Celestial mechanics

TraX investigates the dynamics of small bodies in the Earth–Moon system, where the small bodies can be either Near Earth Asteroids (NEAs), dust particles, or a spacecraft. To understand and predict the motion of celestial bodies is one of the oldest problems of mankind. We will consider the motion of the bodies as described by Newton's equations. Even though the basic equations are known, extracting useful features and a global picture remains a challenge. At present, many methods to deal with local problems have been developed, but there is a lack of techniques to cope with global features of the dynamics. In this project we propose to use an approach that can be seen as a combination of local and global tools: We will compute invariant structures in phase space that represent small scale features of the dynamics. We will then use their stable and unstable manifolds to establish how global transitions between these local structures can occur. Advances in the problems studied in this proposal are linked to and will lead to more general advances in dynamical systems and applications.

In addition to the classical problems of dynamical astronomy, today the field also includes the design and control of trajectories for space missions. Several space agencies and private companies are considering the exploitation of raw materials from asteroids, e.g., gold, iridium and platinum. In this context, near Earth asteroids (NEAs) offer the intriguing option to attach a propulsion system to the asteroid and capture it into a suitable orbit of the Earth-Moon system by means of a small manoeuvre, as planned, for example, in NASA's Asteroid Redirect Mission. We will also devise plans for a variety of possible missions that are energy efficient because they take advantage of the natural dynamics of the system.

Partners of TraX study the possibility of using such stability zones in the Earth-Moon as possible “parking lots” for NEAs. To this end, one has to devise a sequence of small perturbations of the natural dynamics that will turn the original orbit of the NEA into a captured orbit. One has to consider not only the size of the manoeuvres that will determine the efficiency of the mission. In addition, the mission must be designed such as to avoid the risk that the NEA might collide with Earth in case that any of the manoeuvres fails.

A second strand of work in dynamical astronomy considers the dynamics of a spacecraft with a solar sail. A solar sail is a novel system of space propulsion based on the impulse provided by the solar radiation pressure (SRP) on a highly reflecting surface. Although the acceleration given by a solar sail is small, it acts continuously and its accumulated effect allows for some space missions that are difficult to carry out by a spacecraft with a standard chemical thruster. This technology has already been tested in space by the Japanese space agency JAXA and NASA in 2010.