CPC B64G 1/242 (2013.01) [B64G 1/2427 (2023.08); B64G 1/66 (2013.01)] | 20 Claims |
1. A method to provide a nominal trajectory to land an object on a secondary body orbiting a primary body, the method comprising:
selecting a Jacobi constant for a nominal trajectory, the nominal trajectory being a landing trajectory for the object to land on the secondary body at a nominal landing site;
selecting initial conditions comprising a plurality of velocities tangent to the nominal landing site, each of the plurality of velocities having the Jacobi constant;
selecting a surface of section for the primary body;
propagating the initial conditions backwards in time for trajectories to intersect the surface of section;
producing a Poincaré map from the intersections in the surface of section, keeping track of iterations of the trajectories passing through the surface of section;
producing a Swiss Cheese plot of the k-th iterates by producing a Poincaré map of the k-th iterate in at least 2 steps:
(i) plot all points using Delaunay variables in 2-dimension;
(ii) plot points from the k-th iterate such that the points using Delaunay variables can be distinguished from the points from the k-th iterate;
using the Swiss Cheese plot of the k-th iterate by locating a plurality of resonant trajectories of the k-th iterate by locating those points of the k-th iterate on the Poincaré map that are close to the center points between vertical holes in the Poincaré map which determine a resonance;
selecting one of the plurality of resonant trajectories as the nominal trajectory.
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