Optimal Low-Thrust Trajectories to Reach the Asteroid Apophis

Apophis is considered by the Greeks as chaos, the God of destruction. For this reason, in current times, this name returns to scene to represent a destructive potential threat to the Earth. It is the name of an asteroid that orbits a region that represents a high risk of collision with the Earth. This asteroid was discovered in 2004 and received the initial name of 2004MN4. Then it was named Apophis, and several researchers and institutes are monitoring and designing missions with the goal of finding more information about the asteroid. The present research has the goal of finding optimal (in the sense of minimum fuel consumption) interplanetary missions, based in low thrust propulsion systems to send a spacecraft to Apophis. The spacecraft is assumed to leave the Earth from a Low Earth Orbit (LEO). An indirect optimization method is used in the simulations to find the trajectories. Two different engines will be used to determine the trajectories: the PPS1350 and the Phall 1. This is done to get some insights of the differences between a propulsion system that has a fixed magnitude for the force and one that has a magnitude that varies with the distance between the spacecraft and the Sun. Another reason to perform this research is to test the parameters of the Phall 1, that is an engine under development. Key-Words: Astrodynamics, Celestial Mechanics, Space Trajectories, Low-Thrust, Solar Electric Propulsion.