Satellite Constellations

Number theory in satellite constellation design

Satellite constellation design is a complex problem involving the interaction of a large number of variables. This makes extremely difficult to perform analysis both analytically and numerically. To overcome this situation, it is possible to analytically define satellite constellations and study their properties using these analytical formulations. One efficient approach in this regard is the use of number theory. In general, one would think that since satellites are distributed in position and velocity, we should based the constellation definition on real numbers. However, this is far from true. In fact, the end result of the constellation is to distribute an integer number of satellites in an integer number of orbits, which at the same time, are distributed in an integer number of orbital planes and altitudes. Therefore, even if we do not consider them, the relations between integer numbers are going to drive the properties of the constellation as a whole. For this reason, ART focuses on finding these relations and provinding a deeper insight into the properties of satellite constellations.

 

Application of constellation theory to space traffic management

Each passing year more and more satellites are being launched into space, increasing the density of objects orbiting the Earth. This is especially true in Low Earth Orbits due to the technological and economical advantages that it provides to space missions. However, to this day, no international agreement has appeared on how to allocate orbits and space. This will difficult the sustainability of the space sector for future missions as the number of satellite conjunctions increases every year. To that end, this goup aims to propose slotting mechanisms for space traffic management such that each slot is able to prevent any conjunction to any of the other slots of the configuration. This allows not only to create a safer space sector, but also to assure the access to space for future generations. Additionally, this research aims to provide estimates of the current and future orbital capacity of the space sector, providing a deeper insight on which are the driving factors that affect that capacity. An example of the current trend and what can be achieved using slotting architectures can be seen in the following figure.

 

Satellite constellation design under orbital perturbations

Any satellite's orbit is going to be constantly affected by orbital perturbations during its mission life. Therefore, it is in our interest to guarantee the stability of the satellite formation both in the short and long terms. There are some orbital perturbations that due to their periodic nature can be included in the nominal design of the constellation. One example of them is the gravitational perturbation due to the non-spherical potential of the Earth. Conversely, there are other perturbations, such as the atmospheric drag or the solar radiation pressure, that are neither periodic nor can be predicted with enough accuracy. This means that these perturbations have to be compensated with orbital maneuvers. What makes this problem more interesting for satellite constellations is that each satellite can have a different orbit or different physical characteristics, which can affect the long term evolution of the orbits. An example of such effects can be seen in the figures below. These figures represent the evolution of the inclination in two satellites that share the same ground-track but have different orientation with respect to the Sun.