Project 2: Planet Builder

Asteroids of equal size orbit the sun in initially circular orbits at various radii. There is a lower and upper radius bound, so that the asteroids are in a formation like the asteroid belt between Mars and Jupiter. You get to push the asteroids a bit to change their trajectory. When asteroids collide there is conservation of momentum and the asteroids remain joined (and larger). Energy is not conserved: the newly formed asteroid heats up! Your goal is to create a single planet made up of at least half the initial asteroid mass within a fixed time T. Each time you exert a push, the energy required for that push is accumulated into your score; you want to minimize the total energy used. (Using a lot of energy to form a planet quickly scores worse than forming the planet more slowly with less energy, as long as the planet forms within T time units.)

Asteroids are influenced in their trajectory by the sun, whose gravity is strong. The gravitational attraction of other asteroids is assumed to be negligible and is ignored by the simulator. All interacations (including your pushing of asteroids) happen in the plane of rotation of the solar system. A push perpendicular to the movement of the asteroid will change its orbit, but sill retain the circularity of the orbit; a non-perpendicular push (or collision) may lead to an elliptical orbit.

For a cool related game concept, see Osmos.