Leaving Earth to Fight the Asteroid
The orbits around the Earth or the Moon are called cislunar space. In some rare cases, asteroids can be intercepted in cislunar space, but many asteroid has to be intercepted outside of the cislunar space. Relative velocity between the asteroid and kinetic interceptor or nuclear interceptor does not fluctuate much. For kinetic interceptor, the faster the relative velocity is, more effective the interception become. However, at the same time, it will be more difficult to hit the CG, as mentioned in the interception section. Therefore, current relative velocity is estimated as 5-10 km/s. For the nuclear interceptor, the relative velocity should be much low.
However, the speed of an asteroid varies greatly, especially if asteroid's orbit is more eccentric (or elongated). An asteroid travel the fastest at periapsis and the slowest at apoapsis. In order to maximize the effectiveness, asteroid should be intercepted at its apoapsis. Apoapsis is usually very far away from Cislunar space for Apollo NEOs.
In order to intercept an asteroid at its apoapsis, the interceptor must leave the cislunar space and enter a heliocentric orbit, an orbit around the Sun. In order to enter a heliocentric orbit, an interceptor from the Earth must accelerate to 11.2 km/s, while an interceptor from the Moon must accelerate only to 2.42 km/s. Because kinetic energy is function of mass and velocity squared, if an interceptor was launched from the Moon, it requires less than 1/21 of energy to deploy it to heliocentric orbit, compared from launching it from the Earth.
