astronomical observation no. four: the waltz of neptune and pluto.

neptune and pluto have a 3:2 orbit-orbit resonance. the two planets waltz because neptune makes three orbits each cycle. however, pluto is not making three steps as well, so they are not really both waltzing. more precisely, it is like a pianist playing eigth notes with the left hand and simultaneously playing triplet quarter notes with the right.