[meteorite-list] meteoroid temperature-Assumptions(P. III)

[MexicoDoug at aol.com]

Part III  

So the directional answer is best gotten to by a  bunch of assumptions and 
simplifications, including that the thing is rotating  on a nice skewer and 
isn't too big so that depth becomes an issue, which adds  some calculus for all 
those onion rinds.  So sticking to something say a  couple of meters in 
diameter... Otherwise we deal with things like what is the  temperature of Mercury 
(Solar side, mass, backside, transition zone, latitude,  rotation, greenhouse 
effect if any, and composition which will affect what  radiation can be absorbed 
and converted into heat.  A simple way to think  about the latter is thinking 
about a microwave oven.  If the object to be  heated is made with lots of 
water, it has a strong absorbance in that range, but  the glass door doesn't (even 
on the inside).  So a Tektite sent in orbit  very well could have a lower 
temperature than a cometary water containing  carbonaceous type body which in 
turn creates nice effects in part due to these  warmings in the estelas.  An 
example like Mercury, of one not rotating with  respect to the Sun causes other 
complications.  So best to think of an ant  in a spacesuit when asking your 
question.  The center of the meteoroid will  be cooler at its equilibrium 
temperature so wherever the ant walks or burrows  will depend on the temperature.  
Average temperature is a much easier  proposition, but knowing that wouldn't help 
the ant's survival chances at all if  he ends up in the Ant:-)arctic vs. 
Sahara of the meteoroid.

If one  assumes that a meteoroid has no greenhouse effect and is made of 
stone or  iron-nickel, and absorbs typically a full spectrum in the range of what 
the sun  mainly radiates for heating i.e. UV-Visible light, lots of 
simplifying  assumptions can be made.  You can look at Venus and see what a Greenhouse  
effect does, or even Jupiter, which I suspect is somehat warmer still than the 
 NASA page reference I used, because it actually puts out more energy than it 
 received that little stunted star...or figure out at what distance comets 
get  tails (snowball's sublimation temperature).  You get the idea:)

The  basics would include the following, I would think, calling the meteoroid 
shape a  sphere for simplification, which of course is not true but good 
enough, also  that the Sun is like a Black Body at 5800 degrees K from Wein's  Law.

Taken together with the idea that radiation from any source drops  off as the 
square of the distance from the source. (Which is understandable by  knowing 
that the surface area of a sphere, ie, non-directional emmiting source,  
4*Pi*r^2 increases by the square of the radius.), you can get a handle on  
temperature caused by the Sun on objects floating in the Solar System.  And  in the 
case of the meteroid, we only get a quarter of the total area exposed to  the 
Sun in the simplified case of a spherical meteoroid (area sphere = 4*pi*r^2  vs. 
great circle exposed = pi*r^2, a factor of 1/4).

Using the two laws  in a numer of ways, but sparing the the tedious math, the 
Sun's photosphere  ("surface") clocks at near 5800 degrees K being basically 
a heat source  (150,000,000 km from earth minus Sun's radius, aww lets just 
say the center of  the Sun since we can then measure in AU and are not dealing 
generally with the  inner Solar System to make a huge difference with the Sun's 
700,000 km or so  radius.  Using the inverse square law then you get the 
energies in my table  I gave you.

Then, I derived the temperature in the above table (all in an  excel 
spreadsheet) using the Stephan-Boltzmann Law, for you with this exact  formula:
T = [R/sigma*(a/e)*(areacrosssec/areatot)*(1/R^2)]^(1/4)
and  substituded the differewnt absorptivities and emissivities...presto, a 
solar  meteorite thermometer.  You can graph them too and it is easy to look 
at,  but I couldn't figure out how to graph in plain text for the list:)
Saludos,  Doug
Wheeew!  I think I'll take some time off the list and build some solar  
collectors and spacecraft housings for my old Chevy now.  On second  thought, maybe 
I'll just change the oil, if I get a chance...Acadamian  Bah:(