The team starts by learning how to detect asteroids from parallax observation (from Earth as we orbit the sun), and how to predict which asteroids pose a threat (by predicting orbits).

Model the particle beam power and duration it will take to nudge a problem asteroid off a collision course. Analyze the mass distribution and arrival frequency of meteorites, and their destructive potential. Devise a formula or algorithm that prioritizes the threat level of an asteroid based on diameter and collision probability.

Come up with a design for the deflector gun and it's robotic steering mechanisms. What type of beam energy? How is it powered?
What is the power density (watts / square meter) at varying target distances? Will there be enough "clout" to deflect the largest expected asteroids inhabiting the solar system? Decide where the gun should optimally be located on the moon (taking into account Earth safety, field of view for shooting, earth communication, and installation).

After the deflector gun system has been built and rehearsed on Earth, design a team of spaceworker robots who will deploy the gun at the desired location on the the moon.

Build a model that demonstrates the system's value to mankind.