Page 1 of 1

Newton's 3 body problem

PostPosted: Tue Apr 02, 2024 11:19 am
by everything


some summary from business insider
https://www.businessinsider.com/why-thr ... tal%20path.

While Netflix's "3 Body Problem" is a science-fiction show, its name comes from a real math problem that's puzzled scientists since the late 1600s.

In physics, the three-body problem refers to the motion of three bodies trapped in each other's gravitational grip — like a three-star system.

It might sound simple enough, but once you dig into the mathematics, the orbital paths of each object get complicated very quickly.

Two-body vs. three- and multi-body systems
An artist's impression shows the solar system seen from the Earth
Our solar system is a multi-body system, with multiple planets, moons, asteroids, and comets circling around a single star. adventtr/Getty Images
A simpler version is a two-body system like binary stars. Two-body systems have periodic orbits, meaning they are mathematically predictable because they follow the same trajectory over and over. So, if you have the stars' initial positions and velocities, you can calculate where they've been or will be in space far into the past and future.

However, "throwing in a third body that's close enough to interact leads to chaos," Shane Ross, an aerospace and ocean engineering professor at Virginia Tech, told Business Insider. In fact, it's nearly impossible to precisely predict the orbital paths of any system with three bodies or more.

While two orbiting planets might look like a ven diagram with ovular paths overlapping, the paths of three bodies interacting often resemble tangled spaghetti. Their trajectories usually aren't as stable as systems with only two bodies.


All that uncertainty makes what's known as the three-body problem largely unsolvable, Ross said. But there are certain exceptions.

The three-body problem is over 300 years old
The three-body problem dates back to Isaac Newton, who published his "Principia" in 1687.

In the book, the mathematician noted that the planets move in elliptical orbits around the sun. Yet the gravitational pull from Jupiter seemed to affect Saturn's orbital path.

Re: Newton's 3 body problem

PostPosted: Tue Apr 02, 2024 11:24 pm
by Trick
This can not be understood by mathematics, the “problem” dwells into the internal mysteries. It’s all lost in chalky equations on a blackboard . Instead follow trismagus advice- ‘as above so it is below’.
Do your santishi correctly and you will understand

Re: Newton's 3 body problem

PostPosted: Wed Apr 03, 2024 6:37 am
by Steve James
A (single) mathematical formula can't be produced -that can describe or predict N-body motion.

Otoh, thinking that a mathematical formula could exist is a human limitation. Math is a closed system. So, we'd say that it's impossible to divide by 0. It's like asking what came before the big bang. Our language doesn't allow us to answer "What came before before?" :) Even if it's possible to conceive, no answer can make sense. Makes a great koan, though.

Re: Newton's 3 body problem

PostPosted: Wed Apr 03, 2024 7:58 am
by everything
ha, great answers. back to the santishi, yes. ironic the answer is do "3 body posture". can we even understand that? according to the answers here, probably not.

Re: Newton's 3 body problem

PostPosted: Wed Apr 03, 2024 8:38 am
by D_Glenn
According to the Yijing
2+2=4
2x2=4

3+3=6
3x3=9

So 3 is the beginning of the myriad changes