As planets orbit the Sun, they don't just follow their paths: they give each other a slight tug. It's like a dance where each partner feels the movements of the others. Scientists set out to determine how strongly this mutual attraction alters the planets' trajectories.

It turns out there are small corrections that were previously overlooked. They arise because gravity doesn't propagate instantaneously but, like light, at a finite speed. For Jupiter and Saturn, these corrections are tiny, but over time they can accumulate and noticeably shift the orbits.

For the Mercury–Venus and Jupiter–Saturn pairs, scientists calculated how these corrections change the distance between the planets. The changes turned out to be oscillatory — the planets seem to sway slightly in their orbits. Over time, the amplitude of these oscillations can grow.

This is important for future space missions: if we know all the intricacies of planetary motion, we can plot spacecraft trajectories more precisely.