Posted on 09/17/2023 6:07:39 AM PDT by SunkenCiv
...Two objects orbiting each other, like a lone planet around a star, can be described with just a line or two of mathematical equations. Add a third body, though, and the math becomes much harder. Because each object influences the others with its gravity, calculating a stable orbit where all three objects get along is a complex feat...
More than 300 years ago, Isaac Newton wrote down his foundational laws of motion, and mathematicians have been working on solutions to the three-body problem pretty much ever since. There is no single correct answer; instead, there are many orbits that can work within the laws of physics for three orbiting objects.
Unlike our planet's simple loop around the sun, orbits for the three-body problem can look twisted and tangled, like pretzels and scribbles. The 12,000 newly discovered ones are no exception — the three hypothetical objects start at a standstill and, when released, are pulled into various spirals toward one another via gravity. They then fling past one another, moving farther away, until the attraction takes over and they once again come together, repeating this pattern over and over again...
Three-body systems are quite common in the universe; there are plenty of star systems with multiple planets, or even multiple stars orbiting each other. In theory, these new solutions could prove extremely valuable to astronomers trying to explain the cosmos. But they're only useful if they're stable, meaning the orbital patterns can repeat over time without breaking apart, flinging one of the component worlds off into space. Just because they're theoretically stable doesn't mean they'll stand up to the many other forces present in a real star system.
(Excerpt) Read more at livescience.com ...
1. Central body plus two nonintersecting ellipses.
2. Central body plus two intersecting ellipses.
3. Figure 8 (this one might not work in real life)
4. Two central bodies; third body in an ellipse around them
5. Central body, ellipse around it - 3rd body in an ellipse around the 2nd.
I need 11995 more.
“Just because they’re theoretically stable doesn’t mean they’ll stand up to the many other forces present in a real star system.”
I thought they were referring to Biden, but I guess it holds true for astronomical objects too.
This is all racist, don’tcha know.
Pi is a real number, it’s just not a rational number.
It may be way more complicated - a process of orbital change that may run through all your states 1-5, and in-betweens, and others yet, over time. The question then is if this process of change is predictable, which is the implication in these solutions.
Thanks for that!
Oh, I was about to mention the book. I didn’t know they had a mini-series already! Thanks for that.
I’ve heard that weightlessness obtains to the center of the earth. Does the same hold true of every physical object, that is has a weightless gravitational center? I have also wondered how many axes in motion are possible at the same time on a single sphere.
355/113
There’s an old saw that teachers would sometimes use, that if there were a tubelike tunnel straight through the Earth, an object which was dropped in would oscillate down one side, up the other, until it finally stopped dead and hovered at the center of the Earth. It’s not true. :^)
Thanks PIF.
How strenuous.
So what would happen
Didn't Teddy Kennedy and Chris Dodd solve that equation decades ago with the help of a waitress that happened to be studying theoretical mathematics at the local university?
It just covers the first book, hopefully they will do both The Dark Forest and Death’s End soon.
I suspect some of the ‘stable’ orbits are more like fractals than folks are willing to admit.
What would a actually happen I suppose would depend on the mass and shape of whatever object is dropped. Suppose it were a perfect sphere weighing ten pounds, cropped into a hole twice the diameter of the sphere?
My hunch is that it would stop at the center (taking only gravity into account and not the forces caused by heat).
The ball would achieve its maximum velocity in a few seconds (like a skydiver), then slow down a bit because the atmospheric pressure would increase in the descent, then because the Earth isn’t uniformly dense, would start rolling down the side of the tunnel.
https://freerepublic.com/tag/potsdamgravitypotato/index?tab=articles
Yes, that was an excellent read. Have you read the sequels?
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