[extropy-chat] SURVIVAL: When asteroids or comets strike
spike66 at comcast.net
Sat Apr 10 18:33:04 UTC 2004
> Mike Lorrey
> SURVIVAL: When asteroids or comets strike
> Question: If an asteroid is spinning, would its angular momentum be
> translated into explosive energy upon impact? If so, how much
> would a 3 km body tumbling at 1 rotation/10 minutes add to the impact
> from its rotation? Mike Lorrey
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.
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