2,540 research outputs found
Evolution of the L1 halo family in the radial solar sail CRTBP
We present a detailed investigation of the dramatic changes that occur in the
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 (Doedel et al. 1991) the
families can be fully mapped out as the parameter is increased.
Interestingly, the emergence of a branch point in the retrograde satellite
family around the Earth at 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
, resulting in a third new family. The linear stability of
the families changes rapidly at low values of , 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 and provide a comprehensive overview of
the halo family in the presence of radiation pressure. The results demonstrate
that even at small values of 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.Comment: 31 pages, 17 figures, accepted by Celestial Mechanics and Dynamical
Astronom
Gravitational Ionization: Periodic Orbits of Binary Systems Perturbed by Gravitational Radiation
The long term perturbation of a Newtonian binary system by an incident
gravitational wave is discussed in connection with the issue of gravitational
ionization. The periodic orbits of the planar tidal equation are investigated
and the conditions for their existence are presented. The possibility of
ionization of a Keplerian orbit via gravitational radiation is discussed.Comment: ps file, 35 page
Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
We extend our previous analytic existence of a symmetric periodic
simultaneous binary collision orbit in a regularized fully symmetric equal mass
four-body problem to the analytic existence of a symmetric periodic
simultaneous binary collision orbit in a regularized planar pairwise symmetric
equal mass four-body problem. We then use a continuation method to numerically
find symmetric periodic simultaneous binary collision orbits in a regularized
planar pairwise symmetric 1, m, 1, m four-body problem for between 0 and 1.
Numerical estimates of the the characteristic multipliers show that these
periodic orbits are linearly stability when , and are
linearly unstable when .Comment: 6 figure
On the Ionization of a Keplerian Binary System by Periodic Gravitational Radiation
The gravitational ionization of a Keplerian binary system via normally
incident periodic gravitational radiation of definite helicity is discussed.
The periodic orbits of the planar tidal equation are investigated on the basis
of degenerate continuation theory. The relevance of the Kolmogorov-Arnold-Moser
theory to the question of gravitational ionization is elucidated, and it is
conjectured that the process of ionization is closely related to the Arnold
diffusion of the perturbed system.Comment: 19 pages, REVTEX Style, To appear in JM
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