Re: Responses on Asteriod Problem

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

Bill Prescott wrote (in part):

> Getting back to the flywheel part of our question,
> do any of you have any thoughts on the practicality of
> building such a device as I described?  Do the numbers
> [mass, energy, diameter, spin speed] look right? And
> what would be the best material to deal with the stress
> forces?  Do you think the solar energy part of the solution
> seems reasonable and within today's technology?

Let me address a simple question using a specific numerical
example. I hope this will put Bill's question in the proper
numerical context. I will assume that the mass of the asteroid
is 10^20 kg while its velocity (at the distance of 100 a.u.=
1.5*10^13 m from the sun) is 10^5 m/s. In other words it
is about 5 years away from intercepting our orbit around
the sun at the very unfortunate time and place. How much
energy must be converted into kinetic energy to deflect
the asteroid?

In the spirit of Fermi method I will assume that solar system
is replaced by a massless imaginary wall perpendicular to
the trajectory of the asteroid. If nothing is done then the
wall is hit at a point P. We want the wall to be hit at a
point Q situated 1 A.U. away from the point P.

In other words we want to deflect the trajectory (assuming
it is done quickly) by an angle of 1/100 radians. This
implies that the asteroid must receive an additional
momentum (perpendicularly to its path) equal to 1% of its
momentum, or 0.01*10-^25 = 10^23 SI units.

An efficient way to accomplish this is to produce an
explosion in the center which breaks the asteroid into
two equal fragments ejected perpendicularly to the path.
The momentum of each fragment would have to be
0.5*10^23 SI units. (Do not ask me how to produce a
desired directionality of such event.) The kinetic energy
of each fragment (P^2/2*m) would be about 10^25 joules.
The kinetic energy of two fragments is would be about
2*10^25 joules.

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.

Note that 2*10^25 J is much larger than solar energy
intercepted by the asteroid in five years. The only
conceivable approach is to program robots to fabricate
a bomb from the material found in the asteroid.

In another message I wrote:

> > What if nuclear fusion is used as a source of power for
> > giant rocket engines placed on the asteroid (in order to
> > change its orbit)? The material (ice and rocks, but not
> > iron) from which the celestial object is made can, in
> principal, be used as fuel. Developing such engines,
> > and the technology for placing them effectively on
> > asteroids, may be a worthwhile "insurance policy."
Ludwik Kowalski