Re: Meteoroid temperatures.
http://home1.gtedot net/res04m7h/temperature.html
Title: temperature
In outer space the sun tends to warm a meteoroid.
As the stony or iron body
heats it radiates energy to space from its surface
area Atotal. There are thus two
processes that come into equilibrium: absorption
of sunlight largely in the visible
part of the spectrum and emission of thermal energy
in the infrared portion of
the spectrum. We can treat this as a time-independent
equilibrium problem because
(1) we are considering small bodies that will rapidly
transport heat to all parts, and
(2) a meteoroid travels over a small fraction of its
Keplerian orbit during this time
thus the solar power that falls on a meteoroid changes
little in the time it takes to heat
or cool. The orbital speeds are in terms of
tens of kilometers per second. To travel a
distance of, for example, a million kilometers requires
at least several hours and
perhaps a day.
This is a greybody problem, not a blackbody problem.
Also we must pay attention to
the fact that the absorption and emission occur in
different bands of light. The respective coefficients for absorption a
and emission e vary by the type of meteorite
as well as
details of the spectrum.
The solar constant So is approximately 1350
Watts per square meter near the
Earth's orbital distance from the sun (1 Astronomical
Unit). In reality this
constant varies slightly with time, but that is not
important to our goal of
providing an estimate of a meteoroid's equilibrium
temperature Teq. The
solar power density is soaked-up by a cross-section
area Across of the meteoroid
facing the sun.
The power radiated is a sharp function of the temperature.
The Stefan-Boltzmann
constant s governs this
relationship.
The heat balance is:
Power in = Power out
which is given by:
a So Across = e s Teq4 Atotal
Rearranging:
Teq = { (a / e) (So / s) (Across / Atotal ) }0.25
A meteoroid can be modeled as a sphere. This
is generally an incorrect shape. A plate
is another extreme geometry, also not generally correct.
The formulae for the areas
of these cases in terms of diameter or width D are:
Sphere
Across = p
(D/2)2
Atotal
= 4 p (D/2)2
Plate
Across = (0 to 1) D2
Atotal
= 2 D2
The plate is not in general perfectly oriented toward
the sun, but is expected to
rotate slowly. I will model the space body as a sphere
with a ratio of areas equal to 1:4.
Inserting this gives the approximation:
Teq = 0.707 { (a / e) (So / s) }0.25 = 278 (a / e)0.25
This can be generalized to any location in the solar
system where meteoroids
are likely to be found by applying an inverse square
law as a function of distance
from the sun in A.U., RAU :
Teq = (278) {(a / e) (1 / RAU2 )}0.25 = [(278) (a / e)0.25 ] / (RAU)0.5
The most important thing to note is that near Earth
the temperature is, to a first
approximation, close to room temperature if the optical
absorption and thermal emission
properties are similar, as I will assume for a carbonaceous
meteorite.* Given that
meteorites are not identical, fifty degree variations
can be easily imagined
and even larger deviations may be found given a suitable
composition of a meteoroid.
For a light silicate meteorite I will use 0.67 for
the ratio of absorption and
emission coefficients.
The following table gives crude temperature estimates
for stone and iron
meteoroids,
respectively, as a function of which portion
of the solar system they are moving through.
I will treat iron meteoroids as having a thermal properties
ratio of about 3; i.e., at a given point in space the metal meteoroid will
be hotter than a light silicate by almost 50 percent. Ouch!
The following table includes approximate temperatures
for light silicate and carbonaceous
meteorites, respectively, and a simplified generic
iron choice. Particular meteorite
compositions may vary considerably from the estimates
of this table. Small iron meteorites
can be expected to cool quickly from their relatively
high temperatures near Earth when
they land.
| REGION OF SOLAR SYSTEM | STONY
METEORITE TEMP:
Light Silicate or Carbonaceous |
IRON METEORITE TEMP |
| MERCURY .39 AU | 130 C / 172 C | 312 C |
| VENUS .72 AU | 23 C / 56 C | 159 C |
| EARTH 1 AU | -21 C / 5 C | 93 C |
| MARS 1.52 AU | -69 C / -52 C | 23 C |
| ASTEROID BELT 2.8 AU | -123 C / -106 C | -53 C |
It is doubtful that any of our meteorites are from
the vicinity of Mercury but perhaps.
The extremely high temperatures near Mercury are striking,
as are the extremely
low temperatures in the asteroid belt and beyond.
Even near Earth it is seen
that some stony meteorites will have interiors below
the freezing point
of water.
The Monahans chondrite fell in Texas a few years ago.
It gained notoriety when
pockets of water were found in salt crystals.
This is the first time scientists have seen
concentrated water as opposed to waters of hydration
in a meteorite, which are
noted for example among the clays and such of carbonaceous
chondrites. Salt depresses
the freezing point, but only by a certain amount (i.e.,
a few tens of degrees below zero Celsius). From the table above it
is seen that this liquid water was frozen brine when the meteoroid was
farther out in the solar system; e.g., the natural state for the longest
time
was ice crystals. I feel that most of the meteorite
public is confused and believes
liquid water was sloshing around inside the parent
body these many past billion years.
Tsk, tsk, tsk.
* The temperature of the Earth's surface would actually be closer to
-25 C were it not for our
atmosphere. Go global warming, go!
CAVEATS!
No discussion of residual heat for large bodies or
time constants that govern
transport of heat through large bodies while transiting
the solar system
are considered here. Do not apply these temperature
estimates to the outer planets,
although they can give some crude estimates of inner
planet average temperatures
if the true albedo of the planet is used to estimate
the portion of solar spectrum
reflected, and the remainder that is absorbed (caution:
a planet is thick so it does
not transmit light through the solid part, although
limb effects of atmospheres
can be of interest to astronomers).
Earth's oceans and the atmospheres of the various planets
affect the albedo and
distribution of temperatures. Inclinations,
latitude, rotation, and orbital variations
also affect planetary surface temperature distributions.
Jupiter generates a lot of
internal heat that alters the balance equation presented
here, and can affect its moons
through tidal friction. The determination of
a planet's temperature variations is
much more complex than this simple model for small
meteoroids. Comets are also
more complicated objects than discussed in this section.
Such details as planet-shine on a meteoroid when it
approaches a major body on a
collision trajectory (e.g., about to become a meteorite
on Earth) are ignored.
An important question is whether it is reasonable to
assume that the bulk of a
meteorite is near its equilibrium temperature shortly
after it lands. Thus it will
be necessary to treat the time-dependent behavior
of meteorites next.
NEXT: METEOR HEATING