We present a detailed investigation of the dramatic changes that occur in the \mathcal { L } _ { 1 } halo family when radiation pressure is introduced into the Sun-Earth circular restricted three-body problem ( CRTBP ) .
This photo-gravitational CRTBP can be used to model the motion of a solar sail orientated perpendicular to the Sun-line .
The problem is then parameterized by the sail lightness number , the ratio of solar radiation pressure acceleration to solar gravitational acceleration .
Using boundary-value problem numerical continuation methods and the AUTO software package \citep Doedel1991 the families can be fully mapped out as the parameter \beta is increased .
Interestingly , the emergence of a branch point in the retrograde satellite family around the Earth at \beta \approx 0.0387 acts to split the halo family into two new families .
As radiation pressure is further increased one of these new families subsequently merges with another non-planar family at \beta \approx 0.289 , resulting in a third new family .
The linear stability of the families changes rapidly at low values of \beta , with several small regions of neutral stability appearing and disappearing .
By using existing methods within AUTO to continue branch points and period-doubling bifurcations , and deriving a new boundary-value problem formulation to continue the folds and Krein collisions , we track bifurcations and changes in the linear stability of the families in the parameter \beta and provide a comprehensive overview of the halo family in the presence of radiation pressure .
The results demonstrate that even at small values of \beta there is significant difference to the classical CRTBP , providing opportunity for novel solar sail trajectories .
Further , we also find that the branch points between families in the solar sail CRTBP provide a simple means of generating certain families in the classical case .