Re: Asteroid Problem

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

For quick calculations, it might be easier to look at slowing down or
speeding up the asteroid.  While it depends on the angle of crossing
relative to the earth's path, I get something like a two minute change in
arrival time as enough to allow the earth to clear the asteroid path.  This
is about a .0004% change (with 1 year lead time) which should require an
average speed change of less than 1 m/s (if the asteroid is moving at less
than a quarter-million meters/s).   Plug in the mass and at least you can
easily get the force/energy needed.

Rick

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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu

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----- Original Message -----
From: "Ludwik Kowalski" <kowalskiL@MAIL.MONTCLAIR.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, August 27, 2001 10:16 AM
Subject: Re: Asteroid Problem


> Thanks for constructive comments; I am not an astronomer.
> Was the assumed speed, 10^5 m/s, realistic? In any case, it
> would be useful to post an improved estimate of the amount
> of energy needed to deviate an asteroid. Some of us may
> like to present this problem to students but are not familiar
> with realistic parameters. Can you help us, Michael?
>
> Michael Bowen wrote (in part):
>
> > 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?