Al-jerfaly, N. (2023). On the Location of The Lagrangian Collinear Points In The Photo-Gravitational Relativistic Restricted 3-Body Problem. Bulletin of Faculty of Science, Zagazig University, 2023(2), 6-22. doi: 10.21608/bfszu.2021.105949.1098
Nadiah Mosleh Al-jerfaly. "On the Location of The Lagrangian Collinear Points In The Photo-Gravitational Relativistic Restricted 3-Body Problem". Bulletin of Faculty of Science, Zagazig University, 2023, 2, 2023, 6-22. doi: 10.21608/bfszu.2021.105949.1098
Al-jerfaly, N. (2023). 'On the Location of The Lagrangian Collinear Points In The Photo-Gravitational Relativistic Restricted 3-Body Problem', Bulletin of Faculty of Science, Zagazig University, 2023(2), pp. 6-22. doi: 10.21608/bfszu.2021.105949.1098
Al-jerfaly, N. On the Location of The Lagrangian Collinear Points In The Photo-Gravitational Relativistic Restricted 3-Body Problem. Bulletin of Faculty of Science, Zagazig University, 2023; 2023(2): 6-22. doi: 10.21608/bfszu.2021.105949.1098
On the Location of The Lagrangian Collinear Points In The Photo-Gravitational Relativistic Restricted 3-Body Problem
Taibah University, Faculty of Applied Science, Department: Applied Mathematics
Abstract
we outlined the history of the restricted three body problem, beginning from the early works due to the brilliant scientist Lagrange, Euler, Jacobi, Poincare etc. we also continued to the up to date references. We formulated the basic scientific materials relevant to our work, e.g., the restricted three body problem, the Equation of motion in the rotating frame. We addressed the Lagrangian point, computations of their locations. We explained the curves of zero velocity and the permissible motions. In the field of the restricted three body problem. We obtained the locations of the three collinear points of the photo-gravitation relativistic restricted three body problem. The history of the restricted problem began with Euler and Lagrange continues with Jacobi (1836), Hill ( 1878) , Poincare' (1892-1899), and Birkhoff (1915 ). In 1772 , Euler first introduced a synodic ( rotating) coordinate system , the use of which led to an integral of the equations of motion, known today as the Jacobian integral. Euler himself did not discover the Jacobian integral which was first given by Jacobi(1836)who, as Wintner remarks ,''rediscovered "the synodic system. The actual situation is somewhat complex since Jacobi published his integral in a sideral (fixed) system in which its significance is definitely less than I the synodic system. Hill (1878) used this integral to show that the Earth -Moon distance remains bounded from above for all time (assuming his model for the Sun-Earth-Moon system is valid), and Brown (1896) gave the most precise lunar theory of his time.
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