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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6c532e-1ce0-4289-91a1-13082803c4bf%2F589beb33-f176-45ca-9fcd-154a9a872322%2Ft1ft6m_processed.png&w=3840&q=75)
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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