[extropy-chat] SURVIVAL: When asteroids or comets strike
dgc at cox.net
Sat Apr 10 20:50:36 UTC 2004
>Back of the envelope calc, one significant digit:
>3 km diameter, roughly spherical, assume a density
>of about 3g/cm^3, 3000 kg/m^3, mass ~ 3000*4*1500^3 ~ 4e13 kg,
>impact velocity from outside the gravity well ~ 1e4 m/sec,
>rotation omega ~ 6 radians / 600 sec = .01 rad/sec,
>rotational energy ~ .5*.01^2*.4*1500^2*4E13 ~ 2E15,
>kinetic energy ~ .5*4e13*1e4^2 ~ 2e21
>so the rotational energy in the scenario you describe
>carries about one millionth the kinetic energy at impact.
>But notice that the kinetic energy scales as the cube
>of the radius whereas the rotational energy scales as
>the fifth power, so if you were to bump up the radius
>by 1000 times, keeping the rotation rate and density
>constant, the rotational energy is nearly the same as
>the kinetic energy.
>Mike you saw how I did that. Spin up your own spreadsheet.
>moment of inertia of a sphere is 2/5mr^2 and rotational
>energy is 1/2*I*omega^2 and you know the rest.
However, you may want to consider how you are going to keep your
spinning body from tearing
itself apart. For example, you can make it from Kevlar threads.
Basically, you are attempting
to increase the total energy of the systems, so you need to maximize the
energy storage per
mass. rotational energy is basically stored in the stress on the
material. I suspect that
your best bet to increase the additional energy per mass is E=MC^2.
total energy would then
be 1/2MV^2+MC^2. OF course, If you can find some antimatter, you can do
this, since the normal-matter target would contribute half the mass to
the non-kinetic term.
For standard materials, I think you are better off adding energy by
asteroid to a higher velocity rather than spinning it. Your "gun" must
add the same amount
of energy either way.
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