US 11,905,043 B2
Methods and systems for trajectories, approaches, flybys, landings, and orbits in three-or-more body systems
Martin W. Lo, Pasadena, CA (US); Brian D. Anderson, Pasadena, CA (US); Ryan Burns, Pasadena, CA (US); Damon Landau, Pasadena, CA (US); and Jared T. Blanchard, Stanford, CA (US)
Assigned to CALIFORNIA INSTITUTE OF TECHNOLOGY, Pasadena, CA (US)
Filed by CALIFORNIA INSTITUTE OF TECHNOLOGY, Pasadena, CA (US)
Filed on Oct. 20, 2021, as Appl. No. 17/506,436.
Claims priority of provisional application 63/230,222, filed on Aug. 6, 2021.
Claims priority of provisional application 63/142,836, filed on Jan. 28, 2021.
Claims priority of provisional application 63/094,131, filed on Oct. 20, 2020.
Prior Publication US 2022/0119133 A1, Apr. 21, 2022
Int. Cl. B64G 1/24 (2006.01); B64G 1/66 (2006.01)
CPC B64G 1/242 (2013.01) [B64G 1/2427 (2023.08); B64G 1/66 (2013.01)] 20 Claims
OG exemplary drawing
 
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.