Capture in Patch CR3BP

* Türkçesi için

Capture between manifolds can be considered more advance way in Patch-CR3BP. In this litrature, Patch-CR3BP can be also called Restricted 4 body Probem, which is simply composed of patch of two different binary system. Two different CR3BP (binary system) can be patch two main way as it is shown below;

a) is co-linear* Patch-CR3BP (such as Jupiter (M0) and their Moons {M1 and M2}, or Sun (Mo) and Planets {M1 and M2}), and b) is bi-circular* Patch-CR3BP {Such as Sun (Mo), Earth (M1), and Moon (M2)}. The examples are shown in below;

As it is seen again, Poincaré cut (right plot) help us to determine the jump point (Transfer patch point), between two manifolds from different systems, in Jupiter-Europa-Ganymede. Because Both Binary system are in same plane, we can conveniantly use the planar invariant manifold tubes, and so Ponincare cut can be taken practically. But if the tubes are plotted as 3D, then Poincare cut become 4D, and more complicated for the visualization of the solution space.

So then, let’s see the other patch case example;

(a) and (b) Vary the phase of the Moon until Earth-Moon L2 manifold cut intersects Sun-Earth L2 manifold cut. (c) Pick a point in the interior of the Earth-Moon L2 manifold curve but in the exterior of the Sun-Earth L2 manifold curve. (d) An orbit will get ballistically captured by the Moon when integrated foreward; when integrated backward, orbit will hug the invariant manifolds back to the Earth. [*]

In this patch, the inclination (~5°) between the Sun-Earth and Earth-Moon planes are neglegted for simply solution. But if the inclination (~5°) is added, the problem become more comlicated, of course.

* Figures are borrowed from [W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross], and for more information please see this book.

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