Meteoroid Deceleration Calc'ns Real World Problem

[Mstreman]

Homework Statement

NOTE: First time user. I am a member of an Ad Hoc fireball analysis group and my physics colleague is on travel. We have investigators in the field and therefore need to expedite an estimate. My background is geology and chemistry and I get "brain freeze" reasoning through applied physics and math.

PROBLEM:We need an estimate of the elapsed time and distance for supersonic "dark flight" of a meteoroid/fireball. This is not homework but a real world case ongoing now I need assistance with. The values you generate will be applied to ground witness reports to estimate the ground track of this fireball. I am also open to any other parameters one can estimate about this event. We are still working on angles of decent/points on the trajectory from two photo observations. Working backwards with sonic boom arrivals we might be able to estimate heights above the ground for phases of this event. A generalized curve for trajectory would also assist in plotting the ground track. Any assistance anyone can offer either here or off forum would be a valuable contribution.

BACKGROUND and VALUES: A entering meteoroid(future meteorite) begins incandescent flight around 140-120 miles above the ground where compression heating begins to fuse the surface producing plasma, generally referred to as incandescent flight. The cosmic velocity ranges in value but is initially 30-40,000 mph but not necessary for these calculations. Some point usually below 20miles but not below 5 miles above the ground, the meteoroid ceases to emit light (extinction) as its velocity falls below approximately 4000mph or 1,788.889m/s (called the Retardation Point) It then enters a phase called "dark flight" continuing to produce a a sonic boom until the velocity falls below approximately 340.29 m/s. At some point below supper-sonic flight, all cosmic velocity is depleted and acceleration under normal gravity takes over.(9.80665 m/s²)

Homework Equations

I am too sleepless and too many years from college physics to think clearly. Assume a drag coefficient of either a sphere .47 or angled cube .80. Mass unknown but model a single mass at extinction point of 5kg, 20kg, and 50kg. If necessary assume average ambient air Temp of 18C( Speed of sound 341.97m/s) The true trajectory will be a curve but for simplicity assume a line slope of 65 degrees if need be.

The Attempt at a Solution

I do not have skill currency to solve this myself nor have I been able to formulate the approach to a solution of time and distance between start of dark flight and end of supersonic flight. I have a general understanding of theory and components but not the math skills. Again this is not a homework problem but this seemed the obvious place for newbies.
Guidance is most welcomed. Time-- in this situation-- really is "of the essence".

Eman

 

[Mstreman]

Additional values:
Stoney-iron meteorites have a density of 4.3-5.8 g/cm3;
iron nickel meteorites density is 7-8 g/cm3.
Stone meteorites , have mass density range of 2.2 and 3.8 g/cm3

Assume a stone meteorite with a density of 3g/cm3

5kg will be 14.7 or15 cm in diameter
20kg yields a 23.3 or 23cm diameter
50kg yields 31.7 or 32cm diameter

I believe I am trying to solve for a negative acceleration value without knowing the Deltas of time or distance. I believe I need a formula that gives me a value produced by drag on an object of x diameter through an average else changing atmospheric density. So now to locate a standardized pressure gradient of an air column surface to 50km. What values do I need to find to determine deceleration owing to drag of an object passing through the atmosphere? Maybe it will start to come back to me and I'll have a solution before noon.

 

[George Jones]

Try this guy,

http://people.stu.ca/~jamesw/.