surface is granular and very loose. All this became clear from the analysis of photographs of the jet of dust emitted after the impact. It should be remembered that SL9 and Temple-1 are the nuclei of comets, and it is possible that Apophis is not. In any case, it is clear that one of the most important tasks at this stage is to accurately map the trajectory of the asteroid in space, to verify whether or not it may collide with the Earth. If the answer to this is "yes", we will have to investigate it thoroughly.
Map the path of an asteroid wellThe measurements with the help of the planetary radar, conducted when Apophis passed near the Earth in late January and August 7, 2005, completely removed the threat of the collision in 2029 (and of a possible collision in 2035), but still did not manage to eliminate the possibility of a transit through the "keyhole" with a possible collision in 2036. Since Apophis orbits the Sun every 323 days and crosses the Earth's orbit twice in each cycle, it is possible that it will hit the Earth even in the more distant future.
A significant improvement in knowing the route of Apophis can come from the analysis of his appearances in the more distant past, if more old photographs are found in which he appears; from performing additional radar observations, which will be possible in 2013; or from launching a spacecraft to meet him in the coming years. This last possibility was raised by NASA and the US government both as an opportunity to learn much more about Apophis' orbit, and as a way to study what happens to the asteroid when strong tidal forces act on it.

Radar "map" of the near-Earth asteroid Toutatis

The members of the B612 association (as the name of the asteroid on which the little prince lived in Antoine de Saint-Exupery's book of the same name) proposed to fly a research spacecraft towards Apophis, which would land on it measuring instruments as well as a "radio beacon" that would enable receiving extremely accurate data on the asteroid's position and speed. With their help, it will be possible to know for sure if a collision will occur in 2036, or not. Radio beacons and radar transponders (a radar transponder, is a device that, upon receiving a radar signal, transmits a radar signal back) routinely operate on earthly vessels whose exact location must be known, such as airplanes. In addition, other scientific equipment that will be placed on the asteroid will measure the "earthquakes" that will occur in Apophis as it passes by Earth. This would be a great way to learn about the internal structure of a near-Earth asteroid without digging down to its center and without detonating explosive charges on it, as geologists do to learn about the interior of the Earth.
And what if it turns out that Apophis is indeed going to collide with us?As inhabitants of the Earth, we are interested in reducing as much as possible the dangers to ourselves and future generations. Therefore, the obvious question is, what is the human race going to do if it turns out that in 2036 Apophis is going to collide with Israel. The question is true not only for Apophis, but for any other threatening asteroid or comet. One of the solutions proposed in the past was immortalized in the science fiction movies we mentioned, "Armageddon" and "Deep Impact": launching a spaceship loaded with nuclear bombs, which will disintegrate the threatening asteroid into pieces.
From the descriptions given above regarding the nature of near-Earth asteroids and comet nuclei, it is clear that this possibility of a nuclear explosion is not desirable, because the internal texture of the body is unknown. If it is only a wave of stones lacking self-strength, an explosion near or on the surface of the body may cause it to split into several sub-bodies, some of which at least will hit the Earth; And the combined effect of several large hits can be worse than one single hit. Another possibility, which has also appeared in the literature, is to carry out the nuclear explosion at some distance from the asteroid, so that only the high radiation effect that will be released in the explosion will be used to deflect the asteroid. If it is indeed a body whose self-strength is small, this solution should also be invalid, and for the same reason.
It may be possible to divert an asteroid from its orbit, thereby preventing a fatal impact, if only we manage to hit it with the help of a massive body. The best example of this is the impact of the sub-spacecraft in the "deep impact" operation on the nucleus of the comet Temple-1. The impact occurred on July 4, 2005, when the subspacecraft was placed in front of the nuclear and it collided with it at a relative speed of about 10 km per second. The collision between the two bodies was a plastic collision, in the physical sense. The subspacecraft and the comet nucleus formed one body after the impact.
A collision between a body like the "Deep Impact" subspacecraft and a comet's nucleus, which contains 1,000 times more matter than there is in Apophis, would change the velocity of the comet's nucleus by 0.08 mm per second. This change in the speed of the comet's nucleus may slightly change its trajectory, so that the method can also be used to divert an asteroid from an impact trajectory, at least in principle.
More creative and less "explosive" solutions were also proposed. One version is that a spacecraft can be landed on the surface of the asteroid that will contain a powerful ion engine and a facility to produce fuel for this engine. The ion engine works by electrically accelerating ions (electrically charged particles). The electrical acceleration is done through an electric field, which can bring the material to speeds of hundreds of kilometers per second (compared to a few kilometers per second for rocket engines that consume chemical fuels). However, the total thrust of ion engines is many orders of magnitude lower than that of chemical engines. To achieve a significant result, an ion engine must operate for a long time, therefore, to divert an asteroid from an impact path, action is required for many months and even years.
Although the possibility of landing a small factory on the surface of the asteroid seems difficult, it is not impossible. In this case, too, the limitation could be due to the texture of the asteroid: if the texture is extremely loose, as is feared, the fuel factory and the engine itself could sink and be swallowed up in the depths of the asteroid, and not stay close to it, while creating an impulse to divert it from an impact path. The analysis of the various situations resulted in a disappointing result: even if we know that a disaster from space is about to occur, we have no way to defend ourselves against it. This is where the "space tug" came into the picture, which performs the diversion operation without touching the asteroid at all.

Space tugThis possibility, of diverting an asteroid from its orbit without direct contact between the diverting agent and the asteroid, was proposed in 2005 by two NASA astronauts, Edward Lee and Stanley Love, both members of the B612 Association. The proposal is based on gravity. The acceleration of gravity results from the universal law of gravitation: between any two bodies there is a force, the magnitude of which is proportional to the mass of each of the bodies and its strength decreases with the square of the distance between the bodies. Let's say we manage to place a spaceship, which weighs 20 tons and has a radius of 10 meters, at a distance of 20 meters from Apophis. It is clear that Apophis will pull the spaceship towards it: it is even possible to calculate the gravitational force if we assume for simplicity that the shape of the two bodies is spherical. Since the approximate radius of Apophis is 160 meters, the mass of the spaceship is 20,000 kg and that of Apophis is 46 billion kg, it is possible to calculate the magnitude of the force of attraction between the two bodies from placing it in the gravity equation. The calculated force between the spacecraft and Apophis will be only 1.7 newtons, a small force by all accounts - roughly like the pressure exerted by a glass of water on the hand holding it.
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Dragging space
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If the spacecraft reaches the vicinity of the asteroid and shuts down its engines there, the mutual gravity will cause it to slowly fall to the surface of Apophis. But if she activates a relatively weak engine, which will give her a thrust force of 1.7 N, this will be enough to prevent her from falling towards the asteroid. From the point of view of an imaginary observer on the surface of the asteroid, the spacecraft will appear to be hovering over the asteroid and maintaining a constant distance from it. This tiny force will act, in fact, on both the spacecraft and the asteroid, which are one body with a mass that is the sum of the two masses, and will give the combined body a small acceleration.
One of the weaknesses of the "space tug" idea is the requirement for a long operating time of the engine. After a day of its activation, the speed of the asteroid and the spacecraft (moving together in space, as mentioned) will change by a quarter thousandth of a centimeter per second. After a full year of operation, the change in speed will already be more than a millimeter per second. This means that after a year, the asteroid will be more than 180 meters away from where it would have been had the spacecraft's engine not been fired. To miss the "keyhole" mentioned earlier, the engine of the spacecraft used as a space tug must be turned on for about four years.
With the same method, a larger asteroid, which may collide with the Earth, can also be diverted from its orbit, by placing a heavier spacecraft near it (with a greater gravitational force between it and the asteroid), which will operate more powerful engines for a longer period of time. To divert an asteroid from an impact path on the Earth, it must be given an offset along the path, greater than the radius of the Earth; This seems difficult, but is possible in principle, and the problem becomes a question of allocating resources for this type of diversion operation.
It was said earlier that the engines needed for this operation are ion engines, which emit a stream of charged particles that move at high speed after being accelerated in an electric field. Engines of this type exist, although they do not provide extremely high thrust levels. They were successfully tested in space flights, and in some cases operated for hundreds of days. The installation of ion engines in a spacecraft that will be used as a space tug should be done so that the thrust of the engines does not hit the face of the asteroid (because then the asteroid will be pushed away from the spacecraft, and the entire towing method will not work). For this, the engines must be installed so that the jets are directed "aside" from the asteroid; This is also possible, but will require a certain increase in the thrust of each engine, since only part of it will be used to push the spacecraft away from the asteroid.
The gravitational "space tug" proposal solves one of the difficult problems involved in diverting an asteroid from its orbit and makes it possible to prevent a disaster on a regional scale, which could occur due to the impact of a small body, several hundreds of meters in size, on the Earth. The method as described can be changed if it is a much larger and more massive body, such as the asteroid that caused the extinction of the dinosaurs. It was a body with a diameter of about 10 km and its mass is 27,000 times greater than that of Apophis. In order to move such an asteroid enough to prevent a collision, a much heavier spacecraft is needed, which will be located close to the asteroid and operate more powerful engines and for a longer period of time. The problem in this case is the amount of time available to humanity from the moment of discovering the fact that a deadly asteroid is about to hit the Earth, until the predicted time of the impact. This amount of time should be used to study the impacting asteroid, to build the deflection tool, and to operate it in space near the asteroid to achieve the necessary deflection.
As mentioned, the basic principle of a "space tug" is the action of gravity between the spacecraft and the asteroid. To prevent the spacecraft from falling into the asteroid, engines must be activated that will provide an impulse equal in magnitude and opposite in direction to the force of gravity between the two bodies. The thrust of the spacecraft's engines is what causes the asteroid (and the spacecraft) to be diverted from a collision course with Earth. The greater the force of attraction between the asteroid and the spacecraft, the greater the required thrust, and therefore the more efficient the diversion process. Hence, it is desirable to place a spaceship with as much mass as possible, because the force of attraction between it and the asteroid will be greater. The problem is that flying large masses from the Earth into space is an expensive process in terms of energy and money, and it is simpler to produce most of the spacecraft's mass "on the spot", from the asteroid material that must be diverted from orbit. If there are water molecules close to the surface of the asteroid - in the form of ice that sticks the dust grains and pebbles together, or in the form of water molecules adsorbed to other materials - heating the material with concentrated solar radiation will cause the emission of water vapor. These can freeze back inside the body of the spacecraft, thus building up the large mass needed to divert it from a collision course.

Conclusions and reflections on the fate of humanityThe statistics of major impacts on the Earth show that fatal impacts on a global scale occur every hundred million years (the last of which wiped out the dinosaurs 65 million years ago). If we refer to smaller impacts, which do not lead to the extinction of most forms of life on earth but "only" to a disaster on a regional scale, with tens or hundreds of millions of casualties, the chances of damage in the near future are much higher.
The captains of the industrialized countries have begun to take steps to study the problem of fatal injuries, and especially in the United States, research is underway to map the offending bodies and study their nature. In Israel, which is a "tiny target" for natural damage from space, the Israel Space Agency and the Ministry of Science and Technology are taking similar steps, and a national knowledge center is being activated on the issue of bodies close to the country that may threaten it. Global mapping is now approaching the goal of identifying 90% of the population of threatening bodies whose size exceeds one kilometer. In the coming years, additional, larger telescopes are about to come into operation to map the population of even smaller bodies, up to 300 meters in size.
The mapping program led to the discovery of the small body Apophis, only 320 meters in diameter, which may collide with the Earth in 2036 or later. While studying the nature of the body, the scientists are also discussing methods to remove it from the earth and thus reduce the danger from it. These things show a certain maturity of the human race, which today is also able to deal with some of the blows that fall from the sky.