Problem 3. An astronaut is confined to the straight line between two planets of equalmasses M with a distance L between them. For simplicity, we take the mass of this astronautm = 1. The equations of motions for this astronaut by Newton's law of universal gravitationisMMx=-G + G-x² (x - L)2'where G > 0 is the gravitational constant. Find the fixed points, and classify their linearstability. What is its linear stability classification?

Given the equation d2xdt2=−GMx2+GM(x−L)2⇒d2xdt2=−GMx2+GM(L−x)2 [As (x-L)2=(L-x)2]This is a…

Answered: M x= -G +G M x2 (x — L)²' -

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