How Lagrange points solved one of physics' biggest problems

[Admin]

The origins of the Lagrange points are sunk deep within one of the most difficult problems faced by mathematicians and physicists over the past 400 years: the three-body problem.

How Lagrange points solved one of physics' biggest problems : Read more

 

[Helio]

The Lagrange points aren't as simple to derive as one, like me, would think. Although a FBD (Free Body Diagram) is the heart of the solution, there are more variables than one would think for something that looks straight forward.

Here is the math, per my little search. The solution will still require, surprisingly, the iteration process for improved accuracy, or is there a solution without iteration tweaks?

 

[Catastrophe]

Helio, of course we are dealing with the infinite number of body problem, but with almost all of these having negligible effect (during our lifetimes and maybe a few billion years beyond). However, eventually, some will have measurable effect. I was thinking of the system: Sun, Jupiter, Saturn, Uranus, Neptune, Galilean satellites and Titan and Triton (and maybe Centauri system) as an example. Bit of math needed there?

Cat