Ever since I saw a figure-eight periodic orbit, I have developed a strong interest in the periodic orbits of the three-body problem. After reading this article, my interest grew even more. It turns out that the three-body problem, which cannot be integrated directly, still contains so many interesting things... Therefore, one of my research goals for the winter break is the periodic orbits of the three-body problem.
First, a report on current exploration results:
I have developed my own method for finding periodic orbits;
It seems I have solved the equation for the figure-eight orbit, but its correctness is still unknown;
It appears I have discovered more periodic orbits, also with unknown correctness (these are all under verification).
Thoughts:
Research on these periodic orbits is purely theoretical; in other words, it has almost no practical significance. Therefore, the study focuses on the equal-mass three-body problem.
However, in my personal opinion, although the periodic orbits of the three-body problem are very interesting, they are not as significant as studying problems built on existing orbits, such as Lagrange points. Perhaps those problems have more guiding significance for aerospace applications.
So, I will spend about another week researching periodic orbit problems, and then attempt to study restricted special orbits (where the mass of the third body is nearly zero).
The results will be published on Scientific Space and Mufu in the near future.