Sunday, June 7, 2015

Seveneves and the Roche limit

For an author it's important to get things that the reader might find hard to swallow out there and dealt with as soon as possible.  I didn't really enjoy Neal Stephenson's last book, REAMDE, past the halfway point because too many improbably occurrences had piled up and my suspension of disbelief didn't recover.  By contrast his newest novel, Seveneves, seems to be doing an excellent job of getting the improbable stuff dealt with quickly and I've been enjoying the book without any hangups.  I've only gotten through chapter 7, acknowledged, but I've got a feeling I'll continue to enjoy this one.

But of course the second improbable thing gives me a chance to talk about some physics I find interesting so I'm going to dissect what I think Stephenson gets wrong.  Not because I think the author is a bad person or wrote a bad book but just because I think the physics is nifty and reading this prompted me to share it.

The basic setup of the book is that the moon is hit by some high energy cosmic event that basically blows it up.  That's improbable thing #1 but hey, we haven't totally figured out physics yet.  After that the moon breaks into seven fragments that go into orbit around each other in a cluster at several times the original diameter of the moon.  The periodically collide with each other and break into more and more fragments.  Our protagonists figure out that eventually they'll break up so much that they'll get away from the old lunar orbit and either collide with Earth or form a new ring.  That's improbable thing #2 and also the driver of the plot.

There are a few things wrong with that but they'll take some explaining.  The first is that size matters and large objects don't behave the same way as small objects.  Way back in 1638 Galileo wrote Discourses and Mathematical Demonstrations Relating to Two New Sciences which is the first I've ever heard of anyone talking about this principle.  Galileo observed that small animals like cats can survive falls much better than large animals like horses even over a couple of meters.  The thing is that a things strength increases in proportion to its cross section but its weight increases as its volume.  So as an animal's length increases its ability to support itself against falls decreases as its length squared over its length cubed, or just inversely proportionally to its length all things being equal.  That's how an ant, say, can lift 40 times its body weight but a human could never do that.

This applies to structures and moons as well as animals.  If you're familiar with 10 cm cubes of stone and want to think about how 1 m cubes behave just pretend that the larger cube is like the smaller but with only 1/10th the strength.  Stone is pretty strong but a humongous cube wont be able to support itself.  The edges will fall off under their own weight and you'll have a pile rather than a cube.  The radius of the moon is over 1,700,000 meters so it would be incredibly fragile if you did something like bring it to the surface of the Earth.  A merely mountain sized mass of rock would crumble into a pile.  Something the size of the moon would flow like water.  That's why all celestial bodies over a certain size end up as spheres rather than the bumpy shapes of smaller moons and asteroids.

So if you were to hit the moon with a big jolt and cause it to break up it wouldn't break up into 7 pieces that would then maybe split in half if they hit each other.  It would be more like the breakup of a mass of dust.

This sometimes goes against our intuitions.  I know I've read 9/11 truther websites where they say that the twin towers can't have just collapsed because when a 10 story building collapses in an earthquake it doesn't look anything like what happened to the World Trade Center.  But really the Twin Towers were 10 time taller and so only one tenth as able to withstand their own weight once it had been unleashed on them and it's no surprise that they could be reduced so completely to rubble.

The other problem is the way the moon overcomes its own gravity when it fragments too far.  When you've got a moon orbiting a planet you've got its own gravity trying to keep it together but you've also got the tidal forces of the planet's gravity trying to pull it apart.  A moon's gravity is just as strong no matter where it is but the planet's pull on the moon and the resulting differential get stronger the closer a moon is to its planet.  There's this thing called the Roche Limit that tells you when a moon is far enough away to stick together and when it's gotten so close that it is pulled apart into a ring system.  And the Earth's moon is way, way out beyond that limit.  It's about 500 km for the Moon when the Moon's actual orbit is way out at 400,000 km.

If you've got a few big hunks of moon orbiting their mutual center of mass then there isn't an obvious path from that to their fragments escaping that orbit.  Now, when rigid objects hit each other and shatter you often have pieces fly off going faster than the objects that collided.  But again that tends to happen with hard objects rather than the effectively very soft objects that the moon chunks would be.

So basically I don't buy the setup in Seveneves.  But it's ok since it's something I swallowed at the start and the rest of the book is good enough to make me forget it so far.

UPDATE:  Finished the book and I really enjoyed it up 'til the timeskip at the 2/3 point and enjoyed it enough after.  I think the book would have been better with an Ender's Game style "And this is what happens in the future" last chapter instead of that last third but I'm still happy with the book overall.

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