The Schpat Dope

Just like The Striaght Dope only not as well researched or funny

Saturday, September 03, 2005

Meteorite or Plane Poop?

Brendon askes

Dear Schpat,

I've been following a story on IOL about a meteorite that crashed in Zimbabwe. The thing is that from the story it seems that this might not be a meteorite, the first give-away was the 15cm crater. My question is: Was it really a meteorite?

Schpat replies

Hey Brandon, thanks for the question. It reminds me from that sceen from Joe Dirt

"Not that I'd ever sale ya meteor..not in a million years. But just fer kicks, let's see how much yer worth."

"That's not a meteor. That's a big pile of frozen shit!"

"What? N-no. That's a meteor. It fell from the sky."

"I'm sure it did, cause it fell from an airplane. See the peanut there?"

"Maybe it's space peanut. Yeah."

"Nope, that's a big ball of frozen poopy."

You might not have asked it, but I know you were thinking it, Is this a petrified ball of plane poop? But back to your question, first we need to examine the facts at our disposal. There original Zimbabwe Herald story appears here. From reading the story we note that the level of literacy for the average Zimbabwean Reporter is rather low and also a few things about the "meteorite". Here they are in no particular order:

It is black with white spots
It is 21cm long and 13cm wide
It Weighs 4.1kg
It sounded like a helicopter
the noise was followed by dust clouds
It hit the ground leaving a 15cm "crater"

From even this scant evidence SchpatDope can make an assessment as to whether or not this object was a meteorite. (I warn you brave readers this gets kinda mathsy, but don't worry you can probably skip those bits and go straight to the conclusions)

Test One: Appearance
Well, black with lighter pieces does fit one of the more likely general descriptions of a meteorite. As the article, so very painfully, points out meteorites can be made up of rocks with pieces of metal in them. These types of meteorites are called "chondrites", named for the small "chondrules" within them. These chondrules are actually not even metal at all but rather small, between 0.5mm and 2mm, silicate crystals, mostly iron, aluminium or magnesium silicates. But we can forgive our intrepid reporter for this small mistake.

Chrondrites make up between 65 and 85 percent of all meteorites to hit earth. So the fact that our test sample has the appearance of your average run of the mill space rock is a point in its favour.

Test Two: Density
Having already established that statistically if our test subject was a meteorite it would probably be a chondrite we can test the density to see if it falls within the range for chondrites, between 3.2 and 3.7. The formula to calculate density is:

p = m/v


m is mass in grams
v is volume in cm^3
p is density in^-3 or kg.m^-3

Well we know the mass so all we need now is the volume. Here come our first two assumptions, we have only been given measurements for two dimensions of a three dimensional object. We are going to assume that we were only given length and width because height is equal to width. Our second assumption is that this meteorite forms a vaguely ellipsoid shape so that we can use the formula for calculating its volume. The formula is:

(4/3) * (Pi) * a * b * c


a, b and c are the semi-axes in cm

that gives us:

(4/3) * (22/7) * 11.5 * 6.5 * 6.5 = 2.013cm^3

therefore the density would be 2.013^-3

This is a very low density for your average meteorite and therefore the meteorite would be underweight. The problem is that this test involved two rather large assumptions so it's inconclusive at best. We can however now say that assuming the object has a density that falls into the correct range we can calculate the unspecified height of the ellipsoid to be about 8cm. This will prove useful in our next test

Test Three: Impact Force
Yeah this is the thing that started me wondering whether or not this actually was a meteorite. I mean a 15cm crater for an object that fell from space, my ardent fandom of all things sci-fi just wouldn't let me believe this, surely these things involve explosions and cataclysmic events? The only way to find out is to do the math, the formula is:

F = m * a


F is force in Newtons
m is mass in kg
a is acceleration in m.s^-2

In our case we're trying to calculate the force required to decelerate (negative acceleration) the object to zero. The formula for acceleration is:

a = (v - u) / t


v is final velocity in m.s^-1
u is initial velocity in m.s^-1
t is time in seconds

Determining v and t are easy, the object would end up at rest so v is 0 and it all happens almost instantaneous so lets say 0.1 for t, one tenth of a second. u is a bit more difficult though. How fast was this thing going before it hit the ground? Sci-Fi would have us believe almost the speed of light, but I sense another formula on the way:

v(t) = Sqrt[( 2 * m * g ) / ( C(d) * p * A)]


v(t) is terminal velocity in m.s^-1
m is mass in kg
g is gravitational acceleration in m.s^-2
C(d) is the coefficient of drag
p is density of the fluid
A is objects cross-sectional area in m^2

Yup terminal velocity! it's a complex one.

For Cross-sectional area lets use the known width of 13cm and the hypothesised height of 8cm so A = Pi * 6.5 * 4 (I've assumed another elliptical shape here), that gives us 81.71cm^2. The object should fall so that there is least resistance and so this make sense.

m is 4.1, g is 9.8, C(d) is 0.5 (using the one for a sphere will be close enough), p for air at STP is 0.00129 (also close enough for our purposes) and A is 0.008171m^2

u = v(t) is Sqrt[( 2 * 4.1 * 9.8) / ( 0.5 * 0.00129 * 0.008171)] = 123.5 m.s^-1

"Wow!" you say, yes wow indeed that's not even half the speed of sound, let alone light! But you say: "it's still 445km.h^-1 and that's pretty damn fast and would definitely explode when it hit the ground, or at least leave an impact crater of like 15m. Yeah that's it, they must have meant 15m not 15cm!"

Well my friend you're starting to sound more like ol' Joe Dirt all the time. remember we haven't finished the math yet!

a = ( v - u ) / t

a = (0 - 123.5) / 0.1 = -1235m.s^-2


F = m * a

F = 4.1 * -1252 = -5065 N

"That's a lot!" you say. Well not really, it's about the same as my car (a ford sierra weighing in at 1600kg) hitting a concrete wall at 1.134k.h^-1 or 0.315m.s^-1. At that speed I doubt it would even break a light! You still don't believe me that the crater would be really small, check this out then. That's a 30cm ruler next to the actual crater made by a meteorite in Mbale (Uganda) in 1992. During the shower a young boy was actually hit on the head by a small fragment of the meteorite, and he lived. Admittedly the fragment was only 1cm in diameter and weighed 3g and its fall was broken by the banana tree the boy was sheltering under. You can check out the whole story here.

Also the fact that the people heard the sound before they saw the object in the sky also goes to prove it was travelling at subsonic speeds.

I'm going to give a partial positive result for test 3, as we had to work off an assumption about the height of the object.

Final Conclusion:
One positive, one partial positive and one inconclusive. The partial and inconclusive could quite easily be cleared up by finding the height measurement. On the face of this evidence I think that yes, this is in fact a meteorite, I'd probably bet on it.

One last thing however, it's not strictly scientific but that never really stopped us before. The reliability of the reporter, one Freeman Razemba, may be a little suspect. In January this year he reported a story about a local "traditional healer" who had surrendered his goblins to the tribal chief so that they could be destroyed. Apparently this "traditional healer" had been using the goblins' magical powers to have his way with women, sexually, without them knowing about it. However when the goblins started abusing his daughters he thought enough was enough! Read the whole article
here, and decide if you trust this guy!

Thanks for the great questions guys, but keep them rolling in. Mitsy and I are always on the lookout for interesting topics. Oh and join the SchpatDope mailing list.


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12:35 AM  
Blogger Synkronos said...

"Also the fact that the people heard the sound before they saw the object in the sky also goes to prove it was travelling at subsonic speeds."
Nope. That just goes to prove that they weren't looking in the right direction. Even at supersonic speeds, light still travels faster than the object in question. Unless it's travelling at c, but I fear that that might be another even more mathsy SchpatDope. What does indicate that it was moving at subsonic speeds is the fact that there was no sonic boom. And your calculations for v(t) look good too ;)

Force, however, is not what you're looking for. What you're looking for is Kinetic Energy (KE)
KE = 1/2(m * v^2)
= 1/2(4.1 * 123.5^2)
= 1/2(4.1 * 15252.25)
= 1/2(62534.225)
= 31267.1125 Joules
All of this energy would have been transferred to the ground, since the object was brought to rest. Time doesn't matter, and since we don't know it, that's a good thing.

On to your car example.
v = SQRT(2 * KE / m)
= SQRT(2 * 31267.1125 / 1600)
= SQRT(39.083...)
= 6.25171101579 m.s^-1
= 22.5... km.h^-1

That's slightly more likely to leave a dent. Not catastrophic, but certainly a worry to the passengers and the owner of the wall.

This site has a list of formulae for determining various things to do with an impact, including a formula for determining a rough estimate for the size of a crater. I don't have time to work through it now, I've already spent too much time finding it, but there you go =)

11:14 AM  
Blogger schpat said...

That's odd, referring to my notes I see that I did originally intend to do an Energy comparison, I even had a whole boat-load of comparisons from this web site to share with you. Unfortunately though working late at night I did get confused halfway through and stuck in the force stuff instead. After a long, and sometimes heated, conversation with the SchpatDope Advisory Board I do understand what my problem was. Energy and force are not the same thing, energy is force combined with distance. But the problem I had was that force is not constant over the time it takes to slow the object down and the distance is not necessarily the same, the KE = 1/2(m * v^2) formula takes the calculus into account. Mitsy says she could have told me that, she's busy doing it in high school physics, but the SchpatDope was written way after her bedtime! Next time I'll wait till morning and get her to have a read before posting.


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