Project Description

The space sector has experienced a continuous growth in the last decade with more and more companies interested in accessing it. This has resulted in a large increase on the number of space missions, being the best exponent of that found in the Low Earth Orbit region. Particularly, missions based on constellations and flight formations have become more common than ever due to the potential possibilities and reduction of costs that they provide, being megaconstellations, space structure comprised by hundreds or thousands of satellites, a new phenomenon that started in the last years. This has led to a situation where conjunctions between satellites have dramatically increased in some regions, making much more complex to design constellations that are able to efficiently perform their missions while avoiding conjunctions with other satellites. Therefore, it is paramount to develop techniques that allow not only to define, but also to study and understand these complex systems efficiently. To that end, we propose the combination of analytical formulations based on Number Theory with optimization techniques to analyze these systems and extrapolate their results to the Space Traffic Management problem. This will allow obtaining efficient solutions while providing a much better insight into these systems.

Start Date

Fall 2021

Postdoctoral Qualifications

Ph.D. in Aerospace Engineering, Applied Mathematics or related discipline.

Experience in either astrodynamics or in optimization techniques for large multidimensional spaces. Having experience in both domains would be highly advisable.

Some knowledge on Number Theory would be also interesting, although not completely necessary.

Open and interdisciplinary mindset that allows working in problems involving very different fields and approaches.

Co-Advisors

David Arnas, darnas@purdue.edu, School of Aeronautics and Aerospace.
Xiangxiong Zhang, zhan1966@purdue.edu, Department of Mathematics, https://www.math.purdue.edu/~zhan1966/.

Bibliography

David Arnas is an Aerospace Engineer with a Ph.D. in Mathematics and Statistics. His research interests are satellite constellation design, celestial mechanics, perturbation theory, number theory, applied mathematics, and the development of algorithms for different purposes.

Relevant publications:
Arnas, D., Casanova, D. and Tresaco, E., 2021. n-Dimensional congruent lattices using necklaces. Advances in Space Research, 67(11), pp.3725-3743.
Arnas, D., Lifson, M., Linares, R. and Avendaño, M.E., 2021. Definition of Low Earth Orbit slotting architectures using 2D lattice flower constellations. Advances in Space Research, 67(11), pp.3696-3711.
Arnas, D. and Casanova, D., 2020. Nominal definition of satellite constellations under the Earth gravitational potential. Celestial Mechanics and Dynamical Astronomy, 132(3), pp.1-20.
Arnas, D., Casanova, D. and Tresaco, E., 2021. 2D Necklace Flower Constellations applied to Earth observation missions. Acta Astronautica, 178, pp.203-215.
Arnas, D., Casanova, D. and Tresaco, E., 2017. Time distributions in satellite constellation design. Celestial Mechanics and Dynamical Astronomy, 128(2), pp.197-219.