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