Inside the Boardroom with Alan Bagley - SETI Institute

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Astrobiology Artist’s concept of an asteroid striking near an inhabited region. © David A. Hardy/ www.astroart.org Planetary Defense in Space by Claudio Maccone Saving the Earth from collision with asteroids and comets is the number one imperative for all those who care about the survival of humankind. Unfortunately, this deadly threat was not clearly perceived until 1980, when the American Nobel laureate Louis Alvarez suggested that the dinosaurs were wiped out by the collision of a ~20 km asteroid about 65 million years ago. Ever since, a few scientists of good will have tried to convince their governments that something must be done (the set of all such actions is called “planetary defense”), but without any significant success so far. Apart from the obvious lack of funding, the problem of how to divert an asteroid threat is so difficult to tackle that even the scientists don’t know exactly what to do, let alone the managers of the national space agencies and the various military establishments. Also, movies like “Armageddon” and “Deep Impact” have dramatized the story, but the solutions they portrayed are simply impossible because no Shuttle would be capable of reaching so far into space, and with such short notice. In 2002, this author put forward a new idea: orchestrate planetary defense from outposts in space, rather than sit and wait on the Earth. This would give us at least a bit more time (days) to try to divert asteroids by shooting missiles against them from two space bases, best located at the Lagrangian points L1 and L3 of the Earth- Moon system. The author showed that: (1) This defense system would be ideal for deflecting small impactors, less than 1 km in diameter. These are the most difficult ones to detect far in advance, and with sufficient orbital accuracy. (2) The deflection is achieved by pure lateral push (momentum transfer). No nuclear weapons in space would be needed. This is because the missiles are hitting the impactor at the optimal angle of 90° from their arrival direction. (3) In case one missile was not enough to deflect the impactor off its collision trajectory, the new, slightly-deflected impactor can be hit at 90° by another missile. So, a sufficient number of missiles could be launched in a sequence from L1 and L3 to finally throw the impactor off its collision trajectory with Earth. The Five Earth-Moon Lagrangian Points In 1772, Joseph Louis Lagrange demonstrated that there are five positions of zero gravity in a rotating two-body system, like the Moon around the Earth. Three are located on the line joining the two massive bodies, and are nowadays called “colinear points,” or L1, L2 and L3, as shown in Figure A. Two more points (L4 and L5) form equilateral triangles with the two massive bodies, and so are called “triangular points.” The distance to L1 is about 32,300 km, and to L3 is roughly 382,000 km. 10 SETI Institute Explorer
Figure A - The five Lagrangian points of the Earth-Moon system and their distances from Earth and Moon expressed in terms of R, the Earth-Moon distance (supposing the Moon’s orbit to be circular). Figure B - The two families of confocal ellipses and confocal hyperbolas. Trajectories for Best Deflection The best trajectories for deflecting impactors involve launching missiles from either of two colinear Lagrangian points, L1 and L3. Consider a family of ellipses and a family of hyperbolas that have all the same two foci, said to be “confocal.” The great property of confocal conics is that any pair of different confocal conics, namely one ellipse and one hyperbola, always intersect each other at angles of 90°. Consider one of the two foci, for example the one on the left. Imagine the Earth is situated there. Then both the confocal ellipse and the confocal hyperbola are trajectories (paths) that moving bodies around the Earth follow naturally, because of Kepler’s First Law. Now imagine that a dangerous impactor arrives from infinity, namely from outside the gravitational sphere of influence of the Earth. So, it must follow a hyperbolic trajectory with respect to the Earth, with Comet Wild 2 is about five kilometers (3.1 miles) in diameter. the focus of this hyperbola located just at the center of the Earth. The ellipse confocal to the impactor’s hyperbola is the path of a missile launched against the incoming impactor from any point in space, but better from the two colinear Lagrangian points L1 and L3, each located on one side of the Earth for defense on both sides. The selection of the colinear Lagrangian points L1 and L3 as space bases for missiles is now self-evident: they ensure the cylindrical symmetry of the problem around the Earth-Moon axis. So, the direction in space from which the impactor is arriving becomes irrelevant: we will just be studying confocal orbits in the Earth- Moon-asteroid plane. Being confocal, the missile’s ellipse is automatically orthogonal to the impactor’s hyperbola, meaning that the collision of the missile with the impactors always occurs at a right angle with the impactor’s path. This is really the best we can hope for, since the missile’s full momentum is then transferred to the impactor sidewise. Finally, if one missile fails to sufficiently deflect the impactor, we can always send additional missiles along the new ellipse that is confocal to the new and slightly deflected impactor’s hyperbolic path. Once again, the mathematical representation of the trajectories matches perfectly with the physical problem of diverting impactors. Ellipses for Missiles Shot from L1 and L3 NASA/JPL-Caltech/NOAO Figure C (which is not to scale) shows an example: the incoming impactor is missing the Earth (represented by the larger circle located at the origin), but is of course deflected along an hyperbola. A missile shot from the Lagrangian point L3 (the smaller circle on the left) can hit the impactor before it approaches the Earth, colliding with it at an orthogonal angle. In Figure D is shown an actual impact trajectory. But a missile shot from the Lagrangian point L3 along the shown ellipse, confocal to the impactor’s hyperbola, could rescue humankind. Similar considerations apply to missiles shot from L1. Political Problems and the Lagrangian Points The Cold War ended about ten years ago, but many people still have Cold War attitudes. Since nuclear weapons in space are forbidden by international treaties, a proposal to locate missiles with possible nuclear warheads at the Lagrangian points Figure C - Impactor missing the Earth, and elliptical path of the missile shot at it from L3. The orthogonality of the two paths at their collision point is evident. Figure D - Impactor hitting the Earth. Before it reaches the Earth, it could be diverted by the collision of a missile shot from L3 along the shown ellipse, orthogonal to the impactor’s path to achieve maximum deflection. L1 and L3 would immediately be perceived as an attempt to revive the Cold War. see PLANETARY, pg. 13 Second Quarter 2005 - Celebrating our 20th Anniversary 11
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Inside the Boardroom with Alan Bagley - SETI Institute

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