Solar Sail Surfing Along Invariant Manifolds To Increase The Warning Time For Solar Storms

Abstract

Space-weather events have a large impact on Earth. In particular, Coronal Mass Ejections (CME) pose huge potential dangers to human technology both in orbit and on the surface of the planet, such as disruptions to power grids, increased radiation doses to astronauts and damage to sensitive components of satellites. Warnings for space-weather events are currently given by satellites in the vicinity of the L1 point. When a CME passes by that point, the satellites emit a warning that reaches the Earth, on average, one hour before the CME. This thesis aims at using solar-sail technology to move a satellite closer to the Sun, detect the CME sooner, and thus increase the warning time.

Solar sails continuously generate thrust by reflecting solar photons off a large and highly reflective sail membrane. This continuous acceleration can be used to generate Artificial Equilibrium Points (AEPs) in the Circular Restricted Three-Body Problem (CRTBP) that are displaced away from the five classical Lagrange points. Like for the classical case, periodic orbits exist around these AEPs, enabling, for example, CME monitoring in a periodic orbit around an AEP that is located closer to the Sun than the Sun-Earth L1 point from where current satellites detect CMEs. There have been some theoretical mission designs taking advantage of this possibility, but the increase in warning time is modest for any near-term sail performance.

This thesis investigates the use of solar-sail technology to travel upstream of the CME and significantly increase the warning time. The study considers the actual shape of CMEs as a constraint for the solar-sail trajectory that surfs along invariant manifold-like structures emanating from AEPs and Lyapunov orbits around sub-L1 points, i.e., AEPs sunward of the classical L1 point, to travel upstream of the CME.

As a preliminary solution, two strategies are evaluated. The first strategy considers a series of heteroclinic connections between different AEPs in the sub-L1 region. The second strategy uses a homoclinic connection of a Lyapunov orbit around a sub-L1 point. The trajectories aim to travel upstream along the path of the CME and back to the initial AEP or Lyapunov orbit to guarantee periodicity and, therefore, CME monitoring for as long as the sail remains operational. The homo- and heteroclinic connections are sought for by looking for connections between the unstable and stable manifolds emanating from the AEPs and Lyapunov orbits. To minimize the discontinuity in states at the linkage of the unstable and stable manifolds, a genetic algorithm approach is used to optimize the piece-wise constant attitude of the sail along the manifold trajectories and the location, i.e., which AEP or where along the Lyapunov orbit, from where the manifolds emanate.

Though the homo- and heteroclinic connections exhibit a discontinuity in the attitude of the sail at the connection of the unstable and stable manifolds, they provide a good initial guess for further optimization with a direct pseudospectral method, implemented in the software tool PSOPT. In the optimal control approach, the attitude of the sail is allowed to vary along the trajectory (instead of the piece-wise constant sail attitude in the genetic algorithm approach) such that the sail travels as far as possible upstream of the CME while staying as close as possible to the central axis of the CME.

The genetic algorithm results from both strategies show an improvement in warning time with respect to the warning time achieved by current satellites in the environment of the L1 point. Under the assumptions taken in this research, the trajectories using the homoclinic connections from a Lyapunov orbit out-perform those that employ heteroclinic connections between AEPs. The best genetic algorithm solution offers an up to 10 times longer warning time than current satellites at L1.
This solution shows a small discontinuity in the states at the linkage of the unstable and stable manifold trajectories in the order of thousands of kilometers for the position and centimeters per second for the velocity. However, the
discontinuity in the attitude of the sail of approximately 70 degrees renders the trajectory unfeasible before further optimization.
Furthermore, some parts of the trajectory are too far from the axis of the CME to intercept CMEs approaching the Earth.

Finally, the trajectories obtained with PSOPT show that the sail remains within a defined distance to the axis of the CME while traveling upstream of the CME due to a control law that modifies the attitude of the sail at a rate achievable with state of the art technology. This strategy allows a 15 times longer average warning time compared to the warning time provided by current satellites at the L$_1$ point.