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I just finished watching the newest kurzgesagt video on if the earth got kicked out of the solar system here:

https://m.youtube.com/watch?v=gLZJlf5rHVs

And I wanted to use that scenario in a story but I instead want the earth to be pulled far enough away to be come perpetually snow cold without being uninhabitable and in 1,000,000 years or so slowly fall back into it’s old orbit. How could I make that happen without messing up the other planets permanently. They can be dislodged too but I need them to fall back into their original place too.

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    $\begingroup$ You can't. There is no way for something to "fall back" into its orbit like that. Besides which, humans would die out long before it was even remotely relevant. $\endgroup$ – user3482749 Dec 1 '20 at 21:46
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    $\begingroup$ Welcome to Worldbuilding! When you have a moment, please click here to learn more about our culture and take our tour. Just to set your expectations (having not seen the video), Once the Earth leaves, it's gone. If it's thrown into a distantly-eliptical orbit, this might be achievable, but it needs to remain in the habitable zone or everything dies, so you're suggesting pushing it to the orbit of Mars. Any solution that could get it back to the original orbit kills everything. $\endgroup$ – JBH Dec 1 '20 at 21:47
  • $\begingroup$ Related: Could humanity survive the sun going dark? $\endgroup$ – Alexander Dec 1 '20 at 21:49
  • $\begingroup$ What if it was pushed into Mars orbit then the asteroids following the rogue sun passed behind the earth without touching the earth and slowing it down so that the sun’s gravity pulled it closer until it was back in its original orbit? $\endgroup$ – user11937382 Dec 1 '20 at 21:57
  • $\begingroup$ @user11937382 Would another group of asteroids speed it back up? Unfortunately, this is where science and fiction part company. There isn't (IMO) a believable way for this to happen that wouldn't kill everybody (if it could be made to happen at all). On the other hand, it sounds like you've come up with the premise of a really good story! There's nothing wrong with that. $\endgroup$ – JBH Dec 1 '20 at 22:09
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The Earth could be moved from its orbit by the passage of a large enough object through the solar system. A brown dwarf or large rogue planet might well do the trick. But there would be problems with this approach.

Firstly the orbits of the other planets would almost certainly be disrupted and the degree of that disruption would increase as the amount of change to Earth’s orbit increased. You can’t have a massive object that only affects the Earth. The best hope would be an object approaching the Earth when the other planets were on the far side of the sun or perhaps approaching from a direction perpendicular to the plane of the ecliptic.

Given the right conditions the Earth could be drawn away from the Sun on to a very highly elliptical orbit so would freeze and then eventually return to the sun. However the return would not last long and it would soon be heading out into the cold again.

There is no way to achieve exactly what you want realistically. It would need two close encounters with large objects one to pull Earth away from the Sun and one to bring it back. But the chance of even one such encounter let alone two is extremely low. And the planets would be scattered far and wide.

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Frame shift: Terraforming Terra Firma:

The Earth was once a snowball planet, but it's not today. Given the premise that Earth is shifted out of it's orbit into a new, much colder orbit, and humanity can survive the shift (not so cold as to destroy the atmosphere, kill everyone, etc.) why not look at "shift back to it's original orbit" as "shift back to it's original climate?

Given humans and technology, plus a million years to do it in, then there really isn't a better candidate for terraforming than Earth. If people are willing to terraform a relatively miserable ball like Mars, then Earth, with all it's known qualities and resources, would be so much easier to take a Mars-like Earth and convert it into an Earth-like Earth.

All the things people talk about for terraforming Mars work better here. Okay, it might be easier gravitationally to launch ships from the surface of Mars, and most Mars expeditions assume access to shipped-in Earth equipment. But we're assuming a sort of subterranean Earth existence where people have underground cities, factories, hydroponics, etc. Depending on how cold it gets and how much sun you want, plus if it's an elliptical (sometimes warm) orbit, you may have rare summers, possibly even living oceans (under deep ice).

So clever humans make the ground dark, use geothermal heating, and start putting up solar reflectors. We dump greenhouse gasses into the air. We do all the things we were going to do to Mars.

I'm not sure if the environment will fully recover. But I bet we could turn an Earth-sized Mars with all our stuff already here into a fairly respectable place to live. Given enough time.

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I love Kurzgesagt, and I also just watched that video, which is why I clicked on your question because it was such a coincidence I was like "hang on, what kind of devilry is this?" (;-D)

Anyway, if I remember correctly, in the video they said the chance of this rogue (I think) brown dwarf (or similar) tugging Earth away from the Sun like that is about 1 in 100 000 in the next 5 billion years.

So, not zero, but not very likely.

And then as mentioned in another answer or comment above, the chances of it happening again just a million years later to bring Earth back home would be even more remote.

So, to keep your excellent story alive, I suggest adding the old favourite secret ingredient: Handwavium.

Not too much, just a pinch, like my grandma said about coriander - "a little is your friend, a lot is your enemy."

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