Two masses m, and m2 with position vectors r, and r2 respectively,interact through an attractive central force proportional to the inverse ofthe square of their distance, F = k /|r; -r2 |. Explain mathematically whyit 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 tothe center of mass system. (b) Graph the effective potential for thecoordinate r = | r | and analyze it qualitatively indicating what kind ofsolutions 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.

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.