Are there literal attractors in nature?

Are there literal attractors in nature? Take Apollo 11 as an example. The astronauts went from 1 to 2 upon launch. Then 2 to 3 with an additional burn. From 3, 2 of them went to 4 then back to 3. They went from 3 back to 1 and skipped 2. 1 through 4 can be thought of as different stable regimes and the astronauts move from one to the other. Synchronization can be thought of as a lot of things doing the same thing at the same time. That is a good description of the Saturn V launch vehicle. Its weight include massive amounts of fuel which all does the same thing, it combusts over a short amount of time. Synchronization has been suggested to occur with some regime swaps.

apollo“The theory suggests that the system is pushed past a threshold at which stage the components start to interact…  …– as tremendous energies cascade through powerful subsystems.”- Robert Ellison

Earth’s mass provides one attractor with two regimes. Surface and Orbital. Theoretical attractors may also work this way. 2 above might be called higher energy than 1. On Apollo’s trip to the Moon it obtained even higher energy is it transitioned to the next regime. I assume they braked as they got close to the Moon which may be another form of synchonization just as air braking using the Earth’s atmospher may be. The astronauts moved to another attractor called the Moon and later returned. How does all this scale down? Gravity of smaller objects might be too small to see anything like we see with the Solar System. However when we wonder about molecules, that can swap electrons, we might compare it to this diagram.

“The theory suggests that the system is pushed past a threshold at which stage the components start to interact…”

 

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Do attractors exist in Nature?

When we look at a temperature plot of past GMATs we may think we see an up and down motion like a Sine wave. This is perhaps most clearly seen over the past 400,000 years as the climate entered and exited Glacial periods. It is suggested that the Climate keeps overshooting its equilibrium. When we ask what that was for the past 400,000 years we’d answer that it’s not either a Glacial or Inter Glacial temperature. So on that time frame we’d argue that the system is bistable. But does it still have an equilibrium? I say yes. And it orbits that just as the Earth orbits the Sun. I am suggesting we can see the Sun Earth system as a useful example of an attractor and the system that orbits it. The mass of the Sun and Earth’s velocity keep Earth on a very predictable path. The Earth is trying to reach the Sun as it is in freefall but that is countered by its velocity and we get a nice predictable arc.

overshoots

 

My graphic is trying to show a hypothetical temperature series going back 100s of thousands of years. Then one is asked to believe that the climate consistently overshoots its equilibrium as evidenced by the Glacial Inter Glacial record. Then trying to find something in Nature more plausible than an up down motion we use an orbit. Important to our Solar System. Important for instance as electrons orbiting their nucleus. Orbiting is in the very large and the very small and it’s hard to conceive of our lives existing without these orbits.