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-   -   Planet cracker (https://forums.sjgames.com/showthread.php?t=71973)

sir_pudding 08-06-2010 01:15 AM
Re: Planet cracker
 
Quote:
Originally Posted by lwcamp (Post 1028052)
Just for reference, in the thread that you link to the relativistic spacecraft would have a kinetic energy of 3.6E22 J (if I did the math right). From the ever useful Atomic Rocket boom table
http://www.projectrho.com/rocket/rocket3x1.html , about 1/6 of the way down the page
that's about an order of magnitude less energy than the Chicxulub event that ended the dinosaurs. It would cause a lot of consternation to the people living there, but would not really damage an earth-like planet.
So as suspected the collision rules break down at relativistic velocities. I wonder where the breakpoint is?

Edges 08-06-2010 03:44 AM
Re: Planet cracker
 
Quote:
Originally Posted by lwcamp (Post 1028052)
Just for reference, in the thread that you link to the relativistic spacecraft would have a kinetic energy of 3.6E22 J (if I did the math right). From the ever useful Atomic Rocket boom table
http://www.projectrho.com/rocket/rocket3x1.html , about 1/6 of the way down the page
that's about an order of magnitude less energy than the Chicxulub event that ended the dinosaurs. It would cause a lot of consternation to the people living there, but would not really damage an earth-like planet.

With four orders of magnitude more energy, you could remove all of an earth-like planet's atmosphere. For five orders of magnitude more energy, you could turn all of earth's oceans into steam. Six orders of magnitude more energy allows you to melt the earth's crust, making the entire earth molten. It would take nine orders of magnitude more energy to blast the earth into gravitationally unbound rubble.

Luke
Nice table. Thanks.

MattStriker 08-06-2010 07:35 AM
Re: Planet cracker
 
Quote:
Originally Posted by Edges (Post 1027980)
I get a sphere around 6.5 km in diameter at the core of the earth if transformed into antimatter would destroy the earth assuming your core density is correct (I know your antimatter reaction number is) and the death star guys in the post #6 link got their number right.

After a quick search, some estimates for core density are a little lower (12.6-13g/cm^3). So 6.5 km should be plenty.
Hmm. Does your calculation use the whole mass, or just half of it? The way the planetkiller works in-universe is that it produces an even mix of matter and anti-matter from the converted mass...

JHDude 08-06-2010 09:26 AM
Re: Planet cracker
 
Thanks for the link lwcamp! My only question is would these numbers be accurate for a continuous beam? For example: the table states that 2.9x10^31 Joules are needed to reduce Terra to gravel (the desired effect of the planet cracker). Is this energy delivered all at once? Or does the sum total of the energy imparted have to be equal to that?

lwcamp 08-06-2010 11:10 AM
Re: Planet cracker
 
Quote:
Originally Posted by JHDude (Post 1028198)
Thanks for the link lwcamp! My only question is would these numbers be accurate for a continuous beam? For example: the table states that 2.9x10^31 Joules are needed to reduce Terra to gravel (the desired effect of the planet cracker). Is this energy delivered all at once? Or does the sum total of the energy imparted have to be equal to that?
That's the energy needed to overcome the gravitational binding energy of the planet. It does not matter how it is delivered, so long as there is not time for a significant amount to radiate away into space. Considering as it takes a full day or so for the sun to radiate away that much energy, and the sun has a much larger surface to radiate from than the earth (by four orders of magnitude), you should be fine if your planet killer takes less than a few decades to deliver its energy.

Luke

Edges 08-06-2010 03:19 PM
Re: Planet cracker
 
Quote:
Originally Posted by MattStriker (Post 1028169)
Hmm. Does your calculation use the whole mass, or just half of it? The way the planetkiller works in-universe is that it produces an even mix of matter and anti-matter from the converted mass...
Yeah, that's for equal matter/anti-matter. I should have made that clearer. Actually, using the value for reducing the earth to an asteroid belt in Luke's handy-dandy table, and assuming a core density of 12.8g/cm^3, you need a sphere of 1/2 matter, 1/2 anti-matter around 3.65 km in diameter exploding at the core.

sir_pudding 08-06-2010 03:36 PM
Re: Planet cracker
 
Quote:
Originally Posted by lwcamp (Post 1028259)
That's the energy needed to overcome the gravitational binding energy of the planet.
Why use gravitational binding energy as the threshold? A planet is "killed" for all strategic intents and purposes long before it is rubble. How much to just render the surface unusable for geologically meaningful timespans?

hcobb 08-06-2010 03:42 PM
Re: Planet cracker
 
Why not just put the planet in an antigrav field? Without its self gravitation, Earth will blow up quite nicely.

Fred Brackin 08-06-2010 04:32 PM
Re: Planet cracker
 
Quote:
Originally Posted by sir_pudding (Post 1028404)
Why use gravitational binding energy as the threshold? A planet is "killed" for all strategic intents and purposes long before it is rubble. How much to just render the surface unusable for geologically meaningful timespans?
That's a lower energy but more complex situation and quite a bit more difficult to calculate.

However, it you take that figure of the Earth having c.200,000,000 square miles of surface area and figure that about one megaton of nuclear explosion will totally sterilize one square mile of surface area then 200,000,000 megatons will scrub the Earth's surface.

This is a _very_ fuzzy estimate but the c. 10, kiloton blast at the Trinity test site has had relatively little long term effect. They give tours of the place. About the only thing they tell you not to do is pick up and carry away the few bits of radioactive glass still left. Partly this is because so much of it already has been carried off.

This is for direct effect of course. You might be able to get by with less energy if you're going to trigger a runaway greenhouse effect or something similar.

On the other hand, actually breaking up the entire crust of the Earth is going to take a good bit more energy.

lwcamp 08-06-2010 08:36 PM
Re: Planet cracker
 
Quote:
Originally Posted by sir_pudding (Post 1028404)
Why use gravitational binding energy as the threshold? A planet is "killed" for all strategic intents and purposes long before it is rubble. How much to just render the surface unusable for geologically meaningful timespans?
Going from Atomic Rocket's boom table again
http://www.projectrho.com/rocket/rocket3x1.html#boom

3.2E26 J: Energy required blow off Earth's atmosphere
6.6E26 J: Energy required to heat all of Earth's oceans to boiling
4.5E27 J: Energy required to vaporize all of Earth's oceans
2.9E28 J: Energy required to melt Earth's crust
1.0E29 J: Energy required blow off Earth's oceans
1.5E30 J: Energy required blow off Earth's crust

Luke


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