M x= -G +G M x2 (x — L)²' -

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