show that the lowest two non-vanishing multipole components of the gravitational field of a cubical planet are the monopole and the octupole. what's the next-lowest non-vanishing multipole?
(a solution without a multipole expansion and the added bonus question on the shape of the surface of a lake on such a planet is discussed in the paper "the gravitational field of a cube" by J.M. Chappell, A. Iqbal, D. Abbott and M. Chappell)
with that, we wish all readers of CQW a nice summer vacation and hope to see you again in october. if you came across an interesting question that would fit our blog, you're invited to appear as a guest author: please contact us for that purpose under cosmologyquestionoftheweek"[AT]"gmail"[DOT]"com.