What you learned in the general derivation of the gravitational multipole expansion, can now be applied to this specific example of a a double ring system. You will understand better how the details of the shape of a dumb-bell relative to a double ring system determine the corrections to the baseline value of their gravitational energy.
One task related to this video:
On the slide with the expression for the quadrupole energy, three special configurations are drawn for the dumb-bell and the double ring (alpha>0, alpha=0, alpha<0). Predict the lowest-energy orientation of the dumb-bell in each of these three cases (don’t calculate, just think).
Report your answer in the forum underneath. You have to submit your answer first, before you can read the answers of your colleagues. If after reading the answers of your colleagues you realize your answer is wrong or incomplete, please submit a correction/addition to your own answer. Feel free to comment to answers of your colleagues as well.