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# Another "Strange Central Force"?

Inspired by the recent challenge problem, I tried to simulate the motion of a particle under different "strange central forces" - those described by

$$F = - a r^k$$, where $$a$$ is a positive constant of appropriate physical dimension, and $$k$$ is a real number. It turns out that the trajectory of the body is always a closed non self-intersecting curve only for $$k = -2$$ and $$k = 1$$. Is this a known result? How can we prove this?

Note by Ivan Stošić
4 years ago