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I'm writing a novel about an extraterrestrial civilization using it's planet as an interstellar ship, let's assume they somehow figured out how to do so (sci-fi magic) and they were aiming to find intelligent life, which they detected by radio signals from our system. Their intentions are not hostile.

I think that it's important to note that once it's arriving to our solar system they would completely halt their magical travel system to not affect in any way the orbits of the remaining planets; the magical travel system is based off of the Warp Drive by Miguel Alcubierre, a device that bends space-time to achieve speeds faster than light, so I assume planetary-system entry would be completely detectable, as would be the approach of the planet to the origin of the radio signals.

Let's say that the planet "docks" into orbits of the planets they visit, so there must be a safe distance to not cause catastrophes on the host planet. (I think that's what would happen) Any insight would be really appreciated, and I would like to apologize if the question isn't clear :(. Thank you for your time.

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    $\begingroup$ I think "safe distance" and "Earth orbit" are mutually exclusive for a mass 3x that of Earth...you'd get unpredictable 3-body interactions between the earth, the moon, and the rogue planet, probably resulting in completely bonkers tidal stresses at best and ejection into a new solar orbit or collision at worst. $\endgroup$ – Qami Apr 5 at 18:24
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    $\begingroup$ That's more or less what I was expecting for an answer, I thought of the setting being "they are not hostile, however..." as in "Earth gets almost obliterated, so once the visitors try to reach Earth, humans respond with violence" $\endgroup$ – sentinel1265 Apr 5 at 18:33
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    $\begingroup$ Honestly, they might be better off keeping their magic travel system on. If it works by, say, manipulating gravity, they could potentially use it to correct any perturbations they might make while entering and while remaining in the Solar System. $\endgroup$ – BMF Apr 6 at 0:14
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    $\begingroup$ Worth noting that the real magic isn't the Alcubierre drive, but whatever moves the planet at sublight speeds. The sheer energy involved in using a planet as a spacecraft is almost inconceivable. $\endgroup$ – jdunlop Apr 6 at 1:28
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    $\begingroup$ (It's equally inconceivable that anyone who could build such a thing would naively approach an inhabited planet and not expect a hostile response unless they "parked" at sufficient distance.) $\endgroup$ – jdunlop Apr 6 at 1:39
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There are two, and exactly two safe spots to place this huge interloper.

At the L4 or L5 Lagrange points. (That's the Sun-Earth L4 and L5 points, 150 million km thataway ahead or behind us in orbit!!)

In effect, Earth would become the L4 or L5 Lagrange companion of the ship!
And that ship had better stay exactly at the right distance, in exactly the orbit Earth used to have to itself, otherwise things will very soon become very ugly.

There will still be negative effects in the rest of the Solar System, but these should be very small compared to the effect on Earth.

Subquestion to those with more grey matter than I...

How long would a L5 position be stable for, when the "planet" in the equation is only 3x the size, not 26x+ as required for Lagrangian longterm stability?
and
What would the effect be on our Moon's orbit? I strongly suspect that having a moon orbiting a planet that is itself in L5 is not very stable at all? At least not without some adjustments?

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    $\begingroup$ Thank you, gotta say your answer gave me some solid insight to achieve truly peaceful relations between both celestial bodies; regarding your questions, I really can't think of anything, I didn't even thought of that in the first place but I hope to see them solved, it's a really fascinating matter $\endgroup$ – sentinel1265 Apr 5 at 18:55
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    $\begingroup$ Another option might be to continue to use the magical travel system to actively keep things stable. Keeping the orbit of a smaller planet stable seems like small potatoes compared to traveling between solar systems. One hand-wavey way to do this might be to say the magical system allows gravity interactions between their planet and the sun, but blocks it between their planet and Earth. "Narrow aperture" or something. $\endgroup$ – TREE Apr 6 at 11:24
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Earth's orbit will be forever changed. Chaos ensues.

You can use this handy calculator to estimate the forces between an object with the mass of Earth and an object with the mass three times that of Earth at various distances. Even if the friendly visitors park their planet 10,000 miles away, their planet will create enormous gravitational forces. Sustaining that kind of force over any period of time would pull the planet out of its orbit. Earthlings can survive in a very narrow range of temperatures. The climate change that the planet is currently experiencing poses serious threats to plants and animals even though the temperature changes are relatively small. Altering Earth's orbit would be disastrous.

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  • $\begingroup$ Thank you, the calculator will come in very handy :) and really good for someone to do a quick note on Earth's current situation with climate change $\endgroup$ – sentinel1265 Apr 5 at 18:44
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    $\begingroup$ Ten thousand miles away is twenty times closer than the Moon! I think your example could use a little distancing. $\endgroup$ – jdunlop Apr 6 at 1:26
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    $\begingroup$ @jdunlop Well even at the distance of the Moon, you'd be talking about serious changes to life on Earth. One thing missing from the original scenario is how far the tourists can move from their spacecraft's parking location. If they can fly a few AU without any trouble, then we wouldn't have to worry too much about the effects of their planetship's gravity. $\endgroup$ – Andrew Brēza Apr 6 at 15:10
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Rocks fall; everybody dies.

Unless they use a lot of handwavium the tidal forces are going to be immense. As a result, you'll get annoying things like abnormal tides killing sea life, landslides, and disruption of satellite orbits.

Although these phenomena might not kill everybody, they will definitely cause a lot of issues and disruptions. It's simply unavoidable.

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    $\begingroup$ Thank you, as I mentioned above, that's more or less what I was expecting for an answer, the setting I'm thinking of is not "absolute" so any answer could be really helpful, such as yours $\endgroup$ – sentinel1265 Apr 5 at 18:35
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    $\begingroup$ They cannot enter a normal earth orbit. They perhaps could find a stable orbit around the sun in between earth and Mars and ferry over or something though. $\endgroup$ – Eric G Apr 5 at 18:40
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    $\begingroup$ I will take your insight in high consideration, thank you $\endgroup$ – sentinel1265 Apr 5 at 18:46
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I decided to build upon PcMan´s awnser by trying to simulate this scenario using my (not all that accurate, but hopefully good enough for this) gravitational simulator. So i tried placing a 3x earth mass planet at earths L5 point and let physics do its thing. (My simulator could not handle having the moon in this aswell as the earth-moon distance is too small, but i suspect the moon to be rather stable during all of this as it sits rather deep in earths gravity well)

The result is that the lagrange points themselvs are utterly unstable, although what happend instead was that earth and this planet ended up in a horseshoe configuration with about 500 years as half-period. So what that means is that as the 2 planets are in slightly different orbits they end up with slightly different orbital periods(lets say that earth ends up with a shorter period), so then earth would slowly catch up to the other planet from behind and get sped up abit by the other planets gravity. At the same time the other planet would get slowed down a little as earths gravity pulls it backwards a tiny bit. This has the effect that the earth gets pulled into a higher orbit with longer period and starts falling behind the other planet, so they separate again. And then 500 years later earth has wrapped around the sun and starts approaching the planet from the front instead, and the same reversing process happens again and so on.

This means that as earth is on the inner,faster orbit the year would be about half a day shorter and when on the outer,slower orbit the year would be about half a day longer. Also note that all this orbital swapping has a tendency to give earths orbit higher eccentricity and that might mess with seasonal stability and the global climate.

This configuration is somewhat stable, atleast in the short-term. In my simulations it lasted about a million years or so but after that some rather nasty overlaps and resonances started happening and then a rather sudden disintigration of the whole setup, where in one case earth crashed into the sun. Ouch!

In these animations earth is represented by the green dot and the other planet by the orange dot. (i dont know how to get the gif to embed, sorry...) This first animation shows the horseshoe orbit as it looks at the start(after it has settled down abit)

https://imgur.com/tUTwG1i

And this second one shows the instability at about 1.1 million years

https://imgur.com/gtLkyJj

So in summary: Placing this planet in earths orbit will work for about a million years but not more than that, so if the aliens want to stay for longer than that some kind of more permanent location will have to be found. But that seems abit out of topic for this question.

Or just do some good-fashioned stationkeeping using whatever magic brought their planet here to start with, as predicting and preventing this kind of instability is very easy compared to moving a whole planet between star systems. (The prediction part is something we humans can pretty much already do btw) Just give either or both of the planets a tiny nudge in the right direction every hundred years or so and this setup can last for aslong as you want it to.

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  • $\begingroup$ "This means that as earth is on the inner,faster orbit the year would be about half a day shorter and when on the outer,slower orbit the year would be about half a day longer." The unfun part of this is that such a chanhe in day length will cause more climate change in a year than what we have caused in the last century. Think about the next great extinction. Only humans, rats, roaches and some pets might survive. $\endgroup$ – The Square-Cube Law Apr 9 at 12:30

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