Re: Responses on Asteroid Problem

[Michael Bowen <fizzbowen@MINDSPRING.COM>]

At 22:21 2001/08/26, Ludwik Kowalski wrote:
> <snip>
>
> How does this compare with nuclear energy released in an
> explosion of a "1000 megaton" of nuclear weapon. The
> megaton refers to TNT. Let me assume that the "heat of
> combustion" of TNT is the same as for gasoline (~50 kJ/kg
> = 5*10^4 kJ/ton = 5*10^10 joules/megaton = 5*10^13 joules
> per bomb.) The number of such bombs needed would be
> 2*10^25/(5*10^13) or 400 billion.

Although not in the true spirit of Fermi, one can find
[http://www.physics.usyd.edu.au/teach_res/db/d0005d.htm] that the heat of
combustion for TNT is ~5000 kJ/kg. (Interestingly, this is an order of
magnitude /less/ than the corresponding values for equal masses of simple
alkanes, e.g. methane or propane; kg for kg, even dung beats TNT by a
factor of more than 3. Is it the speed of the reaction, rather than the net
delta-Q, that counts? Or perhaps the molar heat?)

This cuts the number of bombs needed in Ludwig's estimate by a factor of 100.

[Ludwig, I suspect that you meant to guess 50 MJ/kg for gasoline.]  :-)

Also, 10^20 kg is a pretty hefty (although not inconceivable) asteroid; if
made of water ice and trace metallic impurities, this implies a volume of
10^20 liters or 10^17 m^3, and thus a radius (if spherical) of about 300
km, which is comparable to the sizes of the largest observed asteroids.
There are only a few of these known in the entire solar system. A more
common but still respectable chunk (say, the size of Eros) would cut the
radius by 10 and the mass, energy, momentum, and bomb count by an
additional factor of 10^3; I think that with these modifications we're now
down to "only" 4 million bombs.

I think the needed angle of deflection is also less than 1/100 radian. To
avoid a direct impact, one need only change the impact location by about
than 10^4 km (less, actually, but let's build in a safety factor; we don't
want it exploding in the atmosphere during a near miss, a la Tunguska).
This is less than 10^-4 AU. From a distance of 100 AU, I think this makes
the necessary deflection angle about a microradian. This is optimistic,
however, as astronomers are unlikely to spot an object of asteroid size at
100 AU; it's simply too dim and far away.

Here's another question that I haven't calculated yet, but that might be
interesting: For a water-ice "asteroid" (probably "comet" would be a better
description), how much heat would it take to simply boil the thing away
into space, and how would that compare with the energy required to deflect
it? One wouldn't have to heat it to 373 K; once liquefied, the surface
should boil off readily into the surrounding vacuum, although one would
have to supply at least the heats of fusion and vaporization, the latter of
which is still substantial. Could a fleet of small, warm, radioactive
robots "swim" through (or over) the ice to accomplish this, and could such
a fleet be safely recalled or otherwise disposed of (e.g., sent into the
sun) after its work was finished?

--MB