  We develop the mathematical theory for an automatic, space-based system to
deflect NEOs by virtue of missiles shot from the Earth-Moon L1 and L3
Lagrangian Points. A patent application has been filed for the relevant code
dubbed AsterOFF (=Asteroids OFF !). This code was already implemented, and a
copyright for it was registered. In a paper published in Acta Astronautica,
this author proved mathematically the following theorem: "Within the sphere of
influence of the Earth, any NEO could be hit by a missile at just an angle of
90 degrees, was the missile shot from the Lagrangian Points L1 or L3 of the
Earth-Moon system, rather than from the surface of the Earth". As a
consequence, the hitting missile would have to move along a "confocal ellipse"
(centered at the Earth) uniquely determined by the NEO's incoming hyperbola.
The author further shows in this paper that: 1) The proposed defense system
would be ideal to deflect NEOs that are small, i.e. less than one kilometer in
diameter. 2) The traditional theory of Keplerian orbits can successfully be
applied to get an excellent first-order approximation of the mathematical
formulae of the energy-momentum requested to achieve the NEO deflection. Many
engineering details about the missiles shot from L1 and L3, however, still have
to be implemented into our simulations. 3) Was one missile not enough to
deflect the NEO completely, it is a great advantage of the "confocal conics"
used here that the new, slightly deflected NEO's hyperbola would certainly be
hit at nearly 90 degrees by another and slightly more eccentric elliptical
missile trajectory. A sufficient number of missiles could thus be launched in a
sequence from the Earth-Moon Lagrangian points L1 and L3 with the result that
the SUM of all these small and repeated deflections will finally throw the NEO
off its collision hyperbola with the Earth.
