These days I am reading about divergent series, and there is a paper which wrote about the history of divergent series: Divergent series: past, present, future ...
In the article, there is an example about the computation by Laplace of the secular perturbation of the orbit of the Earth around the Sun due to the attraction of Jupiter, which used a divergent series:
As remarked by Abel, divergent series occur very often in many natural problems of mathematics and physics. Their use has permitted to do successfully a lot of numerical calculations. One example of this is the computation by Laplace of the secular perturbation of the orbit of the Earth around the Sun due to the attraction of Jupiter. The calculations of Laplace are verified experimentally, although the series he used were divergent.
I never heard about that before. I was searching but I couldn't find out what is the divergent series he used. Could you please let me know if you have some clues? Thank you!