Space Trajectories. Space Debris Cleaning

Near-Earth space is populated by thousands of pieces of debris of all sizes. Estimates suggest that there are around one million objects between 1 and 10 cm in size, and 36,000 objects larger than 10 cm. These objects, travelling at orbital speed (7 to 8 km/s), represent a constant threat to operational satellites and the space station. They require daily tracking and precise trajectography in order to anticipate the risk of collision, and if necessary to take evasive action.

Debris comes from old satellites and launcher stages abandoned in orbit since the beginning of the space age. The erosion of these vehicles (mainly by impact with particles) constantly generates new debris, which in turn is a source of new collisions. To curb this exponential growth, known as Kessler syndrome, we need to avoid abandoning new vehicles in orbit, and also eliminate the largest existing pieces of debris. Several studies have led to the conclusion that the elimination of at least five large pieces of debris per year (old satellites or launch vehicle stages), in addition to scrupulous compliance with regulations, is necessary to at best stabilize the debris population and not compromise the use of space in the decades to come.

A particularly critical region is that of sun-synchronous orbits (SSO) and polar earth orbits (PEO) in the 700-900 km altitude range. These orbits, which are well suited to Earth observation, concentrate a large number of satellites and consequently of debris.

The clean-up program consists of launching a series of dedicated vehicles, each tasked with capturing and de-orbiting five selected pieces of debris. The choice of debris leads to a combinatorial problem of the travelling salesman type. This intrinsically complex problem has two additional difficulties:

• debris orbits vary with precession, making the combinatorial problem time-dependent;

• the cost of the missions is that of orbital transfers between the selected pieces of debris, which requires solving a series of optimal control problems.

This article deals with the problem of planning cleaning missions. The aim is to ensure that these missions can be carried out by identical vehicles at the lowest possible cost. The optimization problem is formulated in the first part, then a transfer strategy adapted to high and low thrust cases is defined in the second part. The third part describes a three-stage optimization procedure based on the simulated annealing method. The method presented enables missions to be optimized, taking into account the deorbiting strategy (by the vehicle or autonomous kits) and the priorities assigned to the debris. An example of application...