Using a numerical optimization tool such as Mathematica’s FindMinimum function, find the coordinates (x′, y′) of the Lagrange point L4 in the restricted three-body problem. Do not assume, as you probably did in Problem, that L4 is located at one of the corners of an equilateral triangle whose opposite base is formed by the two primaries. However, you should start the search for the coordinates of L4 by using a point near the position of the suspected solution.
(a) Using the coordinate convention given is Section 7.4 for the restricted three-body problem, find the coordinates (x′, y′) of the two Lagrangian points, L4 and L5.
(b) Show that the gradient of the effective potential function V(x′, y′) vanishes at L4 and L5.
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