  A 250-year old Newtonian problem, first studied by Euler, turns out to share
a lot of similarities with the most extreme astrophysical relativistic object,
the Kerr black hole. Although the framework behind the two fields is completely
different, both problems are related to gravitational fields that have quite
intriguing analogies with respect to orbital motions of a test-body in them.
The fundamental reason responsible for their extraordinary similarity is the
integrability of both problems, as well as their common multipolar structure.
In this paper we demonstrate the existence of a multitude of either
qualitative, and sometimes quantitative, similarities between the two problems.
Based on this analogy, one could use the Newtonian problem to get insight in
cases where the relativistic treatment of the field of a Kerr black hole
becomes quite complicated.
