From: nolan@lpl.arizona.edu (Mike Nolan)
Newsgroups: sci.astro
Subject: Re: Toutatis Captured by Radar Images
Date: 24 Jan 93 20:50:41 GMT
Organization: Lunar & Planetary Laboratory, Tucson AZ.

In article <schumach.727766698@convex.convex.com> schumach@convex.com (Richard A. Schumacher) writes:
> [Tom van Flandern writes:]
>>what it tells us about origins.  The rms velocity between any two asteroids
>>is about 5 km/s -- somewhat more near the Earth's orbit.  Collisions
>>between such objects would be catastrophically destructive.  So the joined
>>fragments must have been previously in orbit as satellites of the asteroid,
>>brought down gradually by tidal forces until a gentle contact occurred.
>
>Mmmm, not necessarily. A small body striking a larger one might easily 
>disrupt the larger without dispersing the pieces. No doubt someone has
>already attempted to calculate a distribution of such collisions based
>on the known distribution of asteroid sizes and orbits.

In fact, most models of asteroid collisions predict quite low
velocities for the majority of the ejecta: in a 5 km/s collision, the
projectile (smaller asteroid) tends to vaporize itself and nearby parts
of the target, which then leave at about the speed of sound.  The rest
of the target may fracture and be bumped around, but the ejection
velocities tend to be < 100 m/s, with much material (most, if the
target is not completely destroyed) moving less than 10 m/s.  In our
model, the smallest material tends to move the fastest, which makes
some intuitive sense by equipartition of energy.  This makes little
pieces fly off and the big lumps tend to fall back together.  This was
for models, though.  There are data, such as the existance of families
of asteroids with relative velocities a few hundred m/s, which suggest
that the actual behavior is not as the models predict.  It's by no
means a solved problem (it better not be, it's much of my thesis).  But
no matter what speed the bits leave at, it's still hard to get them in
orbit.  If they're moving at less than escape velocity, they'll likely
fall back, faster and they just leave.  The injection burn is hard to
come by.

Using Toutatis as an example, the escape velocity is about 2 m/s
(depends where on the surface you're standing), that's equivalent to
(scribble scribble) about a 8 inch (sorry people in the real world)
vertical jump on Earth, so be careful, even I can do that.  To get into
orbit, you need to be moving about that speed, then get apply a
tangential force to put you in orbit.  I won't say it's impossible, but
it's a small window.

As far as detecting them by radar, while the resolution may be 100 m,
the objects don't have to be that big to be detected.  They do have to
be about as big as the radar wavelength, 10 cm or so (they used
several).  They may (probably) have to be larger than that to give a
detectable signal.  On the other hand, satellites more that one
diameter away might be harder to detect if they're not specifically
looking for them, because of the way radar works: you shine the light
for a bit, then shut up and listen.  If the echo comes back before or
after you listen, you don't detect it.  Similarly if the velocity is
different than you're looking for: out-of-band signals are filtered
out, as they are presumably noise.  I don't actually know what the
limits are on this.

Mike Nolan nolan@{lpl.arizona.edu,arizona.bitnet,looney.span}
Lunar and Planetary Laboratory, University of Arizona, Tucson AZ 85721 USA
Phone (602) 621 2344; Fax (602) 621 4933
Newsgroups: sci.astro