Numerical optimisation of constellation and orbit design for the OLFAR radio interferometry swarm in orbit of the Earth-Moon L4 point

Numerical optimisation of constellation and orbit design for the OLFAR radio interferometry swarm in orbit of the Earth-Moon L4 point

van 't Hoff, Jurriaan (TU Delft Aerospace Engineering)

Visser, P.N.A.M. (mentor)

Delft University of Technology

Aerospace Engineering

2020-09-24

In the field of radio astronomy the Ultra-Long Wavelength (f < 30MHz) band is unique, it has been studied for nearly a century yet it is still almost completely uncharted. Due to the reflective properties of Earth's ionosphere this band is nearly completely inaccessible for ground-based observatories, which can only receive frequencies down to 8 MHz in ideal conditions. This band may only be explored from space, but the creation of space based observatoriesis problematic due to the large telescope sizes associated with these frequencies. The only viable solution to space-based radio observation is the use of radio interferometry, a process which combines measurements of multipleradio receivers to act as a single instrument with a larger aperture. Plans to establish these constellations have existed for some time, but have always been too expensive. With the rise of micro-satellites the concept of a radiointerferometry constellation has become economically viable. The OLFAR mission is one among the many recent radio interferometry concepts, which stands out among its peers through the application of a swarm design philosophy.The most important instrumental property of a radio interferometer is the number of available instrument pairs (baselines), and the distribution of their relative orientation in uvw space. To facilitate radio interferometry at 10MHz and lower frequencies the OLFAR swarm requires orbits which offer relative velocities below 1 m/s, while also being sufficiently stable to keep the baseline between its members below a maximum of 100 km. A minimal separationof 500 meters between satellites is used for collision safety. Early concepts for the OLFAR mission made use of Lunar orbits, where the Moon would act as a radiation shield against Earth's interference. Previous studies have shown thatsuch orbits expose the swarm to unacceptably large relative velocities, which is why alternative deployment locations are still being studied. This thesis studies the applicability of swarm orbit designs around the fourth Lagrangianpoint, denoted as L4. This point offers very promising orbital properties, but it has not been studied in detail due to the swarm's exposure to interference. As a basis for this work it is assumed that the 9dB of interference mightbe worked around through the dynamic range of hardware and longer integration times, making L4-centric orbits aviable deployment location.Particular attention is paid to developing an accurate numerical model for a perturbed orbital environment, which is necessary to provide long-term orbits of good quality. The inclusion of perturbations in this model is based on theirmaximum demonstrable effect on baselines and overall satellite positions over a year in orbit. After establishing the numerical simulation environment the satellite swarm design problem around L4 is posed as an optimisation problemfor heuristic algorithms. Based on small-scale experiments the efficiency of different algorithms and architectures is evaluated, and the best-suited solution is used to optimise swarm designs for the OLFAR missions. The resultingmethod of choice maximises the potential of multi-threading, using 32 connected differential evolution algorithms with 48 population members to perform as a single algorithm with a population of 1536 individuals.Using this method satellite swarm designs and orbits of up to 35 elements are found, which demonstrably meet all interferometry-related mission requirements for over a year in orbit while only relying on passive formation flight. These swarm designs rely on a process which is described as swarm folding to achieve this result. By distributing the swarm as a column mirrored in the barycentric z direction with uniform velocities, the swarm initially folds overitself. This folding motion is periodically repeated throughout the designed orbit after the initial fold as a result of the swarms natural orbits. The folding motion greatly enhanced long-term cohesion of the swarm, and it creates avery dynamic baseline distribution pattern for radio interferometry. It is demonstrated that these orbit designs have near-ideal baseline distributions, wherein they are only limited by the natural limitations of the Lunar orbital plane.Though the application of swarm folding these designs remain compact for long time periods, even in a perturbed environment. The demonstrated designs have feasible mission lifetimes up to 3 years in-orbit, requiring only a fewmanoeuvres during this time to enforce the 500 meter separation for collision safety. Through the application of active formation control it is expected that this can be extended to 5 years in-orbit with the right swarm orbit design. Itis also expected that using the methods in this thesis larger swarm designs might also be found, potentially ranging into 50 satellites. The largest hindrance to further extending the size of the swarm is the risk of near-collision events,which are inherent to the folding motion.

Swarm Satellite Constellation
Orbit Design
L4
Optimisation
Radio interferometry
radio astronomy
OLFAR

http://resolver.tudelft.nl/uuid:e1dd90a2-3130-49ba-aa13-0a436536e4dd

Student theses

master thesis

© 2020 Jurriaan van 't Hoff