Planet-Based Anti-Projectile Missile (PBAPM)

A Planet-Based Anti-Projectile Missile (PBAPM) is a long-range guided missile primarily designed to be launched from the surface of a planet, planetoid or moon into space to intercept an incoming projectile and alter its trajectory enough to prevent an impact event.

Theory
By detonating a high yield nuclear device above, on or slightly beneath the surface of an incoming projectile, the massive release of energy in the form of thermal heat vaporizes a portion of the surface turning the material the surface is composed of into ejecta (similar to the ejecta from a chemical rocket engine exhaust) "nudging" the projectile off course.

A rubble pile requires additional time to act and missiles compared to that used for a single solid projectile. The multiple missiles must detonate in sequence alongside the projectile and, as long as the detonations were far enough away from the target as to not fracture the loosely held object, the force from the repeated blasts should alter the trajectory.

See Nuclear Pulse Propulsion developed by DARPA in the late 1950s and early 1960s

Limitations
PBAPMs are not intended to destroy an incoming projectile because when they are used in this manner, the chances of one projectile on a single predictable trajectory turning into multiple projectiles on random vectors increases dramatically. However, a PBAPM with a large enough yield could theoretically fracture a projectile intentionally to create several, smaller projectiles. These projectiles would then burn up harmlessly in the atmosphere depending on the composition of the projectile, effectiveness of the fracturing, atmospheric composition and density.

Fictional Examples
Pending

Real-World Examples
Pending

Questions

 * 1) How much energy per unit of mass (kJ/kg) is required to destroy an incoming projectile? 
 * 2) How can incoming projectiles be identified and tracked allowing for enough time to intercept with a missile?