[meteorite-list] Physics Questions (Having to Do, Theoretically, with Bolide Trajectories)

[Chris Peterson]

How objects move when they are in some sort of fluid medium (such as an 
atmosphere) depends on the forces acting on them. A falling body in the 
atmosphere has two forces acting upon it, one directed downwards (the 
force created by gravity, and equal to the mass of the object times the 
local acceleration of gravity), and one directed upwards (the force 
created by air drag). How the body behaves depends on the drag force, 
which is proportional to the product of the coefficient of drag, the 
square of the body's aerodynamic cross section, the density of the air, 
and the square of the velocity. The cross section and the coefficient of 
drag are related to the size and shape of the body. Mass is not part of 
determining the force of drag, and therefore density isn't, either. 
However, if there are unbalanced forces (because the body hasn't reached 
its terminal velocity) there will be an acceleration that is dependent 
on mass (A = F / m , per Newton's Second Law).

The situation with a meteor is different, since we can essentially 
ignore the force of gravity. The meteor has only a single significant 
force acting on it, drag. Its behavior can theoretically be understood 
by considering its mass and the force of drag (since this involves mass, 
size, and shape, density is a factor). In practice, we seldom have an 
accurate value for the cross section or drag coefficient, so there's 
necessarily some guessing involved.

When a meteor produces meteorites, the surviving fragments rapidly lose 
their forward momentum. Meteorites always fall vertically (with respect 
to the local wind). The spatial spread of meteorites by mass occurs 
while the body fragments are still in hypersonic or supersonic flight, 
before they've lost their forward momentum and entered the long, 
vertical dark flight. More massive fragments continue farther because 
the mass increases as the square of the cross section, but the 
deceleration is inversely proportional to the mass. What that means is 
that the effect of mass (in A = F / m) dominates the effect of the cross 
section in the formula for F. A much more massive body may only have a 
slightly larger aerodynamic cross section.

Once the bodies are simply falling, they end up at individual terminal 
velocities depending on their sizes, shapes, and masses. For several 
minutes they are acted upon by the wind, which can significantly distort 
the shape of the strewn field with respect to the original path of the 
meteor, since the smaller, less massive bodies are moved more than the 
larger, more massive ones. Indeed, with a stiff tailwind, a strewn field 
can be completely reversed, with the heavy components farther back along 
the meteor path than the light ones- not because they started that way, 
but because they were blown that way.

Chris

*******************************
Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On 3/6/2013 2:37 PM, Peter Richards wrote:
>         To preface this, I'll let you know: I have dealt with some
> persons who such questions have been, rather, "over the head of," (pun
> not intended)... one of whom seemed to settle on the theory that I
> must be hurting my brain with too much thinking, and another who was
> satisfied with a conclusion to a variation of the forthcoming problem
> based on the idea that sand blows to the northeast U.S. from the
> "midwest" region, while larger stones do not (not that these persons
> are professional physicists, thankfully). Maybe this would be better
> directed at a physicist, but since I am dealing with something which
> pertains to meteorites, and certain specific falls, I will submit this
> for consideration by the members of this list:
>        On earth, acceleration of a suspended, then falling, or dropped,
> object, such as from a standstill, is determined by the mass of the
> object in a positive respect and the factor of air resistance in a
> negative respect; hence, a denser material of the same shape and
> orientation falls faster. This is because, here on earth, we have both
> an atmosphere, and a specific directional pull of gravity. I've read
> that, on the moon, where resistance of the atmosphere is negligible,
> if not absolutely nil, two objects of unlike densities will be pulled
> downwards at an equal rate (they say, even an elephant and feather
> will be pulled downward at the same rate, only being resisted by
> gravitational pull from other objects in the universe, I figure). If
> those observations are correct (and I'm not entirely sure they,
> although, it seems as if they very well may be, to me), then we've
> identified two situations, 1. one in which mass and density with
> relation to shape/and orientation does matter, but sum shape/volume
> (short for what determines air resistance) does not, for if an object
> is twice the size of the other, although not twice as dense, but an
> equal density, and shape, and orientation, it will fall at the same
> rate, because the ratio between its own mass and air-displacing
> profile is equal (I am not saying this law is universal, at all
> scales, but for practical purposes maybe it is?), and 2. another, in
> which, shape and orientation don't matter, and nor does the mass, or
> the density .
>       So, finally, my question is this: Do we have a third situation in
> which mass and density has a negligible effect, but air resistance due
> to shape and orientation does (That is to say, compensating for
> gravitational pull correlating to mass, or in a vector in which this
> is negated, the objects would encounter particles travelling at
> them.)? Again, it's somewhat difficult to imagine, but if there were
> such a scenario, would a large heavy object, NOT be held more still
> than a proportionally lighter and smaller object, but RATHER less so?
> Hence, for a fourth time, would higher inertia be totally detached
> from correlating to higher mass, thus correlating only with lower air
> resistance, ie better aerodynamics?
>       One might think that a bolide does not fit these criteria (or
> support this thesis), since the larger, generally less aerodynamic
> pieces tend to travel farthest, but is this not a result of these
> particles having been subject to less air resistance, in sum, than the
> smaller particles, which had broken from the outer surfaces of these
> very objects, due to the very momentum the "main masses" carried, in
> effect, absorbing the shock for them, somewhat (meaning they it is not
> for lack of momentum, due to lower mass, that they end up travelling
> less far)?
>
> (a question of) Peter Richards