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So recently I got slated for missing some glaring obvious flaws in my story on here, which I really do appreciate. I'm approaching the question from a different angle though, in two parts.

What would be required to send the earth spinning both slower AND spinning out of orbit away from the sun? By slower, I mean earth rotations that take a 1000 or so years (give or take 500 yrs).

My very layman's thinking is that a mass large enough on the far side of Earth, passing close enough, may possible be strong enough to alter the planets trajectory without eviscerating all human life? Or as the sun dies is there a change in mass, perhaps the two combined? The mass could be pulled into some form of orbit of the new earth.

I do not need the universe to be preserved as-is, or long-term, but would like humans to still be alive even if in shelters underground until the sun is on the far side of the planet after a few hundred years.

I know this is a lot to ask, I'm reading all the other questions and will delete this is I find my answers there. I'm a psychologist by training so all this is way outside my field of knowledge xD. Thanks!

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    $\begingroup$ This might be a more defensible path. A massive object, passing outside Earth's orbit (pulling it away from the sun) and against it's rotation (slowing it down) may not scientifically slow and move the planet as much as you want - but it's suspend-my-disbelief possible. It would cause a whomping amount of damage, but the Earth's biome would survive. However, your numbers don't work. because when you slow the rotation down enough, a "day" is additionally defined by the orbit. If the world "didn't rotate" you'd have a "day" of one year. $\endgroup$ – JBH Oct 7 '18 at 14:15
  • $\begingroup$ @JBH: How come that slowing Earth's rotation drastically won't boil off the oceans? Where does the rotational energy go? $\endgroup$ – AlexP Oct 7 '18 at 14:16
  • $\begingroup$ @AlexP, It's being absorbed by the gravitational pull of the other planet. As I said in my comment, the idea strikes me in the suspension-of-disbelief range. (Don't forget, science fiction.) $\endgroup$ – JBH Oct 7 '18 at 14:50
  • $\begingroup$ You mention "as the sun dies" a possible cause. According to wikipedia this will not happen for another five billion years. Does that mean that the process of slowing down Earth can take that long? $\endgroup$ – Real Subtle Oct 8 '18 at 8:03
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Slowing down the Earth's rotation all at once would be a catastrophic change no matter how it's accomplished. Everything on the Earth's surface (including the surface itself) has a characteristic angular velocity as a result of the Earth's spin; my back-of-the-envelope math says it's in the vicinity of 1600 kph at the equator (it varies with latitude and also slightly with elevation).

You're going to be increasing the Earth's rotation period by a factor of 365,000 (from one day to 1000 years), which means the rotation speed is reduced by the same factor. The 1/365,000th that remains is basically zero. If this happens instantaneously, everything on Earth will go flying off at its current angular velocity. Since this is less than escape velocity, it will eventually plummet back to Earth. Neither of these does any favors to squishy things like humans and infrastructure.

Even if the change takes place over a period of time, there's the potential for damage. If we allow for one tenth the force of gravity (0.1g or .98 meters per second per second) at the equator, we can slow the rotation of the Earth safely in about 186 years, assuming the force remains constant. I don't know what the actual safe margin for e.g. buildings would be; I assume it's not all that much, since unexpected ongoing sideways acceleration isn't generally planned for in architecture. You might want to build in a little extra buffer to avoid damage. Conversely, if you decide you don't like the equator that much, it might be possible to push that limit without hurting the higher latitudes too badly.

This will wreak havoc with geostationary satellites; they won't deorbit or anything, but they also won't be geostationary and so they won't work right. Given time, we could probably replace them with less efficient satellites in new orbits. And, of course, changing the day-night cycle will eventually cause severe disruption in animals, plants, and people. (Although it may be gradual enough for humans to cope, and some animals, many animals' whole survival strategy will be invalidated and they'll die off. Plants might hang on for awhile, but won't be able to handle 500-year-long nights without drastic changes.)

Being pulled out of orbit isn't too difficult. Earth's orbit is the result of the interplay of its orbital velocity and the Sun's gravity. Adding more velocity will result in a larger orbit, neat as you please. You should be well within tolerances adjusting the Earth's orbit in your mission timeframe. As you might expect, the further the Earth is from the Sun, the less sunlight it receives and so the colder it becomes, and the less energy there is for plants and solar power.

However, there is a problem. A single pass by an object obviously won't produce the small force over the course of centuries that would make this survivable. An object could impart that kind of force if it was captured and made a (semi-)permanent part of the Earth-Moon system. However, if the object is large enough to affect the Earth's own orbit, it will destabilize this system, which could be catastrophic.

If you're okay with having an obviously artificial cause for this calamity, you could posit an alien (or advanced human, if for some reason this struck humanity as a good idea) probe that orbits near Earth, using a combination of gravity tractoring and ion-beam shepherding (using, respectively, its gravity and its propulsion exhaust to make minute changes in the Earth's orbital characteristics over a very long period). The engineering requirements would be on the extreme side but it's theoretically sound, and the probe being powered lets you skip a lot of complications about how it ends up in a stable orbit.

Incidentally, I'm sidestepping the idea of changing the Sun's mass because a) there isn't really a mechanism for that happening naturally, to any great extent, b) weird things happen to stars when you fiddle with their masses (for instance, removing a chunk of the Sun would reduce the luminosity of the rest), and c) that would only affect Earth's orbit, not its rotation.

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Cadence is right, if you take into account only speed.

Speed, however, is just part of the equation. The true currency of Physics is energy. You cannot change Earth's angular speed without spending energy. And the amount of energy required is huge. Randall Munroe, the author of XKCD, did the math for the amount of energy required for us to change the Earth's spin to change the length of days by 0.8 milliseconds:

Here’s the bad news: To get enough spin, we have to hit the Earth with on the order of a billion liters of rock per second (several times the volumetric discharge rate of the Amazon). This adds up to about one six-mile dinosaur-killing asteroid every couple days. Humanity—and life—wouldn’t survive the bombardment long.

Even if you use the gravity of a passing planet to achieve the same momentum change, the result is the same. No work is 100% energy efficient, and a lot would be dissipated as heat, melting the crust and boiling the oceans. On top of that, the tidal forces would reshape the Earth into something unrecognizable.

You just cannot change Earth's rotation in any meaningful way without killing everything and making it inhospitable for billions of years through science. Try some instead. Magic allows for the suspension of disbelief you need.

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