Does the Sun count? Taking my earlier number of 2e20 N, and supposing we use half the Moon’s mass as reaction mass, over a 10 year timeframe (the Moon will have to get a bit closer to Earth as the mass decreases, but not dramatically so), we need to launch 2.3e14 kg/s of lunar mass at 9.6e5 m/s. That requires 1.1e26 W. The Sun is 3.8e26 W, so no actual magic is required.
But rereading the OP, our timeframe is a billion years. The necessary power is thus reduced by 100,000,000 compared to my estimate. That’s actually a rather modest Dyson swarm.
The reaction mass will easily escape the Sun’s gravitational influence, so no worries about that, either. Just don’t aim it at anything important.
Besides, any mass you would move to or from the sun to alter the Earth’s orbit would need to be orders of magnitude more massive than the Earth itself.
I say just wait until we have the technology to build megastructures like ringworlds, dyson spheres, or turn the Earth into a discarded orange peal. Then we can just disassemble the Earth and rebuild it wherever we want.
There are various ways to shift the Earth without destroying it. As Stranger said, they are all fairly magical at this stage, but using a gravity tractor and doing it slowly over time is probably the way that’s most grounded in reality at this point. If you could (magically) shift some asteroids to have an orbit that would impart a bit of outward force every time they past a certain distance from the earth in it’s orbit (and be able to adjust them so that they continued to do so), you could shift the earth maybe a few inches or even feet outward at some small rate. Might take a million years, but we have something like 500 million to a billion to play with, in theory, so what’s a mere million? There are ways to use the Moon to do similar things. It doesn’t have to be more massive than the Earth, just has to be able to shift it a small amount. It’s only if you had to do this quickly that you get all sorts of problems and we get into even more magic needed.
Anyway, the thread wasn’t really supposed to be about that, as it’s MUCH more speculative. I really wanted to know if we could even make good enough predictions to, if we COULD move the Earth, that we could do so without slamming it into something nasty or destabilizing the solar system. If we use the low and slow approach I’m not sure how much play we’d have to fudge things and move other things around on the fly, so I think we’d kind of need to have this aspect nailed down long before we started trying to actually move the planet.
The reality is, if we could do this we probably wouldn’t need to, as we’d have a host of alternatives to save humanity and probably most if not all the other species. But it was an interesting question so thought I’d ask here. Appreciate the replies.
Given that there might be a fairly pressing reason to move an inhabited planet, two cases seem to have significant, and contradictory sets of motives. Either the orbit it’s in now is no longer likely to remain conducive to habitability, or the orbit it will be in is necessary for continued habitability. The problem is that whatever means is used to move the planet will either involve massive immediate alteration of a whole lot of momentum, or a very long trip to the new orbital position. The first case involves significant difficulties for the fragile thing that is currently the only known habitat for life, and the second one an extended time period in less than optimal orbits. The second one has the advantage of producing climate change that would rise above the level of political denial.
Tris
Assumptions about unknown facts are only significant when they are applied to conjecture. The facts themselves are unaffected.
If the purpose is to counteract the effect of gradual changes in the Sun, then a gradual change in the orbit is exactly what you need. It’s slow, but it’s always in “the right orbit”.
To answer the OP, no we can’t be absolutely sure we won’t destabilize the solar system by moving planets around. It’s an N-body problem and those can’t be solved, they can only be modeled. So the question is how good are our models, or rather how good will they be at some time in the future when we may actually be trying to do it? I’m going to go out on a limb here and say they should be good enough.
Forgot to add to my previous post: the Solar system currently is not necessarily in a very long term stable state. For example, the Sun is slowly losing mass and that means all the planets are slowly moving aways from the Sun. But they aren’t moving at the same rate, so they won’t stay at the same relative positions. So eventually, the solar system may destabilize on its own. There’s been at least one model that predicts that, in the long term, Mercury’s orbit will become unstable.
The o.p. didn’t ask about a closed form analytical solution for orbital stability; merely whether we had the capability to assess stability provided some hypothetical means to move intact planets. The answer to this is yes: this is the study of what are termed disturbing functions which are just the difference between perturbing and unperturbed potential functions. Although uncertainties in perturbances and essential measurements can grow, we can assess the stability of an orbit including resonances with other planets to a high degree of confidence out to hundreds of millions of years which should be sufficient for a civilization which has the means to move planetary bodies between orbits to maintain stability. If we could move the Earth into the orbit of Mars (and move that planet elsewhere) it would be quite stable, although adjustments may need to be made periodically to prevent it from acquiring undesireable eccentricity.
The prediction that planetary orbits, including that of Earth, are chaotic over periods of hundreds of millions of years appears to largely stem from the work of Jacques Laskar and collegues, which were promoted by the pop sci press even though they are not held in particularly high regard by the planetary science community in general (and as the press likes to do, the “edge cases” of Mercury impacting the Earth were presented as likely when it was really one case out of a few thousand). The problem with this is that we have strong evidence that the Earth has been quite stable in terms of its orbital elements since the development of complex life, and little evidence of measurable perturbations. The inner planets and Jupiter (and liklely Saturn) appear to have been in stable orbits for billions of years, essentially since the initial formation and clearing of the major planets. The reasons for its resistance to perturbation are not entirely clear; it has been traditionally assumed that Jupiter maintained the orbits of the other planets by damping out large perturbations, but it now seems that there is a more complex relationship between Venus and Earth (with a 13:8 resonance) and Jupiter which creates a band of stability that also allows these planets to maintain a low eccentricity. Venus has the lowest eccentricity of any planet at 0.0068, and Earth is third with 0.0167 after Nepture with 0.0086, while Mercury and Mars have the highest eccentricity of the planets which is due to directly coupling with Jupiter.
The question of the “long term stable state” depends very much upon what means by “long term”. Given a long enough timespan, nothing in nature is stable except for protons and electrons, and outside influences like a nearby passing star or brown dwarf could create a perturbance that we’d never be able to predict. We are likely fortunate to be in a pocket of space in the galaxy which is relatively empty compared to the star density in the arms and especially toward the core, but eventually an object will pass close enough due to natural drift, random trajectory, or collision with another galaxy that the Solar System will experience a significant perturbance.
There is an interesting if tangential issue here with regard to stability; the Earth appears to be uniquely stable compared to the (admittedly still sparse) observations we made of other planetary systems and speculative models of planetary formation. Although stability of a planetary orbit is not an explicit parameter in the Drake equation (it is implicitly lumped in with n[SUB]e[/SUB]) the assumption of a planet being able to develop complex life includes a degree of stability in being able to mainstain liquid surface water (assuming a basis of life in some way like our own using photosynthetic energy and was as a polar solvent). However, such conditions would seem likely to be relatively rare even given stars with wide “Goldilock’s bands”. It may be that this would lead to a paucity of complex life and industrial civilizations; on the other hand, it may just be that the Earth is an unlikely outlier in being able to support life on its relatively exposed surface, and that life is more likely to form in liquid water or hydrocarbon oceans beneath the surface of Jovian-type moons powered by tidally-induced seismic energy where orbital perturbations and star variability have less impact. It follows, then, that we may be better off searching for signs of extraterrestrial life on Enceledus, Europa, or Titan than upon Mars which only had free surface water for a few hundred million years and is at the ragged edge of potential variability.