Bill Gosper <billgosper@gmail.com> wrote:

Wikipedia: Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance.

I'm reminded of one of my long term plans. One of my *very* long term plans. The sun will gradually become a red giant and incinerate our planet. To save Earth, it will be necessary to gradually move it into a larger orbit for the duration. And then into a smaller orbit once the sun becomes a white dwarf. There are at least three main ways Earth might be moved outwards: * Loop asteroids around it and Jupiter, pulling Earth up and pulling Jupiter down. (Of course this has problems once they approach each other.) * Place a giant mirror near Earth, such that sunlight will push the mirror forwards in Earth's orbit, and Earth's gravity will make Earth follow it. * Launch lots of stuff from Earth backwards along its orbit. Fortunately, we have time. We can spend the next hundred million years ignoring the problem, the hundred million years after that thinking about it, and the hundred million years after than gradually accelerating the Earth outwards such that at the end of that hundred million years its outward drift reaches the speed of a snail. However, it's not clear whether on its outward journey it would hit any bad resonances with the other planets that might cause planets to collide with each other or with the sun, or expel a planet from the solar system. (Of course once Earth reaches Mars's orbit, a collision is inevitable.) The obvious solution, at least with Mars, is to move the other planet outwards too. They will all move outwards even without our intervention, due to the sun losing mass to radiation and to the solar wind. Not enough to save us, unfortunately. Nor should it destabilize the solar system. If they retain their orbital velocity (and why wouldn't they?) the orbital radii and the orbital periods should all increase by the same proportion that the sun loses mass. (Kepler's law that says the square of the period is proportional to the cube of the radius doesn't apply here, as it implicitly assumes the sun's mass is unchanging.) I'll give details of my reasoning on request. Kepler's law most certainly *does* apply if we move all the planets outwards ourselves. So we can't just enlarge all the orbits keeping the proportions of their orbital radii constant. Can we get away with enlarging all the orbits keeping the proportions of their orbital *periods* constant? And is there a cheaper way, in which we can leave most of the larger planets alone? Has anyone studied this problem? Is there any known way to study it other than a massive amount of numerical simulation, i.e. a digital orrery? Urgent! Please reply within the next quarter billion years! Thanks.