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Two Figures from NASA's NEO Report
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The following images (figures 4 and 5 from the NASA NEO report) describe different asteroid deflection techniques and the launch muscle required to do each type. 

Figure 4 shows that impulsive techniques using proximal nuclear explosives generally were found to provide greater potential for momentum transfer per kilogram of payload weight delivered to the threat than any other option considered. Standoff nuclear concepts, such as those producing highly concentrated and directionally focused x-rays or neutrons, were shown to present a generally lower risk of fragmenting a PHO than impulsive techniques involving direct contact, but also produce a lower effective momentum change than surface or subsurface nuclear explosives. Performance may vary significantly, depending on the type of nuclear device used and whether it is “off-the-shelf” as opposed to optimized for the PHO deflection mission. Additionally, the performance of kinetic impactors was found to be somewhat less robust than any of the nuclear explosions. However, their effectiveness depends strongly on the structure of the PHO. Kinetic impactors may also be significantly less effective for objects which are essentially loose rubble piles. Conventional explosives were found to have the lowest performance among the impulsive techniques due to their relatively low-energy density. 

Figure 5 illustrates that slow push techniques may be useful for imparting momentum changes smaller than 109 kg m/s. The asteroid tug appears to have significantly greater performance than the gravity tractor for a given launch mass, even accounting for pulsed operation on a rotating PHO. The disadvantage of the asteroid tug is the additional complexity required to anchor the tug to the NEO, particularly if the PHO structure has not been well characterized or the target is rotating very rapidly. 

These figures show that nuclear explosives and kinetic impactors were generally found to provide greater potential for momentum transfer per kilogram of payload weight delivered to the NEO than other alternatives. Additionally, these figures illustrate how the alternatives might be applied to hypothetical deflection scenarios. The inclusion of actual objects in these scenarios was chosen not because they represent actual impact threats, but because they are both publicly known and are representative of classes of potential threats. The hypothetical scenarios include missions to deflect: 

A. The 330-meter asteroid, Apophis, before its close approach to Earth in 2029. This scenario was divided into two design points: 
A1. For the first, knowing the asteroid’s orbit is assumed and a relatively large momentum change is required to deflect the object with the required certainty. Apophis must be deflected by at least one Earth radius or about 6,400 km to achieve a probability of collision of less than 10-6. 
A2. For the second, very accurate information about the object’s orbit is assumed and the impetus necessary to divert the asteroid with certainty is substantially reduced. Apophis must be deflected by at least five km to achieve a probability of collision of less than 10-6. 
B. Apophis after the close approach and before the 2036 Earth encounter, assuming a predicted collision. 
C. The 500-meter asteroid (VD17) that could be a threat in the year 2102.
D. A hypothetical 200-meter asteroid, representative of 100-meter-class asteroids. 
E. A hypothetical asteroid larger than one km in diameter. 
F. A hypothetical long-period comet with a very short time (9-24 months) to impact. 
The approximate performance requirements for each of the scenarios are overlaid on Figure 4 for the impulsive techniques and Figure 5 for the slow push methods.

Figure 4 - Kinetic impactors and nuclear weapons

Figure 5 - "Slow Push" Deflection Methods

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