We have solved the 3-body problem, *under specific conditions*. Consider a different scenario entirely. I ask you “what will the weather be like in six months’ time?”
You don’t know. The weather is unpredictable, after all. *But*, you know that it’s always gloomy in the great lakes region, so you might say “In Michigan, it’s going to be gloomy”. Even if you can’t predict the weather everywhere, you can predict it in specific places because they are consistent.
Back to the 3-body problem. There are certain specific orbits that are consistent, and these are the lagrange points. As long as the telescope is in the right spot where all of the equations come together nicely, its motion is very predictable.
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