title: Design and optimisation of solar sail orbits in proximity of asteroids
Creators: name: Moore, Iain
Publisher: name: University of Glasgow
Year: 2023

description: A solar sail is a large reflective membrane which is capable of producing thrust for a spacecraft by the reflection of sunlight. Such a propellant-less propulsion system can offer solutions to high-energy missions which would be impossible for conventional propulsion systems. As a result, this technology has been proposed by many authors as the ideal candidate for a multiple asteroid rendezvous mission. At the time of writing, there are more than 30,000 known near-Earth asteroids (NEAs) alone. Adding to this those contained in the main belt and elsewhere in the solar system, the abundance of these small rocky worlds becomes apparent. Focusing only on the NEAs, there are many reasons for interest in missions to these bodies. In the first instance, they represent the earliest building blocks of the rocky worlds of the solar system, and are often still in pristine condition, similar to how they would have been since these earliest moments. As such, there is massive scientific interest in visiting and extracting samples of their constituent materials. There is another community which is also interested in the extraction of these materials: the future asteroid miners. This mining could provide propellant for deep space missions, materials for in-space infrastructure and potentially also in the return of minerals which are rare on Earth, and so of great value. However, although these bodies provide many opportunities, they are not without threat. Although the frequency of impacts of large bodies capable of causing considerable damage to Earth-based infrastructure is relatively low, there are still recent examples of just such events. With the potential for large scale loss of life due to an asteroid impacting populated areas, the science of planetary defence requires greater knowledge of the make-up of these bodies. Yet another reason for mission designers to examine further options in achieving efficient missions to these bodies. It would be beneficial, in terms of cost, for a single spacecraft to be able to carry out a mission to multiple asteroids. Such a high-energy mission is ideally suited to the solar sail. Although the literature has provided many works on orbital transfers to multiple bodies, the operation of the sail when in proximity of the asteroid has not received quite as much attention. It is in this phase of the mission, where the science objectives would be carried out, that this thesis focuses. There are numerous challenges which the sail faces in the near-asteroid environment. These include the irregular gravity field, the strength of the acceleration provided by the sail in a relatively weak gravitational field, the often fast rotational velocities of the asteroid and higher demands on slew rates for the sail due to the shorter period of low-altitude orbits. The work will consider three main proximity phases. The first operation is in the control of an orbit using the solar sail in an irregular gravity field. In this operation, the sail must counter the perturbative effects of a non-spherical body. This manifests in the rotation of the orbit node line, referred to as nodal regression. A new tool, referred to as the Control Transition Matrix (CTM), which aids in forcing a periodic orbit solution over multiple orbits is then presented. The second operation deals with the control of a sail at the point of and subsequent to the deployment of a lander and during the deployment of a series of small ChipSat probes. The landing conditions for deployments from various locations around the asteroid are analysed before the deployment is presented from a low-asteroid orbit. The control of the sail along a nominal orbit while the lander is still on-board is presented before the sail control subsequent to the lander deployment is considered. Given the high velocity impacts for a ballistic lander deployed at large distances from the surface, an alternative mission scenario of the deployment of small ChipSat probes is presented. These probes are envisaged to carry out their science goals during the descent and so the landing conditions are less important. The final operation is in the gravitational capture of the sail around the asteroid. This work provides a preliminary analysis of the capability of the sail in achieving this by using a simple on/off control law. Following this, a more detailed two-phase approach is presented. In the first “initial capture” phase, the sail uses the value of Jacobi constant in the 3 body system as a guide to reduce the orbit radius to within a defined region. After this, the “orbit shaping” phase aims to circularise the orbit at this radius. Subsequently, preliminary investigations into an optimal approach are presented. In controlling the effects due to the non-spherical asteroid shape, an optimally controlled solution, where a minimum effort control law is sought, is presented. Following this, a novel method of updating a control law was successfully applied to force a periodic orbit. In the work carried out on lander deployment, it was found that the sail was capable of maintaining a periodic orbit after the point of lander separation by application of time-delay feedback control. For the deployment of a series of small probes, it was found that maintaining a fixed attitude for the sail during the deployment was not considerably different in station-keeping performance compared with LQR control, and performed this with no effort required of the sail. Finally, in the work on capture, the two-phase approach provided successful capture trajectories down to the desired orbit radius. The work showed that, for reducing size of asteroid, there was a reduction in the time to capture. This is due to the fact that the same size of sail is used in the weakening gravity field of each asteroid. This makes the sail relatively more powerful and so able to affect quicker capture. It was also seen that long period capture trajectories are compounded by the need for the sail to spend periods of time waiting for the position of the Sun relative to the orbit to be in such a way as to permit the capture operations to proceed. There was also the successful demonstration of an optimally controlled capture which minimised the orbit semi-parameter over one orbit revolution. The work contained in this thesis provides preliminary analysis for the consideration of future solar sail mission designers in the proximity operations of a sail near an asteroid. The findings presented here have shown that the sail can be of considerable utility in these proximity operations. They also present challenges to the mission designer given the continuous thrust that they may provide. Where a powerful sail may benefit the interplanetary phase of a mission in reaching many more asteroids further from the Earth, this can also present a challenge in the relatively weak asteroid gravitational field. However, these challenges are not insurmountable and so the sail remains a promising option for these high-energy missions.