Random Question About Gravity and Rogue Planets

[ZenithRising]

Hello smart Kerbal folks. I'm curious if any of you can help me get some insight into a story idea I've been rolling around in my head for awhile. I need to hurl the earth out of the solar system with a rogue planet that passes too close. Preferably I'd like to do it with an earth-like planet, not a gas giant, and I'd like to do it with a minimum of tidal forces so the Earth and civilization remains mostly intact as everything freezes.

So, I've got a ton of questions about this scenario I'd love to start to answer:

- Is such a scenario even possible?

- Assuming a rocky rogue planet with a mass of about 1.5 earths, what would the trajectory have to be to put Earth on escape trajectory in a relatively gentle manner?

- How long would it take Earth to become inhospitable to human life in this scenario? i.e. How quickly would it get cold? i.e. How quickly would it escape?

- What sort of acceleration would people on the surface feel?

- Are there other surprising consequences to this close encounter that I'm not considering?

And then some other questions related to other parts of the story:

- What are some good ways to preserve a large amount of information for a multi-billion year time scale?

- How feasible is a small scale geothermal power station designed to last on a billion year time scale (not necessarily with a particularly large power output after the first hundred years).

Anyone happen to know the answers to these questions? Know the equations I should use to do the math myself? Know a good place to start looking this stuff up?

[Deadpangod3]

Um, it might either have to make several passes in front of earth, or be ALOT bigger, and it might steal the moon, and if it got close enough, the atmosphere would start to be pulled onto the rogue planets surface,

Shortly after we will start floating off the surface as the rogue planets gravity overpowers earth's, though by this point the planets would probably be colliding and exploding and all dat good stuff.

Though I want to be wearing a parachute whilst I plummet towards the rogue planet.

[Rakaydos]

If the rogue planet is big enough to slingshot the earth to jupiter orbit, you could theoretically get a "voyager grand tour" ejection... if it happened back when voyager launched, planetary alingments dont happen every week, after all.

[Deadpangod3]

If the rogue planet is big enough to slingshot the earth to jupiter orbit, you could theoretically get a "voyager grand tour" ejection... if it happened back when voyager launched, planetary alingments dont happen every week, after all.

Maybe we could visit Eroupa while we're there if we last that long.

Just need to watch out for those moons...

[merendel]

I think your going to have to apply a liberal dose of HandWavium to justify the senario you described either way. In particular your goal of minimal tidal forces paired with a close pass of a gravitational body big enough to kick the earth onto an escape trajectory are prety much mutualy exclusive. Anything big enough to impart that much acceleration in a single go will most likely kick off massive tectonic activity. The resulting earthquakes on a global scale would prety much flaten our civilization. there might be some survivors of the initial event but dont expect many buildings to remain standing. This is also assuming that the close flyby didnt have other nasty consequences like striping a big chunk of the atmosphere.

I wouldnt expect any significant infrustructure like a geothermal plant to survive the initial pass of the planet. I also wouldnt expect the temp to remain warm enough for any survivers to have time to rebuild. Months at the outside, mars is prety cold compaired to earth and by the time we started geting out to jupiters orbit we would be beyond the frost line, the point where solar radiation is insufficent to keep water fluid. it does depend a bit on the orbit we get kicked into. It might be plausable for it to kick the earth into an ecentric orbit where we get some freezing and thawing cycles over a few orbits before jupiter slingshots us out of the system although the second kick might wreck any rebuilding that survivers managed to compleat, asumeing they survived the cold perioids.

Edited May 13, 2014 by merendel

[Chiboko]

Or it could be even further away and make even more passes in order to avoid the problems pointed out by Deadpangod3. The problem with multiple passes is that such an event would be have to happen in stages over a very long time (years), there is also the problem of avoiding other planets. Mercury, Venus and Mars would cause problems, if the event occurs for more than a decade Jupiter would be added to that list to. Then there is the problem posed by earths changing orbit (if the rogue planet makes multiple passes) that might case it to collide with another planet.

A more believable scenario would be to have a rogue star or massive object such as a brown dwarf pull earth out of its orbit while all the other planets happen to be on the other side of the sun. Such an object could theoretically pull earth out of its orbit in a single pass without causing to many disruptions on the surface; Stars have a lower density than planets resulting in a shallower gravity gradient and less tidal forces. As a small bonus you get to herald the beginning of endless cold and darkness with a short period of daylight all over the world, since the earth would be between 2 stars it would be day on both sides of the earth.

Also the earth gives out conspicuously more heat than it receives from the Sol and a lot of capacity to store up and slowly release heat. (like most ridiculously heavy objects) so it may actually take a few weeks, months or even years before the surface becomes uninhabitable, deep enough underground the heat from the earths core could let life survive for much longer.

[Vanamonde]

This looks like a job for... Science Lab! (Quick, into a nearby moderator control panel!)

[Sirrobert]

While I don't know anything about the gravity stuf, I would imagine the survivers being able to survive deep down in the earth, Matrix style (like Zion, only without the robots)

[problemecium]

All this talk of living underground and parachuting up into the sky in order to land on the other planet surface really makes me think of Patema Inverted for some reason...

[K^2]

No. Earth-like world would have to approach too close to Earth. Tidal forces (or direct impact) would make it impossible to survive. Unfortunately, you do need a gas giant.

Earth's orbital velocity is approximately 30km/s. To escape, you need to boost it to 42km/s. So you need to pick up 12km/s from a fly-by of the rogue planet. In principle, with point masses, you could get a boost to an arbitrary speed. The rogue just has to move fast enough. But you want the planet intact, and that limits the closest approach distance. The absolute minimum is Roche limit for a liquid body. For rogue of Earth's mass, that puts you at about 8,000km. The rogue would take up a quarter of the sky at the closest approach if it came that close. But that limit is just enough to prevent Earth from falling apart. You'd still loose a lot of atmosphere, and you are almost guaranteed all sorts of tectonic problems. Fortunately, tidal forces drop really fast with distance. At 20,000km, you'd experience less than 1/15th of Earth's gravity in the pull, and that shouldn't cause any catastrophic problems.

Doing some orbital mechanics magics, we get maximum boost at that approach to be just 6.3km/s. Which will still knock Earth's aphelion well past the orbit of Mars, but it's not enough to cause a complete escape.

As the size of the rogue increases, so will we have to increase the closest approach distance. With that in mind, the minimum mass required to completely eject Earth from Sun's orbit is about 18 Earths. That's a little larger than Uranus. And so, you certainly need a gas giant.

As for how long the Earth inhabitants would have, it depends on the exact trajectory. But it's going to be matter of weeks before dramatic changes are felt, and matter of months before everything is frozen solid. Not much time at all. And that's assuming that the planet isn't launched on trajectory that takes it near Sol before carrying out of the system. It could be a fiery doom for all living, rather than a cold one.

[hoppeltje]

watch this guys, it seems an interesting video about what u say.

so far as i know there is a big truth in it like 40% but not more.

And this, i dont know how you guys think about religion but thats what the next video is about.

[Zuni]

Well, I thank you for your analogy as my being a smart Kerbal folk, however I am simply a hopeless uneducated moron compared to everyone else here. I'll try to help, anyway.

- How long would it take Earth to become inhospitable to human life in this scenario? i.e. How quickly would it get cold? i.e. How quickly would it escape?

- Are there other surprising consequences to this close encounter that I'm not considering?

- What are some good ways to preserve a large amount of information for a multi-billion year time scale?

-I read something on this a while ago. Basically, a very long time. Earth has a hot core, remember, and it will take billions of years to cool. If we go to the warmest places we can, build bunkers deep underground, and are very co-operative in killing off most of the population, then we might last a few generations.

-The atmospheres of the planets would mix if they got too close, the gravity would lower on the side facing it since both planets are using all their mass.

-Carve it in rocks. That's how we still know stuff from ages ago.

Do you happen to have seen the film Melancholia? It's a little similar to your premise, although the slightly-bigger-earth actually does hit it straight on... Don't let me spoil it though, just go watch it. You'll get some good ideas.

[Skyler4856]

I wonder how long man could last using nuclear energy?

[TheDarkStar]

I wonder how long man could last using nuclear energy?

A really long time. I'm not sure on the exact number, but at least centuries.

[ZenithRising]

Um, it might either have to make several passes in front of earth, or be ALOT bigger, and it might steal the moon, and if it got close enough, the atmosphere would start to be pulled onto the rogue planets surface,

No. Earth-like world would have to approach too close to Earth. Tidal forces (or direct impact) would make it impossible to survive. Unfortunately, you do need a gas giant.

Earth's orbital velocity is approximately 30km/s. To escape, you need to boost it to 42km/s. So you need to pick up 12km/s from a fly-by of the rogue planet. In principle, with point masses, you could get a boost to an arbitrary speed. The rogue just has to move fast enough. But you want the planet intact, and that limits the closest approach distance. The absolute minimum is Roche limit for a liquid body. For rogue of Earth's mass, that puts you at about 8,000km. The rogue would take up a quarter of the sky at the closest approach if it came that close. But that limit is just enough to prevent Earth from falling apart. You'd still loose a lot of atmosphere, and you are almost guaranteed all sorts of tectonic problems. Fortunately, tidal forces drop really fast with distance. At 20,000km, you'd experience less than 1/15th of Earth's gravity in the pull, and that shouldn't cause any catastrophic problems.

Doing some orbital mechanics magics, we get maximum boost at that approach to be just 6.3km/s. Which will still knock Earth's aphelion well past the orbit of Mars, but it's not enough to cause a complete escape.

As the size of the rogue increases, so will we have to increase the closest approach distance. With that in mind, the minimum mass required to completely eject Earth from Sun's orbit is about 18 Earths. That's a little larger than Uranus. And so, you certainly need a gas giant.

As for how long the Earth inhabitants would have, it depends on the exact trajectory. But it's going to be matter of weeks before dramatic changes are felt, and matter of months before everything is frozen solid. Not much time at all. And that's assuming that the planet isn't launched on trajectory that takes it near Sol before carrying out of the system. It could be a fiery doom for all living, rather than a cold one.

Thanks everybody for your great answers! I've been looking into this for awhile on my own, and when I was wondering who could give me some help, I knew the Kerbal community would come through! This is an idea I've been kicking around for awhile, and I'm getting excited about actually sitting down to write it soon. Worse comes to worse I can just use some dramatic license, but I'm hoping there is a way to make it work without fudging the science.

In particular, thank you Deadpangod3 and K^2. A few great things there I'd like to unpack...

So, what I'm looking for is that the surface of the Earth stays nearly entirely intact. Before tectonic forces even come into play, I imagine the dramatic tides caused by a large gravity well passing nearby would wipe the continents before that was an issue. I really want a (relatively) slow peaceful death though, not a catastrophe. So I need to somehow accelerate the entire planet by 40% without causing those disturbances...

What about Deadpangod3's multiple pass idea? If a rocky earth-like planet ended up in a highly elliptical orbit with the earth so that the periapsis was on the space-side of the planet, could it nudge the earth up to escape velocity before the periapsis ends up on the sun-side and without creating tides that completely wipe out civilization?

What about a gas giant or rogue star? I would prefer for literary reasons for the rogue planet to be somewhat earth-like (1.5 earth masses or so would be fine), because the earth will become a very similar rogue planet by the end, and I like that connection, but I could toss the idea if it makes the math that much easier. Would a much less dense, higher mass object be able to generate that 12km/s of acceleration without destroying the surface?

What math should I know? Got a lot of great numbers from you K^2. I'd love to sit down and crunch some numbers myself. I know F=ma and F=G(m1*m2/r^2), and can look up the mass of the earth and what not. I know the Roche Limit is the minimum before a planet is pulled apart, but how would I find the minimum before the tides wipe out anything more than vulnerable coastal regions?

Thanks again everybody I really appreciate it!

[NERVAfan]

If this Popular Science article is to be trusted...

http://www.popsci.com/science/article/2013-07/if-sun-went-out-how-long-could-life-earth-survive

... without the Sun, the average surface temperature would drop to 0 F "within a week" and -100 F "in a year", "most plants would die in a few weeks", " Large trees, however, could survive for several decades, thanks to slow metabolism and substantial sugar stores". That last claim sounds rather implausible to me... trees surviving for decades at colder-than-a-South-Pole-winter temperatures????

Of course, that assumes an instant disappearance of the Sun. If the Earth was launched onto an escape trajectory, it wouldn't freeze over or kill plants within a few weeks... it would take longer than that to get to a distance where the sunlight was too weak to be survivable.

The oceans, according to that article, would stay liquid (under a frozen surface) for hundreds of thousands of years. Maybe this could be used?

[Othuyeg]

If this Popular Science article is to be trusted...

http://www.popsci.com/science/article/2013-07/if-sun-went-out-how-long-could-life-earth-survive

... without the Sun, the average surface temperature would drop to 0 F "within a week" and -100 F "in a year", "most plants would die in a few weeks", " Large trees, however, could survive for several decades, thanks to slow metabolism and substantial sugar stores". That last claim sounds rather implausible to me... trees surviving for decades at colder-than-a-South-Pole-winter temperatures????

Of course, that assumes an instant disappearance of the Sun. If the Earth was launched onto an escape trajectory, it wouldn't freeze over or kill plants within a few weeks... it would take longer than that to get to a distance where the sunlight was too weak to be survivable.

The oceans, according to that article, would stay liquid (under a frozen surface) for hundreds of thousands of years. Maybe this could be used?

The trees might survive, but they would not be doing any photosynthesis. In the arctic areas plants can survive ten months a year below 0 celsius.

The trees lose their leaves and store their sugar and chlorophyll in their roots and wait for the next growth period.

In this state, a tree will survive very very long.

Addition:

My plan of action as the human race in that situation would be to establish as many geothermal and nuclear plants and use the energy to power growth bays with artificial light.

Edited May 23, 2014 by Othuyeg

[Sirrobert]

If this Popular Science article is to be trusted...

http://www.popsci.com/science/article/2013-07/if-sun-went-out-how-long-could-life-earth-survive

... without the Sun, the average surface temperature would drop to 0 F "within a week" and -100 F "in a year", "most plants would die in a few weeks", " Large trees, however, could survive for several decades, thanks to slow metabolism and substantial sugar stores". That last claim sounds rather implausible to me... trees surviving for decades at colder-than-a-South-Pole-winter temperatures????

Of course, that assumes an instant disappearance of the Sun. If the Earth was launched onto an escape trajectory, it wouldn't freeze over or kill plants within a few weeks... it would take longer than that to get to a distance where the sunlight was too weak to be survivable.

The oceans, according to that article, would stay liquid (under a frozen surface) for hundreds of thousands of years. Maybe this could be used?

I find it a little difficult to believe a science article that uses a temprature scale based on frozen seawater and the inside temprature of a cow...

[sjwt]

I find it a little difficult to believe a science article that uses a temprature scale based on frozen seawater and the inside temprature of a cow...

or is using Fahrenheit...

[Sirrobert]

or is using Fahrenheit...

That's what I said...

[K^2]

Would a much less dense, higher mass object be able to generate that 12km/s of acceleration without destroying the surface?

Yeah, like I said, something a bit heavier than Uranus should be able to do the job with minimal damage. The larger you go, the "softer" you can make tidal forces. A rogue star could eject a planet with barely any tidal disturbance.

What math should I know? Got a lot of great numbers from you K^2. I'd love to sit down and crunch some numbers myself. I know F=ma and F=G(m1*m2/r^2), and can look up the mass of the earth and what not. I know the Roche Limit is the minimum before a planet is pulled apart, but how would I find the minimum before the tides wipe out anything more than vulnerable coastal regions?

If you look at the derivation of Roche Limit, you'll see where the tidal force equations come from. They are pretty straight forward, but might be a bit harder to visualize. For actual ejection, you can consider the motion relative to the center of mass. In that case, Earth and Rogue planet end up following hyperbolic trajectories around the center of mass, and you can use all of the math for such trajectories to make necessary computations. Just don't forget to shift things back to the frame of reference where Earth was initially motionless. For an estimate, you can neglect Sun's gravity here. You are just looking for Earth gaining 12km/s relative to its original state.