Two masses m, and m2 with position vectors r, and r2 respectively, interact through an attractive central force proportional to the inverse of the square of their distance, F = k/|r -r2 |. Explain mathematically why it can be reduced to a problem of a single particle of reduced mass p = m,m2 / (m, + m2) with position vector r = r, - 12 measured with respect to the center of mass system. (b) Graph the effective potential for the coordinate r = | r| and analyze it qualitatively indicating what kind of solutions are obtained for different values of energy.
Two masses m, and m2 with position vectors r, and r2 respectively, interact through an attractive central force proportional to the inverse of the square of their distance, F = k/|r -r2 |. Explain mathematically why it can be reduced to a problem of a single particle of reduced mass p = m,m2 / (m, + m2) with position vector r = r, - 12 measured with respect to the center of mass system. (b) Graph the effective potential for the coordinate r = | r| and analyze it qualitatively indicating what kind of solutions are obtained for different values of energy.
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Transcribed Image Text:Two masses m, and m2 with position vectors r, and r2 respectively,
interact through an attractive central force proportional to the inverse of
the square of their distance, F = k /|r; -r2 |. Explain mathematically why
it can be reduced to a problem of a single particle of reduced mass u =
m;m2 / (m, + m2) with position vectorr =r1 - 12 measured with respect to
the center of mass system. (b) Graph the effective potential for the
coordinate r = | r | and analyze it qualitatively indicating what kind of
solutions are obtained for different values of energy.
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