The translator of Cixin's novel, the Swedish Wikipedia and the Swedish Academy Word List all agree:
The Swedish term for the three-body problem is "trekropparsproblemet". That translates back to "the three-bodies problem", with an unnecessary plural suffix in the middle adding a syllable to a word that already has quite a few.
Which technical writer 200 years ago is responsible for this abomination? This is not how we compose words.
"Trekroppsproblemet", with a nice sequence of word stems, is the superior term, but officially it's not recommended, it's not even in the Word List as a variant.