The Drunk Monk and Resonance

In my previous post, I mentioned that Orbital Resonance has the potential to make the planets in the Trappist-1 system highly geologically active by means of Tidal Heating.  I said I would explain in more detail.  First, I'll describe what I mean by Orbital Resonance; in the next post, I'll describe what I mean by Tidal Heating.

Imagine you are at the park with your niece, nephew, or interactive android, on the swings; but he, she, or it, hasn't yet figured out how to "make it work," and asks you for help getting moving.  Now, you could get off your swing and then push your partner firmly, repeatedly, and at random intervals.  But, even if he were able to remain seated in the swing despite this physical onslaught, any onlookers might consider calling the police to report child abuse (even if you were doing this to the android; especially if it looked like this).

Instead, you would offer your niece a push, then then wait until an appropriate moment to apply a second push, and then a third, and so on.  But, how do you know when is the ideal moment?  If you pushed her only once, and then stood back to observe the results, then you'd watch her swing forward ... and then back ... and then forward ... and then back again, and so on.  If you timed how long it took her to swing out and back, you'd find that no matter how strong your initial push, or how long you waited through numerous swingings, this time would be the same.  But, don't observe too long before offering another push: children can be very demanding, and it might be better that they are not aware that you are conducting scientific experiments using them as test subjects.

If you timed your pushes to occur at the same point in the oscillation (and in the same direction), then you would be matching your "forcing" (the pushes) to the natural frequency of the swing.  As you did so, you'd find your nephew flying higher and higher.  You are giving him more and more "swing energy," much to his delight.  This is called "Forcing at the Resonant Frequency."

If instead, you and your niece are planets orbiting a star, then the pulls and pushes are dictated by gravity, rather than your whim.  Whenever planets are at the closest point to each other in their orbits around their parent star, then they are tugging on each other more strongly than at any other time during their orbits.  These tugs can even change the orbits of the planets; it is these very changes that the team studying Trappist-1 used to determine how massive those planets were.  If these tugs happen randomly, then the situation is like the first one above, and the planets remain stably where they are.  However, if the orbits of the planets line up so that they always arrive on the same side of their star at the same time, then the orbits of the planets are now being "Forced at their Resonant Frequency."  If the periods of the two orbits are integer multiples of each other (2 days and 4 days; or  6.3 days and 12.6 days; etc.), then every time they reach the same point in their orbit -- just like your nephew reaching the same point in his swing -- they get a little push from a friend. This is Orbital Resonance.

What does this have to do with heating up a planet's insides and making it volcanically active?  For that, we'll need to discuss Tidal Forces, which I'll do in my next post.