At the time of the report to Congress in 2007, there was a small chance of the asteroid Apophis impacting the Earth.  The observation indicated a potential risk of an impact in 2036. 

 

In order to make the decision whether or not to launch a full-blown mitigation mission, very accurate information about Apophis' orbit was required.  More data was collected in 2011 and 2012 as Apophis approaches the Earth.  In January 2013, NASA ruled out the impact and announced that on April 13, 2029, Apophis will fly by the Earth no closer than 31,300 km above the Earth's surface.  This distance is closer than the altitude of a Geostationary Equatorial Orbit (GEO), 35,786 km above the sea level.

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The events surrounding Apophis indicates that unlike other natural disaster, NEO impacts are predictable in many years in advance.  However, at the same time, with our current capability, deflection must occur years prior to the predicted impact date.  

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With our current capability and posture, we may be able to deflect a 100-200 meter asteroid.  Or, it may present a significant challenge to hit asteroid's center of gravity at meaning velocity (i.e. 10 km/s).  For example, NASA's DART mission is planned to hit the asteroid at 6 km/s.  Deflection using Kinetic Impactor may not be as easy as it appears.  Also, in order to deflect 200-meter asteroid, we need about 10 impactors to hit the asteroid, and in order to deflect 450-meter asteroid, we need at 100 impactors to hit the asteroid.  950-meter asteroid will require deflection by a thousand impactors.

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On the other hand, nuclear blast away from asteroid's surface (shown as nuclear stand off in the figure) will slow down the asteroid without accurately striking the heart of an asteroid.  Also, the nuclear detonation is about 100 times more effective compared to kinetic impactors. 

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So, what about the nuclear options?

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