As a consequence of the KAM theorem the Kolmogorov-Arnold-Moser theorem which I stated but did not prove Every satellite that is the least bit non-spherical like us, the Earth, we are oblate Or on an orbit that is the least bit elliptical Had to have tumbled chaotically in the past So the answer to this problem is true The differential equations for two bodies acting under G m m over r squared forces only have three kinds of solutions Ellipses, parabolas, and hyperbolas And that means that two body systems cannot be chaotic Two of the examples I gave you in this lecture were chaos in the orbit of Pluto and chaos as an explanation for at least one of the Kirkwood gaps So certainly B and C are true here Answer A of this question is a little bit different We didnt talk about the fact that there is a so-called dark side of the moon, but I put the word period into this twice And you should, at this point in the course, understand that something that has a period is not chaotic So the answer here is B and C, but not A Incidentally, the dark side of the moon is not dark The dark side of the moon is the popular name for whats called spin lock The fact that the moon faces the same side to us all the time The only way that it can be that the moon always faces its same side to us is if it rotates once around its own axis for every time it goes around us And thats called spin lock Its a tidal equilibrium that the Earth moon system is in