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(See the more focused version of this question: How long would it take to move Venus and Mars into Earth's orbital zone using gravity assist?)

What methods and time scales might be involved in moving Venus or Mars into stable orbits at Earth-like distances from the sun?

Rearranging the lifeless rocky planets might make terraforming and transportation easier. But the answer need not address usefulness or feasibility. Though I suspect that something like this can be done with less energy and time than interstellar travel, and so will be achieved earlier, that's outside the scope.

Existing laws of physics only. Plausible guesses at future technology are welcome, but much more science than fiction. Try to think beyond the palpable constraints on energies and budgets of the present era. Not yet a Type II civilization on the Kardashev Scale, but well beyond Type I.

Hint: Gravity Assist.

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    $\begingroup$ Maybe the first question is should you? "your scientists were so preoccupied with whether or not they could that they didn't stop to think if they should" Dr. Ian Malcolm, Jurassic Park (1993) $\endgroup$ – James Jenkins Feb 28 '14 at 23:25
  • $\begingroup$ Even if it were possible, wouldn't it have some effect on Earth's orbit/climate, geomagnetism, or tectonic activity to have a massive near neighbour? How close could the orbit of a Venus-sized planet come to Earth without destabilizing its orbit or having some sort of influence on all those things which make our planet relatively safe and comfortable for human habitation? $\endgroup$ – Anthony X Mar 1 '14 at 15:49
  • $\begingroup$ Another thought: I remember reading once a long time ago that the orbits of the inner planets are where they are because of the influence/orbital resonance with Jupiter and Saturn. If that was so, wouldn't it mean that any potential relocation site for Venus or Mars would be an unstable orbit? $\endgroup$ – Anthony X Mar 1 '14 at 21:00
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    $\begingroup$ Lagrangian points only work when the mass of the object you place there is negligible compared to that of the other two. They are no solution for the three-body problem. $\endgroup$ – Philipp Mar 1 '14 at 21:23
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    $\begingroup$ It is these kinds of questions that will keep this site from progressing beyond the "beta" stage. $\endgroup$ – David Hammen Mar 1 '14 at 22:42
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Setting aside the fact that this would be a very bad idea and that there are far less energy intensive ways to terraform the surface of a planet, the most energy efficient way to do this I can think of is by using Oort Cloud objects.

It takes very little $\Delta V$ to make an Oort cloud object dive towards the Sun. In fact, it is the source of most comets. The total mass out there is at least a few Earths. Each object would be sent on a trajectory to swing close to Mars on the trailing side. The object would be flung out of the Solar System, and Mars would slow down a little. Repeat.

It might be possible to reuse an object. A Jupiter flyby could pull an escaping object back into a solar orbit to return to Mars for another tug. If you could cycle such an object, you would make a pump that transfers energy and angular momentum from Mars to Jupiter. Don't worry too much about changing Jupiter's orbit -- it won't change much. 1/3000th as much as Mars' orbit changes.

A more useful application of the approach would be to raise Earth's orbit to keep it habitable as the energy output of the Sun increases over the next few billion years. In other words, keeping Earth terraformed. So do the above on the leading side of Earth to speed it up.

Given the very long time scale of the increase of the Sun's energy, this might be a viable approach. Something like self-replicating vehicles using materials in the Oort cloud, powered by fusion reactors, might make this somewhat affordable. Again over long time scales. I'd mainly be worried about running out of Oort cloud material if you couldn't reuse it. Though you could then start raiding the Oort clouds of other nearby stars. Then we'll have high-potential-energy-mass wars with the civilizations in other star systems who want to do the same thing ...

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    $\begingroup$ By the way, you use the same technique to directly impact Mars with Oort cloud objects and deposit large amounts of water. That could be a big part of terraforming Mars. $\endgroup$ – Mark Adler Mar 1 '14 at 21:23
  • $\begingroup$ Thanks, Mark! Agreed about setting aside the issue of energy utility, that is off topic. And the third paragraph is interesting but also off topic, perhaps for another question. But I like the direction you're thinking. Have you thought of a scheme yet in which the Oort Cloud Objects do not need to escape the solar system? $\endgroup$ – Bob Stein Mar 1 '14 at 21:46
  • $\begingroup$ Why not let them escape? In order to maximize the tug effect, you want to fly them as close to the planet as possible, which would result in their escape. To avoid escape would require a more distant flyby and vastly more such flybys needed to get the same effect. $\endgroup$ – Mark Adler Mar 1 '14 at 22:30
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    $\begingroup$ Using comets to provide the delta-V is a multi-million year effort, requiring millions of passes. See arxiv.org/abs/astro-ph/0102126 . This is a problem for our some far, far removed generation to solve. $\endgroup$ – David Hammen Mar 1 '14 at 22:41
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    $\begingroup$ In a hundred years?! No, not happening. You need more patience. $\endgroup$ – Mark Adler Mar 2 '14 at 22:10
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Rearranging the lifeless rocky planets might make terraforming and transportation easier.

No, it mightn't, because the amounts of energy it would involve are so ridiculously gigantic that terraforming a planet is a very easy job in comparison.

The kinetic energy of an orbiting body is $\epsilon_k = G\cdot \frac{m\cdot M}{2\cdot r}$ where $G$ is the gravitational constant, $m$ the mass of the orbiting planet, $M$ the mass of the body it orbits around, and $r$ the semi-major axis or the average distance between the primary focus of the ellipse and the orbiting body. The minimum energy required to move between two orbits is the difference of the two orbital energies. For Mars moving from its current orbit to Earth orbit, this comes out (if I calculated correctly) at $-9.98 \cdot 10^{31}\rm J$ (Joule). That is the total kinetic energy that would have to be removed from Mars' orbit for it to start orbiting at the average Earth's distance to the Sun.

This is roughly the entire energy output of the Sun for three days!

If you could harness that much energy, terraforming a planet would be something you'd give to kids as homework (well, maybe a term project). And, of course, transportation would be something you don't even think about.

Of course, if you really want to concoct a hard SF scenario where planets are moved between orbits, the above estimation may also give you an idea about methods and timescales. Say, find a way to siphon off 0.01% of the sun's energy output and use it to move the planets over a timeframe of 80 years.

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  • $\begingroup$ Your answer is off. You are forgetting that gravity is responsible for most of the change in velocity. $\endgroup$ – David Hammen Mar 1 '14 at 17:24
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    $\begingroup$ @DavidHammen: you think gravity would overcome energy conservation? $\endgroup$ – Michael Borgwardt Mar 1 '14 at 18:06
  • $\begingroup$ Michael: You are off by a factor 20. Do the math. A 2.65 km/s change in velocity at Mars' orbit (1.5237 AU) would put Mars on a 1.0 AU by 1.5237 AU elliptical orbit. A 2.94 km/s change in velocity at perihelion would circularize the orbit at 1 AU. Given Mar's mass, that's 5e30 joules, not 1e32 joules. $\endgroup$ – David Hammen Mar 1 '14 at 18:23
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    $\begingroup$ @BobStein-VisiBone: My point is that the energies involved are so big that your real goal is almost certainly much easier to achieve in another way using a small fraction of that energy. This is definitely true for the specific goals you cite (including interstellar travel - generation ships would be a lot cheaper and faster that orbit manipulation via gravity assist). Then again "becuase it would be cool" is a valid motivation for this kind of question, you just have to admit it. $\endgroup$ – Michael Borgwardt Mar 2 '14 at 3:58
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    $\begingroup$ @BobStein-VisiBone You asked for "much more science than fiction"... This is what science tells you. You can't change the laws of nature when they don't fit your desires. $\endgroup$ – PhilMacKay Mar 3 '14 at 20:54
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Let's see what it would take to move Mars to an Earth orbit. It's not a pretty picture.

The most efficient way to move from one orbit to another is via a Hohmann transfer. We'll apply a delta-V to Mars to slow it down and put the planet into an elliptical transfer orbit that just intersects Earth's orbit, then another delta-V once Mars reaches perihelion. Assuming Mars is orbiting circularly at 1.524 AU, a retrograde delta-V of 2.65 km/s will put Mars on that transfer ellipse. Half an orbit later, another retrograde delta-V, this time 2.94 km/s, will put Mars in a 1 AU circular orbit. No problem! All we have to do is change Mar's velocity by 2.65 km/s and then later by 2.94 km/s, or a total delta-V of 5.59 km/s, and voila! we have Mars orbiting at 1 AU.

It's a huge problem. Those two instantaneous changes in velocity represent an enormous amount of energy and an even more enormous amount of momentum. Note that this is considerably less energy than Michael Borgwardt's answer. Mars' mass * ((2.65 km/s)2/2 + (2.94 km/s)2/2) is about 5*1030 joules, not 1032 joules.

However, this is only part of the total energy needed. The only way we know how to make an object in space move in some direction is to eject some mass from the object in the opposite direction. Only a tiny fraction of the energy that goes into accelerating the ejected mass accelerates the rocket (or the planet in this case).

Suppose we could eject a (small) mountain's worth of material (1012 kg) at 99% of the speed of light from Mars every single day. This is not the way to get Mars to follow a Hohmann transfer to Earth's orbit. It would takes centuries to build up that 2.65 km/s delta-V needed for the first leg of the transfer. A Hohmann transfer is not possible when moving planets.

Ejecting 1012 kg per day from Mars at 0.99c makes for a very slow transfer. It would take more than 47 centuries to move Mars from it's current orbit to Earth's orbit. The amount of energy consumed in the process of just ejecting the mass is 1036 joules. Almost all of the energy goes into that exhaust stream. Only a tiny fraction goes into moving Mars. In the process, we'll have expelled over 1018 kilograms of mass from Mars. Note that 1012 kg per day is about 1.5 orders of magnitude greater than rate at which coal and iron are extracted from the Earth.

Mining a mountain's worth of material a day and sending it off into space at 99% of the speed of light: We can't do that. It's not even close. Maybe in 47 centuries we'll be able to do that. It's better to wait.

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  • $\begingroup$ Thanks for clarifying the numbers, David! Good treatment of the rocket approach. It sure does seem tedious. I hope you will keep thinking on this. $\endgroup$ – Bob Stein Mar 1 '14 at 21:50
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Within Known Physics

There are three vaguely plausible methods for changing a planet's orbit that come to mind without breaking the accepted laws of physics:

  1. direct application of thrust
  2. Consistent close passes of a series of massive objects
  3. targeted solar flares

Direct application of thrust is going to be incredibly disruptive - it's either by impact or by insolation changes.

Impact as a direct application of force is practical on a societal time scale, but not on an individual time scale. It would require minor alterations to many cometary/asteroidal bodies in crossing orbits, with lead times of one to two decades per each. Remember, a small perturbation can result in a significant change in position over a long time. The important elements of the project require ensuring that the final impact is on the correct position - the trailing (retrograde) face of venus to speed it up, or the spinward (prograde) face of mars. (Remembering the WWIVnet reduction of Niven's ditty: Spin out, out back, back in, in spin. Accelerate to spinward, you move out. To back, move in.) The issue is that this would take thousands of impacts, all of which would need to change the orbital velocity in the same direction, over a scale of a couple centuries, in order to have any appreciable effect. We are just now getting to the technological point where this is feasible - but it will likely never be practical.

The use of altered insolation could produce a change in atmospheric loss in such a manner as to create a very slow, but steady, acceleration. Light pressure is already a known factor in orbital mechanics by itself; the mirror array would be accelerated away, so would need some form of acceleration of its own. Perhaps, a larger sail array. Timescale is, again, centuries. Mass is tremendous - comparable to entire navies. In the case of Venus, the desired thinning effect might be useful, as well.

Moving massive objects by at the correct path is doable, but without a non-N-space drive, requires insane amounts of power to alter them. To accelerate, you need to route them close enough to the correct side. For venus, this means parading a bunch of bodies past the spinward side of Venus, and preferably, most of them doing so on the outbound leg of their own path. For mars, you want them on the trailing side and inbound leg. Ideally, for venus, they also should be moving prograde, while for mars, retrograde. Minor errors? Accumulate new moons. The drawback is that, to get sufficient mass, you're looking at moving large asteroids.

It is theoretically possible to trigger solar flares; doing so could be used to apply recurrent pressure over several centuries. The side effects, however, are that doing so is likely to be seen as a threat of wiping out all life in the system.

Edit: According to Wikipedia, solar wind generates between 1e-9 and 6e-9 nPa. Venus has a cross sectional area of about 1.15e14 m^2, a mass of around 4.87e24 kg, for a total net of about (3.5x1.15/4.8)e(-9+14-24) = 0.8e-19 nm/s^2 or 8e-26 m/s^2. Pressure at venus should be about 2.7x as strong... It would take 1,000,000,000,000,000,000 years to hit 8m/s. A CME can be 1000x more energetic and can add additional from atmospheric heating... It's theoretically useful, but in practice, worthless. If one's engineering them, one can possibly also get deeper upshot, more energy, and more particle density.

Just outside current physics

  1. A giant Alcubierre-White Warp Drive
  2. Gravity Manipulation - if the math is to be believed, gravity is a manipulable force.

The Alcubierre-White Warp Drive, in theory, could be used to place a body into a "fall into orbit" position. It doesn't matter if it generates superluminal pseudovelocities - only that it moves the object by changing the topology of space. Without Dr. White's transformations, the math would indicate insanely high energy requirements; even with, moving a bubble that large is likely to require a stupidly high amount of energy.

Gravity manipulation is believed theoretically possible by a number of physicists. If one can either enhance or impede gravity's pull artificially, one can then make use of that to alter orbits. But the process may be surprisingly convoluted. You move out with it reducing, then turn it to enhancing to accelerate inbound, then turn it to reduce again as one passes perihelion, to increase overall orbital speed. Unfortunately, this also increases eccentricity. Careful manipulation of the process can reround the orbit, but during the transfer process, it's actually going to get closer. In practice, however, almost no one is willing to admit to thinking it within easy reach. Many physicists think it impossible, citing that gravity is a fundamental property of matter, not a force generated by matter; if it's a fundamental principle, it isn't alterable.

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  • $\begingroup$ Thanks aramis! I'd limit to known physics. Excellent new contribution with the insolation. I'd love to see you work out the math constraints of that, e.g. minimum time given perfect Venus-size solar sails. Your #2 in the first list includes both impacts and gravity assist flybys? $\endgroup$ – Bob Stein Mar 1 '14 at 22:51
  • $\begingroup$ The gravity manipulation and alcubierre-white are both in the category of "Things which fit within currently accepted frameworks but haven't been substantiated nor ruled out, and aren't widely accepted as plausible on their own." Which is why I included them. The question with Alcubierre-White isn't if the math checks out, but if it actually describes reality - the math is verified as not being calculated wrong, but may not actually be the correct math to describe the universe. $\endgroup$ – aramis Mar 3 '14 at 6:09
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It's not possible! At least not if you want to keep Earth safe in its orbit. And while I like some suggestions previously mentioned here because playing celestial game of pool sure is fun, they're inherently not possible because of the timescale at which all these orbital changes would have to be applied. So forget about Hohmann transfer on a planetary scale, or slow decrease of planet's orbital velocity by shooting other massive bodies past it or even into it. By the time you'd sufficiently decrease its orbital velocity for it to come close to orbital altitude of Earth, well, it's already in its own sphere of influence and all hell breaks loose.

Also forget about quantum hocus pocus and FTL. Whatever you did to temporarily move a whole planet out of realm of spacetime and general relativity to later beam / teleport / warp it to another place, you've also forfeit ability to manipulate its momentum with it, so once (might be instantaneous?) you'd summon this planet to another orbital position and back to physical reality as we know it, it would have exactly the same momentum imparted on it as it always had, so in case of moving Mars into position of Earth's L3, you'd only end up with Mars having a highly elliptical orbit with exactly the same semi-major axis as it always had, only much larger eccentricity that would cause it to intersect Earth's own orbital path. Given sufficient time, say a few orbits, this wouldn't end up well either.

Celestial mechanics is hard! And it has very little to do with how we think of trajectories and orbits of small spacecraft with largely negligible mass in relation to celestial bodies they move about. Managing orbits of planets is nearly impossible, and what makes it so is that all the massive bodies of a star system are in semi-stable equilibrium because they evolved into ordered state from a primordial chaos of collapsing nebulae. Sufficiently disturb this equilibrium, and you've set off a chain reaction with unforeseen consequences. And moving a whole planet into lower orbit does qualify. To somewhat demonstrate this, let's consider these two graphs:

    enter image description hereenter image description here

        Graphs courtesy of: Renu Malhotra; Source: Scientific American: What Would Happen If Earth and Mars Switched Places?

Their captions are wrong, and they show orbital altitude of Mercury, Venus, Earth and Mars and these planet's perihelion, aphelion and semi-major axis plots, not all official planets of our Solar system from Mercury to Neptune. But nevermind that, what's important is that inner Solar system's current arrangement seems stable, but if we just swapped orbits of Mars and Earth (not even moving Mars into the same orbit with Earth), the whole system destabilizes. in roughly 10 million years, Mercury intersects Venus and Venus Mars, and there's no way of telling what would happen. Would they swap orbits like it's suggested that Uranus and Neptune did four billion years ago? Collide? Nobody knows, because perturbation theory methods that enable us to solve these problems are inherently imprecise once other factors than those accounted for come into play.

So what's wrong with all the current suggestions? Well, they all oversimplify the whole system and don't deal with all the intermediate states between start state A and final state B, merely suggest what's the required change in kinetic energy and how one could achieve that. And with FTL suggestions, the other way around. And that's fine, because in reality, there isn't any solution to your question anyway.

In theory, I can think of a few end states for Mars to orbit at same or similar distance to the Sun as Earth does, for example putting Mars in Earth's opposition so they're co-orbital with Mars roughly where L3 would have been if Mars wasn't there, or putting Mars into a 90° or 270° inclination orbit that intersects Earth's in opposition, or even inclining Mars' orbit 180° to orbit retrograde and lowering its orbit parallel to Earth's but not at exactly at the same altitude, and let them swap altitude each time they approach each other (a horseshoe orbit). And these orbits could even be stable for a relatively long time. If... If other celestials weren't there, and all of a sudden having two celestials where it used to be only one wouldn't perturb their orbits and destabilize the whole inner Solar system.

So even assuming we could solve the issue of which orbit to put another celestial on so it's at the same distance to the Sun as the Earth is, we'd end up destabilizing the whole inner Solar system, and set it back into chaos with each celestial fighting for its place around the Sun. Mercury and Venus would violently change eccentricity, with end possibilities being either plummeting into the Sun, hitting one of the other three inner Solar system celestials, swapping orbits, or be ejected out of the inner Solar system completely. Main belt objects would destabilize orbits too, and the whole Solar system would be back in the Late Heavy Bombardment years. What would be the end outcome, and how would that affect outer Solar system? Nobody knows. But one thing is for sure. There isn't any comfortable way of doing it.

For what it's worth, swapping Earth's and Mars' orbit would require a lot less change in orbital energy, if you could increase Mars' eccentricity to the point of intersecting Earth's at exactly the right time for them to exchange orbits and not collide in the process. I didn't do calculations, but I'd say it should be around 20-30% of the required energy previously suggested. Oh, and according to my calculations, Michael Borgwardt's maths on how much change in kinetic energy would be required appears closer to $\approx -1.6\cdot 10^{32} \text{J}$ that I came out with, but it's really easy to mess with unit conversions required in the process, so I can't claim that's correct either. ;)

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  • $\begingroup$ The long-term stability of the inner solar system is already in doubt. Mercury's ellipticity changes thanks to interactions with Jupiter. Mercury may no longer exist in 5 billion years. It might disappear because its orbit becomes so elliptical that perihelion falls inside the Sun or because aphelion makes it cross Venus' orbit and eventually collide with Venus or be ejected. It might even cause Earth to collide with Mars. See imcce.fr/Equipes/ASD/person/Laskar/papers/2009/… . $\endgroup$ – David Hammen Mar 2 '14 at 17:08
  • $\begingroup$ @DavidHammen True, but I tried to show that moving Mars or Venus so much off their current altitude would cause even bigger problems and much, much sooner ;) $\endgroup$ – TildalWave Mar 2 '14 at 17:10
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    $\begingroup$ "It's not possible" is a challenge, not a fact. Note that the instabilities are over millions of years. The same techniques used to move the planets could be used to apply course corrections to the planets over smaller time scales, e.g. 10's to 100's of thousands of years. A natural instability does not mean it can't be artificially stabilized. In fact, modern fighter aircraft are designed to be unstable, and require active control systems to give the appearance of stability. $\endgroup$ – Mark Adler Mar 2 '14 at 18:18
  • $\begingroup$ I still agree, as I noted in my answer, that it is a very bad idea to try to get Earth and Mars to cohabit the same orbit. However I would need to see a violation of a basic physical law, like conservation of energy or conservation of angular momentum, before I would attempt to declare something "not possible". $\endgroup$ – Mark Adler Mar 2 '14 at 18:20
  • $\begingroup$ @MarkAdler My point is that once you start managing an orbit of one planet to such degree, you better have ability to manage orbits of all object that are affected by it. And that includes all the Main Belt objects and the whole inner Solar system. Those fiddlings of ours with numbers are nothing then. It would permanently and irreversibly change the Solar system's "landscape". For all intents and purposes, I consider it impossible then. Only Dave Lister can do it. Instabilities are in millions of years for an orbital swap, for a co-orbital Mars or Venus, that happens a lot sooner. ;) $\endgroup$ – TildalWave Mar 2 '14 at 18:23
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There's another problem here: None of the rocket approaches are safe even if you could do them.

The thing is the acceleration is going to be small. That means the body you are moving is going to pass very close to the Earth while it's orbit is being circularized.

Can you say "tides"?

(And that's assuming it's even possible to circularize the orbit in the first place. I wouldn't be one bit surprised if this is impossible due to deflection from the flybys of the Earth.)

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  • $\begingroup$ Good contribution Loren to considering safe tides and the complexity of circularzing with gravity assist. I edited the question so as to presume these can be worked out, and to sharpen the focus on timescale. $\endgroup$ – Bob Stein Mar 2 '14 at 21:11
  • $\begingroup$ @BobStein-VisiBone I was only addressing rockets, not gravity maneuvers. Circularization could be accomplished with a flyby of a planetary mass. $\endgroup$ – Loren Pechtel Mar 3 '14 at 5:42

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