For all practical purposes eclipses are two two-body problems ... Sun vs Earth-Moon pair, and Earth vs Moon. The scale of the Sun is so vastly larger and distan

For all practical purposes eclipses are two two-body problems ... Sun vs Earth-Moon pair, and Earth vs Moon. The scale of the Sun is so vastly larger and distances so great from sun to earth there's no need to do 3-body. If the three had roughly the same mass would be different story.