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> Dominos And Death Stars?
Jimthecopierwrench
Posted: April 14, 2012 10:13 pm
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The following scenario: A bunch of dominos each sucessive one slightly taller and more massive than the last. How much more doen't matter - suffice to say that a smaller one can knock over a larger one, which means that in theory with enough steps, the final one could be empire state bulding sized.

But what about in space with rocks?

With a sufficiently powerful computer capable of tracking all of the orbits of rocks and asteroids ... What (beyond the existenceof such a calculating machine) otherwise prevents one from calculating a planetary destruction with a softball sized precision rock throw, that alters tha orbit of a slightly largrer rock, and up through hundreds of thousands of steps until (say) a Mercury sized rock is hurtled into the earth?

Or for a 'good' scenario - doing the same thing to alter or destroy naturally occuring incoming 'armageddon' rocks.

These are the things I think about when i sweep my shop floor laugh.gif


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Geek
Posted: April 14, 2012 10:38 pm
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"You're playing pool with planets!" - David Lister, Red Dwarf

Hmmm, given inertia and interaction with other objects in orbit, I'd say the possibility is extremely remote, but not impossible.

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damien
Posted: April 15, 2012 01:40 am
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Was hoping this was a thread about pizza and movies.

Damien


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Sch3mat1c
Posted: April 15, 2012 07:10 am
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Hmmm interesting.

There was an episode of, pretty sure it was Voyager, where they visited a planet where the people were getting bombarded by a suspicious number of asteroids. Turns out on closer inspection, the asteroids were fitted with alien propulsion, which it just so happens matches the neighboring species' design. Conclusion: aggressor wants planet cleared. Makes it look like natural disaster. Natives evacuate or die off. When dust settles, plant colonies and stake your claim.
Aha: http://en.memory-alpha.org/wiki/Rise_(episode)

To do exactly what you're asking, you'd first have to know the velocities of all involved objects extremely precisely, of course -- once we get enough probes and telescopes into space, around Earth orbit and perhaps exploring the asteroid belt directly, say, it should be easy enough to accumulate that data. Millions of asteroids in the belt, with position, velocity and mass data on each over time, isn't a terribly large amount of data; even deriving that data (from the data generated by all those telescopes, with resolutions much greater than what we have now) will be pretty easy.

The ability to "play pool with planets" will be limited on how much mass is available and how much change in orbit is possible. Suppose you wished to knock Earth out of the solar system completely, just because, oh I don't know, its occupants are generally just total dicks. No matter what direction you choose, you have to impart enough energy to achieve escape velocity from the Sun. Or to go the other way, to let it fall into the Sun, you need to remove all orbital velocity. From Earth's position, the escape velocity is 42 km/s (radially), while the tangential orbital velocity is 30 km/s (these numbers are not coincidence: escape velocity is sqrt(2) times the orbital velocity for some radius of orbit). To escape, a planet has to be redirected from tangential (orbital) motion to sqrt(2) times more velocity, perfectly radial away from the Sun. This means stopping forward motion and going sideways much faster, which is a delta V of magnitude 1.55 times just stopping altogether. It sounds like escape is a bad idea -- you'll need to pack a lot more energy into making things happen.

Suppose you found a planet of 1/4 Earth's mass, propelled it towards Earth, from behind, at twice Earth's orbital velocity (thus carrying half Earth's forward momentum), and position it so it slingshots around Earth, leaving in a trajectory parallel to its initial path, but traveling in the opposite direction at the same velocity -- a change in momentum of 1 Earth. That momentum was sucked out of Earth, and now Earth sits motionless for a second, an interplanetary Wile-E-Coyote before it falls into the Sun.

The same trick works for any mass, but a smaller mass needs a higher velocity and a tighter trajectory -- limiting factor is when the object has to be so close, it skims the atmosphere, screwing up the billiards game for the occupants. I'm looking at the page on hyperbolic trajectories but I don't know quite enough to calculate how the distance of closest approach compares with the angle of initial trajectory and initial velocity, but it should be calculable.

If a perfect geometric series of masses were available for play, it would be a relatively feasible prospect to do directly as you propose -- nudge one which nudges the next, and so on. However, the asteroid belt has a rough power law type distribution:
http://www.sdss.org/news/releases/20010605.edr.img9.html
This means, if you're shopping for a very massive body to nudge the next slightly massiver body, and so on, you'll be hard pressed to find anything more massive than Ceres, and to nudge that, you've only got your pick of Pallas, Vesta and Hygiea. As you go down in size, you have many more to choose from (which means better matches to target orbits,

The next biggest rock in the solar system is Mercury, but you're unlikely to shift the orbit of Ceres (or similarly sized rocks) so dramatically that it falls almost all the way into the Sun -- we're talking about a (literally) astronomical amount of energy removal to get it to such an orbit.

As for the change in orbital energy available, you're basically asking if a given object, in a given orbit, can be nudged to a slightly lower orbit, where its energy adds to the energy of the target, which is pushed down towards another target, and the energy due to all this orbit shifting keeps piling up. Ultimately, the orbital energy available from the asteroid belt equals the amount of energy gained by pushing all the objects to the mean orbit, I think -- to go lower or higher would require input; you gain energy by mixing high with low and averaging them out.

Because the mass in the asteroid belt is fairly small as planets go -- 4% of the Moon's mass, the available energy is also quite small. If all that energy were pushed against Ceres, I doubt it would approach Mars, let alone Earth.

That said, there's certainly enough energy, and more than enough objects to choose from, to bring simple surface devastation upon a planet -- lots of dinosaur killers out there, and being much lighter, plenty of energy to kick them around with.

Tim


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Geek
Posted: April 15, 2012 07:20 am
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The Perfesser always has the "fun fact" answers biggrin.gif


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AwesomeMatt
Posted: April 15, 2012 09:20 am
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The analogy dies.

With dominoes of increasing size, they're precariously balanced and each containing a large amount of potential energy waiting to be released with a small amount of kinetic imbalance.

That means a tiny domino falling only has X energy, but could knock over a much bigger domino which, when it falls has perhaps 10x energy. The width of the base relative to the height determines the size of the "trigger energy":"released energy" ratio and how large of a multiplier you can get away with (how much bigger of a domino you can tip over using the kinetic energy of the smaller one). This presumes rectangular dominoes. If not, the best would be a precariously balanced inverted pendulum with a high mass at the top. The worst would be akin to a sheet of plywood already laying flat.

A tipped over domino impacts the next with much greater force than it took to trigger it to fall.

But with planets, there is no free lunch. There is no sudden surge of potential energy to release as soon as it is unbalanced like there is with dominoes.

If you give a planet a slight nudge, you get a slight reaction out of it, no larger than the energy you put in. That means you could use a fast moving small rock to create a moderate movement in a moderately-sized rock, but no more.

It's kind of like how you could move a car by hurling a shotput into the back bumper. What you're hoping for is the car to be balanced at the top of a hill and the shotput impact sends it forward enough to race down the hill. But, as far as I know, no such planetary "hills" exist in a two-party exchange.
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tekwiz
Posted: April 15, 2012 05:23 pm
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You wouldn't even need multiple objects. The thing about orbits in free space is that any amount of energy can shift the orbit by any amount, if given long enough to act.
Theoretically, you could send a package to an asteroid consisting of a computer & a huge parabolic mirror constructed from plastic film & given means for the computer to alter it's shape. The mirror could then focus the Sun's energy onto a tiny spot on the asteroid. The resulting boiling of the asteroid's substance would act like a rocket & allow the nudging of the asteroid into such an orbit that it falls & becomes captured by the Earth, like another moon.
One nickle iron asteroid of medium small size would contain more steel than the sum total produced by mankind to date.
Placed in Earth orbit, we'd have centuries of steel in one convenient, easy to process package.
A package worth trillions.
Even such trace contaminants such as gold or platinum would be found in multi-ton quantities in the leftovers from refining the steel.


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Sch3mat1c
Posted: April 15, 2012 09:23 pm
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I would argue that "hills" are available, because if you can contrive to bring two bodies (of different orbits) together, you can extract the difference in orbital energy; the result might be a single bound object (i.e., the smaller object enters orbit of the larger one; the transfer of momentum constitutes the energy exchange). Some initial energy is required to alter the smaller object's orbit, but I should think, in principle, at least through a chain of interactions, an effective domino effect is possible.

Tim


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Answering questions is a tricky subject to practice. Not due to the difficulty of formulating or locating answers, but due to the human inability of asking the right questions; a skill that, were one to possess, would put them in the "answering" category.
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