Does the Earth-Sun distance vary over the years?

Answer

A very good question. About which articles, books, and even libraries have been written.

When the sun attracts the earth, so do the other planets. And an exact mathematical strategy to unambiguously account for all effects does not exist. What is important here is that the effects of planets are much smaller than those of the sun: the most disturbing planet is Jupiter, with a mass about a thousandth that of the sun, and on average five times further; using Newton’s law, which says that attraction is proportional to mass, and vice versa to distance squared, that means that Jupiter’s effect is 25 thousand times smaller than that of the sun. That is and seems very small, but on the other hand, the whole story goes on for a very long time, about 4.5 billion years. So there is plenty of time to turn small effects into big consequences, to the extent that those small effects keep piling up.

Celestial mechanics has bent over this problem. The good news is that the disturbances of planets at the Earth-sun distance are periodic, and therefore zero on average. Physically, this amounts to conservation of energy: the energy of the earth in its orbit around the sun is inversely proportional to the distance a between the two, and the change of energy due to attraction of the other planets oscillates around zero, never becoming large. . Unless the planets – due to the change of other parameters such as the eccentricity – suddenly come so close to each other that the disturbances suddenly become very large. Simulations about our own solar system seem to make the latter quite unlikely. The only planet that seems to have to fear for its future with us is Mercury, which has an extended orbit (and thus a changing distance from the others) and little mass, so that it is accelerated significantly for a given thrust.

The calculations so far regarding the stability of the Earth’s orbit tell us not to worry too much. But there is no mathematically conclusive proof of that stability. Perhaps the best proof is ourselves, in the sense that life has been allowed to evolve relatively quietly over all those billions of years.