Three assumptions of radiometric dating
As a result, the exact behavior of 3 or more bodies can’t be written down. Despite that, we do alright, and happily, reality doesn’t concern itself with doing math, it just kinda “does”.The exact energy levels and orbital shell shapes in anything other than hydrogen is impossible to find. For example, quantum field theory, despite being the most accurate theory that ever there was, never involves .As a result (this is not at all obvious right off the bat) if the other moon slows down it gets pushed a little faster at regular intervals, and if it gets too fast it gets slowed down at regular intervals.The moons still have very elliptical orbits (a symptom of being in a 2-body system with Jupiter), but the presence of the other moons does affect how big that ellipse is, and in what direction it “points”.Then jump over the the elliptic orbit post to find the ellipticalness of this.The subtle, unspoken assumption of post is that the Sun doesn’t move (i.e., it was already stated in the “reduced form”).But that last 1% has a lot of weirdness in it, most of which falls out of chaos theory.The more interesting part of chaos theory is the “islands of stability”, or what we in the biz call “chaotic attractors”.
But even with just mechanical pencil and paper there are cheats.
Now, since for every action there’s an equal, but opposite reaction (every force is balanced by another force): Now check this out!
At this point just replace “” with ““, and “” with ““.
While you find that no real life N-body system orbits are stable (exactly repeat themselves), you do find that they settle into patterns.
For example, while the system of Jupiter’s innermost moons: Io, Europa, and Ganymede, never quite repeats the same path, they do manage to “resonate” with each other and settle into a rhythm. Basically, when you have several bodies orbiting a much larger body, the length of the orbits of the smaller bodies will tend to settle into simple-fraction (1/2, 2/3, 1/3, etc.) multiples of each other. The slight ellipses of any real-life orbits cause the gravitational force of the moons, to “pulse” (becoming slightly stronger or weaker) along another moon’s orbit.
Once a physicist gets a hold of all the appropriate equations and a big computer, they can start approximating things.