A dynamical system approach for the station keeping of a solar sail

Abstract

In this paper we have considered the movement of a solar sail in the Sun-Earth system. As a model we have used the restricted three-body problem adding the solar radiation pressure. It can be seen that we have a two-dimensional family of equilibria parameterized by the two angles defining the sail's orientation. Most of these equilibrium points are unstable and require a control strategy to keep the sail close to them. We have designed a control strategy that uses the knowledge of the position of the invariant manifolds and how they vary when the sail orientation is changed. We have tested our strategy with two known missions: the Polar Observer and the Geostorm Warning Mission. Simulations of up to 30 years have been performed taking into account errors on the position and velocity determination of the sail and on the sail's orientation.

On the station keeping of a solar sail in the elliptic Sun–Earth system

“…If β is small, this surface has five connected components, that merge for β large enough. For more details, see [11,12,2]. In Fig.…”

“…In previous works [2,4] we used dynamical systems tools to develop a station keeping strategy for this situation in the Circular RTBP model. The key point there was to understand the dynamics of the system for a fixed sail orientation, and see how it varies with the orientation of the sail.…”

“…Then, this information was used to derive a sequence of changes on the sail orientation that keeps the sail close to equilibria. We already tested these algorithms with the GeoStorm and Polar Observer missions [2,4]. During the simulations we considered the CRTBP + solar radiation pressure as a model.…”

“…The station keeping is based on an extension of the results for fixed points presented in [2,3]. The main idea is to use the Floquet modes of the periodic orbit to find a periodic reference system that simplifies the tracking of the relative position of the solar sail with respect to the nominal periodic orbit and its stable and unstable invariant manifolds.…”

“…In Section 3 we describe the effects of the eccentricity of the Earth on the phase space of the RTBP plus sail. In Section 4 we will discuss how to extend the station keeping strategy introduced in [2,3] to this case, where we need to remain close to a periodic orbit. Finally, in Section 5 we will test the performance of this strategy on the GeoStorm mission.…”