From the first principles, calculate the technical requirements to build the electromagnetic rail gun on the Moon to defend the Earth from asteroids. Technical requirements to be calculated include the following parameters:

1. Energy and power required to operate the rail gun at the required firing frequency.

2. Physical dimensions and weight required for the rail gun.

3. Probability of hitting an asteroid at various locations in space.

4. Realistic dimensions of heat dissipating radiators around the railgun operating in vacuum with the required frequency of projectile firing with 100% target hitting probability.

Rail gun uses metallic Moon's rocks as projectiles and electricity as a propellant. Assume frictionless motion for electromagnetically propelled metallic projectiles inside the rail gun. Use at least three values for kinetic energy and physical dimensions of asteroids. Assume asteroid bundling with various distributions in dimensions and distance between them (proximity).