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