By J. Llibre, R. Martinex, Carles Simo
During this ebook the matter of station protecting is studied for orbits close to libration issues within the sun method. the focus is on orbits close to halo ones within the (Earth+Moon)-Sun process. Taking as start line the limited three-body challenge, the movement within the complete sunlight procedure is taken into account as a perturbation of this simplified version. all of the examine is completed with adequate generality to permit effortless software to different primary-secondary platforms as an easy extension of the analytical and numerical computations.
Read or Download Dynamics and Mission Design Near Libration Points, Volume I : Fundamentals : The Case of Collinear Libration Points (World Scientific Monograph Series in Mathematics) PDF
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Additional info for Dynamics and Mission Design Near Libration Points, Volume I : Fundamentals : The Case of Collinear Libration Points (World Scientific Monograph Series in Mathematics)
Where m is the ratio of mean motions of the Moon and the Sun. Using the LindstedtPoincare method, (xi,yi,Zi), i = 1,2,3, can be computed and the solutions correspond to Lissajous trajectories. 000818^. In order to obtain a halo orbit (ujXy = wz) at least a value of Ay = 46 793 km is needed. For this amplitude the expansion taken for the orbit is no longer valid. In order to eliminate the secular terms, in the perturbation procedure, the expansion is taken of the form: = m1'2xi y = 1 2 z — m^^zi x + mx^ + m3'2X3 + m2Xi + .
08 Stability chart for the equilateral equilibrium points. The stable region is crosshatched Bhatnagar and Hallan [3-1] studied the location and the linear stability of these points in the restricted circular problem when there are perturbations in the potentials of the primaries. They considered the following three cases: (i) The larger primary is an oblate spheroid whose axis of symmetry is perpendicular to the plane of motion of the primaries. (ii) Both primaries are oblate spheroids whose axes of symmetry are perpendicular to the plane of motion of the primaries.
2 Equations of Motion Consider the motion of an infinitesimal body in the gravitational field of two finite bodies (Pi,P2) revolving around their common barycenter in elliptic orbits. The following quantities are denned to be equal to the unity: (1) The mean distance between Pi and P2, (2) The mean angular rate of the finite bodies about their barycenter (6), (3) The sum of the masses of the two finite bodies. The larger mass at Pi is taken as 1 — fi, while the smaller mass at P2 is \i. Fig. 20 Geometry of the restricted three-body problem.
Dynamics and Mission Design Near Libration Points, Volume I : Fundamentals : The Case of Collinear Libration Points (World Scientific Monograph Series in Mathematics) by J. Llibre, R. Martinex, Carles Simo