## Tuesday, August 25, 2015

### Good News Everyone! The Earth Won't Go Flying Out of the Solar System

One of the most memorable science fiction stories I read as a child involves a family holed up in a makeshift shelter after a passing star has flung the Earth out of its orbit. One of the children has to go out every day with a bucket and bring back the day's supply of frozen oxygen to be thawed out in the shelter. Despite remembering the story so vividly, I completely forgot the title and author, but an Internet search reveals them to be: "A Pail of Air," by Fritz Leiber.

But this is just fiction, right?  The Earth couldn't really be flung out of its orbit, leaving us to freeze to death in the icy blackness of space. Or could it?  Well, it's complicated....

Let me digress a bit before getting to the punchline. The laws of physics mostly boil down to collections of differential equations, but these come in two flavors: linear equations and nonlinear equations. Linear equations are, in the parlance of physics, "well behaved."  They are the obedient children who do their homework on time and don't talk back to their parents. But nonlinear equations are the bad boys of physics. They smoke. They drink. They probably carry switchblades. More to the point, they exhibit "chaotic" behavior -- a tiny change in one place can quickly grow to produce huge consequences somewhere else. The classic example is the "butterfly effect": a butterfly flapping its wings in California could theoretically alter the weather so much that five years later, a hurricane strikes Florida. And here's where things get interesting. The equations governing the motion of the planets around the Sun are nonlinear and could, in principle, exhibit just this kind of chaotic behavior. The planets could orbit the Sun happily for billions of years until a small change in their orbits gets larger and larger and expels one or more planets entirely.

Physicists have spent the past few hundred years trying to prove that the Solar System is stable, that it won't suddenly eject one or more planets out into interstellar space. And they've failed. Hey, solving nonlinear differential equations is really hard. But now that we have computers, shouldn't it be easier? The problem is that chaotic behavior makes it difficult to solve these equations accurately even on computers -- tiny errors, which inevitably occur in any computer simulation, can mushroom into huge errors over time. So physicists have been forced to develop clever computer tricks to get around this problem. Last week, Richard Zeebe from the University of Hawaii reported that his suite of simulations shows that the Earth will remain in its orbit for at least the next 5 billion years. Whew! That means that instead of freezing in the depths of interstellar space, the Earth will still be around when the Sun puffs up into a red giant and burns us to a cinder. Have a nice day!

#### 5 comments:

robk said...

so maybe we change earth orbit??that give earth chance to survive when sun go to be red giant ?

Robert Scherrer said...

Yes, various people have suggested this. Luckily, it's not too urgent.

non multum sed multa said...

I remember reading that F Leiber story too. I don't think a plastic bucket would work. The low temperatures would make it brittle and it would fall apart. Every home should be furnished with a stout metal bucket just in case.

Robert Scherrer said...

At those temperatures you could use a bucket sculpted out of ice -- it would be harder than rock!

Hans Georg Lundahl said...

So, A: my prediction on this page of my Geocentric wikia is not supported by the computer simulation?

Is Newtonian Physics a Sufficient Explanation for Celestial Mechanics?

And B: you can't be really sure, since it is a non-linear equation?