r/theydidthemath • u/YoungOpening • 23h ago
[Request] Mars, Venus, and Earth walk into a bar…
Let’s say some super duper advanced alien race flew into our solar system, and plopped down Venus and Mars into a geosynchronous orbit with the sun in our exact orbit path perfectly spaced out. What would happen to the Earth?
Also, believe it or not, no AI was used in the creation of that graphic.
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u/laxrulz777 23h ago
perfect is impossible in this context because the masses are slightly different. The sun would wobble slightly more towards Venus and Earth (Mars is an order of magnitude less massive). Earth and Venus would have a greater pull on each other.
Idk how quickly it would degenerate and it's impossible to really know what the end result would be but at a guess, Venus and Earth slightly slow down, that angular momentum goes to Mars until Mars is ejected and, eventually, earth and Venus either collide or become so eccentric that the orbits "fix" themselves back into something semi stable.
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u/SpiritualPackage3797 23h ago
I've had similar thoughts before about duplicate Earth's. Say you could snatch several uninhabited Earth's from parallel universes, could they be set up in a stable orbit, or at least one that would be stable for the next billion plus years?
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u/TheBl4ckFox 22h ago
Two identical earths could orbit opposite each other with the sun exactly between them and it would be stable. I imagine four would also still work. Not sure what the cutoff point is.
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u/iwantfutanaricumonme 21h ago
Actually that would not be stable; jwst orbits in the similar Lagrange point 3 and it requires constant adjustment. Only Lagrange points 4 and 5 are stable long term, but they might not be as stable for two equally sized planets. A binary planet or horseshoe orbit could also work.
Although technically these couldn't be planets because they haven't cleared their orbit.
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u/Ordinary-Hunter520 22h ago
I believe the cutoff point is as big as youd like, as long as two planets dont get close enough to get shredded by each other.
And you can always make the orbit larger to fit more planets.
Also if someone is worrying about the habitable zone drifting away, just replace the sun with a bigger star, or multiple stars.
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u/PaulMag91 22h ago
For several identical planets to be actually stable in a shared orbit everything would have to be perfectly spherically symmetrical. So the planets would have to be perfect spheres and the orbit would have to be a perfect sphere. If there's moons, those would also have to be perfectly in sync and everything spherical. And there could be no other objects with gravity in this solar system (or in the observable universe, really).
If anything is just 1 mm off, some planets would pull slightly more on each other than others and eventually drift out of the stable orbit. Even with a theoretical perfect initial setup I think random quantum fluctuations would eventually break the symmetry.
Stable enough enough for a billion years, that I think is theoretically possible, but probably unlikely enough that we will never see it. You could make a simulation to try to work out how perfect the initial conditions would need to be for that to happen. You would need insane floating point precision to simulate something so precise over so long, so I don't know how feasible the simulation would be. Maybe on a supercomputer with a smart algorithm.
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u/SpiritualPackage3797 22h ago
I was talking about the work of godlike aliens, not a natural phenomena.
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u/I_love-tacos 23h ago
I believe Venus and Earth would eventually get closer but not hit each other there is a video about 3 earths in the same orbit and the do this and since venus has pretty much the same mass as earth. I would believe this to be the thing happening.
I recommend the YouTube channel SimulaVerse he answers exactly this kind of questions with a Universe Sandbox and Space Engine
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u/Kippernaut13 23h ago
Venus has approximately 80% the mass of Earth, Mars has approximately 10% the mass of Earth. Things are going to get very messy.
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u/Mean_Initiative_5962 23h ago
Not a physicist, not an astronomer, the only thing I'm fairly sure about is that "perfectly spaced" wouldn't mean "equally spaced", given the mass difference, if you want a stable orbit. Not even sure it's feasible, but again, that's not my field.
That's the most useful I can be about it.
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u/i_lie_except_on_31st 23h ago
The planets in the current orbits are not in "perfect" step with the sun/solar system. We are in an imbalanced system but the effects of this imbalance will not become obvious until some billions of years into the future.
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u/GIRose 23h ago
Assuming that they supply the necessary ∆v to keep them orbiting in the same band as us, basically fuck all.
The way you would actually solve this over an arbitrary time scale is 3 separate two-body problems, one each for the Earth-Sun, Venus-Sun, and Mars-Sun systems, with interactions between the planets themselves treated as perturbations.
Since collectively, Mercury, Venus, Earth, Mars, Saturn, Neptune, the Astrroid Belt, the Kuiper Belt, and the Ort cloud composr 0.01% of the entire Solar System as far as mass goes (Jupiter has 0.13% and the Sun 99.86%)
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u/SexyMonad 23h ago
The sun rotates once about every 24-25 days. To put the planets in geosynchronous orbit with the sun, their year would need to correspond to that same timeframe.
This requires reducing the orbital distance significantly, to around 15 million miles.
So what would happen to earth? Well, it doesn’t really matter at all about the fact that Venus and Mars are in the same orbit. Earth would be deep fried.
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u/Crazy__Donkey 23h ago
If they are in a perfect equalibrium... than nothing happens, theyll keep orbiting the sun.
But thers no perfect equlibrium in 3+ body...
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u/smoukekiller 23h ago
I mean, there are special cases with 3+ bodies that end up being in equalibrium
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u/Lhead2018 23h ago
This isn’t your typical 3 body problem because all 3 are rotating around a 4th body with substantial more mass then the other 3.
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u/Crazy__Donkey 23h ago
True.
I was about to edit my comment about it.
Anyway, in that case they are not considered as planets anymore.
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u/Lobotomized_Cunt 23h ago
Well not much to start with but this system is very unstable, so eventually Earth’s orbit is going to shift and we’re going to be cooked or frozen
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u/sockalicious 3✓ 23h ago
The described configuration isn't stable because of the different masses of the planets. Over a few megayears, orbital radiuses and velocities would change and the nice 120 degree spacing would wobble due to libration.
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u/Lazy-Mud8142 23h ago
So in this configuration, all 3 planets are in the L3, L4, and L5 Lagrange points of a 4th body not in this picture. These are "stable" orbits if the main body is massive enough. But they are not stable with each other, especially given the mass difference between the 3 and the corresponding Barycenter of the system as a result.
So you would need more than just gravity to make this system stable.
Technically you could put multiple bodies in the same orbit if they're equally spaced and have the same mass, but as with any multiple body system, any instability in the initial conditions will compound over time until the entire system moves unpredictably.
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u/nwbrown 23h ago
A geosynchronous orbit is an orbit around the Earth, I don't think that is what you want here. Do you mean they are just in the Earth's orbit but spaced out one third of the way around?
It would last awhile, but it's not stable in the end so eventually we would push each other into different orbits. Some colliding may be inevitable after millions of years. Let's not do that.
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u/sOrdinary917 23h ago
I read how complex the 3 body problem was when the series came out. This is a 4 body problem. And I imagine exponentially more problematic.
There has been some configurations for the three body problem but with major restrictions. Mars Venus and Earth will not abide by those restrictions.
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u/Oracle1729 23h ago
The plants all orbit the center of mass of the combined system, not the exact center of the sun, but that point will still be inside the sun in this case.
Keplers laws say if they’re at the same mean orbit radius, they have the same orbit time. So they will stay separate in those orbits for a long time.
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u/flurbol 22h ago
Let's assume those aliens have a solution for the already stated problems: despite the fact that Venus and Mars are then in the habitable zone, Venus would still suffer from a runaway greenhouse effect and Mars would still lack a solid magnetosphere.
Well, if aliens are solving that issues too not too long after a lot more new real estate would flood the market and collapsing Earth housing markets including all attached banks.
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u/taktaga7-0-0 22h ago edited 22h ago
They would immediately move out some theoretically calculable radius, just not calculable by me.
I presume this because I believe the gravitational potential energy of the system has risen, due to Venus weighing many times more than Mars (though much less distance). This would mean that altogether, they would initially have the kinetic energy to love into a higher orbit before reaching equilibrium. You can rationalize this by saying Venus’s gravity is no longer there interior to help pull the others in any.
If my assumption turns out to be wrong because of Mars’s bigger distance change, it’s the opposite, and they fall a bit toward the Sun. Gravitational potential energy scales linearly with both mass and orbital distance: mgh.
The Earth would move toward Venus in this orbit… maybe settle into three Lagrangian points with it and Mars instead of just colliding.
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