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

From: MexicoDoug_at_aol.com <MexicoDoug_at_meteoritecentral.com>
Date: Fri Jan 7 05:36:24 2005
Message-ID: <145.3ca1c636.2f0fc021_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:(
Received on Fri 07 Jan 2005 05:36:17 AM PST