INTRODUCTION
Meteoroids that are very large will produce a fireball in their passage through the atmosphere. They have sufficient mass to burn off in the ablation process and still survive, although in extremely diminished form, to deposit themselves as meteorites on the Earth's surface.
At the opposite end of the mass spectrum, is a meteoroidal body is small enough that it too will survive the process of atmospheric deceleration and will eventually filter down into the lower atmosphere as a small dust particle.
THE PROCESS
The reason why a very small body is able to survive atmospheric entry is not difficult to appreciate. The energy which goes into heating the meteoroid comes from a conversion of the kinetic energy that the body initially possesses by virtue of its high velocity. The atmospheric deceleration process is the means by which the conversion occurs. Now the kinetic energy of a body is directly proportional to the mass of a body which is in turn proportional to the cube of the body's radius. Thus the maximum heat input to the body is also proportional to the radius cubed. In contrast to this the loss of heat from the body occurs principally by radiation from the surface, and this in turn is proportional to the surface area which in turn is proportional to the square of the radius.
As we consider bodies of smaller radius , the cubed term representing the heat input decreases faster than the squared term representing heat loss. In other words, a micrometeorite has a larger surface area per unit mass than a heavier meteoroid, and thus is able to radiate away its acquired heat more affectively.
As long as the net heat gained by the body does not cause a rise in temperature above the vapourisation point of the constituent material the body is termed a micrometeorite - it will eventually fall down through the atmosphere as a minute dust particle.
There is a heat regime wherein the particle temperature may be below the vapourisation point but above the melting point. In this case the micrometeoroid will melt and form into a tiny spherule. Many such spherules have been recovered from around the Earth and at the bottom of its oceans.
The maximum diameter of a micrometeorite is a function of its density and its initial velocity. Typical values, in microns or millionths of a metre are shown in the table below.
The above discussion assumes that all the heat input to the body is conducted throughout the particle vary quickly. This is not necessarily the case, particularly when it is realised that the deceleration of a meteoroid in the atmosphere depends upon the ratio of its cross-sectional area to mass. That is, the deceleration is inversely proportional to particle diameter, and thus small objects undergo a severe deceleration. Alternatively the smaller the object the shorter will be its 'stopping time', and the less time will the heat have to diffuse fully throughout the body. This factor works to the advantage of the micrometeorite in helping keep down its internal temperature.
ZODIACAL LIGHT
Micrometeoroids are extremely numerous throughout the inner solar system and contribute by far the largest mass influx of all the natural space debris that the Earth sweeps up in its course around the Sun. The daily mass of micrometeorites falling into the Earth is estimated as being somewhere between 1,000 and 10,000 tons.
Indirect evidence of the massive dust cloud that exists in interplanetary space can be seen in the phenomena known as zodiacal light and the less well known gegenschein. Zodiacal light is a faint diffuse glow of light that may be seen from dark moonless sites with clear skies just after evening twilight and just before morning twilight. It is most visible in the tropics where twilight is short, and it appears as a nebulous cone of light extending from the horizon at its widest , centered about the ecliptic, to anywhere from 45 to 60 degrees above the horizon at its apex.
This zodiacal light is a faint reflection or scattering of sunlight off innumerable dust grains that are concentrated in the ecliptic plane.
Much more difficult to observe is the vary faint patch of light seen in the night sky (around midnight) at a point directly opposite where the Sun lies (the antisolar point), and called gegenschein. Zodiacal light is due to the forward scattering of sunlight from particles between the Sun and the Earth's orbit. Gegenshein is due to the backscattering of sunlight off dust particles outside the Earth's orbit.
A micrometeorite, in its passage through the upper atmosphere, does not reach a very high temperature and therefore produces no light by which its entry may be detected. It also produces very little ionisation and therefore cannot be detected by radar. Quite different methods than those used to detect meteors must be employed to gather information on the micrometeorite population. Indirect methods employ the scattering of light (eg zodiacal light)to determine the size and distribution of the dust particles existing in interplanetary space. However various interfering effects due to viewing through the atmosphere makes ground observations of this type very difficult. Similar observations from space are proving more useful.
Small particle (micrometeoroid) detectors have been flown on many satellites right from their inception to the present day, The results from these soundings are extremely important and in fact constitute our entire data set of small particle distribution beyond the orbit of the Earth.
Direct methods of learning about micrometeorites employ particle recovery techniques. These have been carried out in many places from the deep ocean floor right up to the ionosphere. Sticky plates have been exposed in supposedly 'clean' sites such as the tops of mountains far removed from industrial areas. Such plates do indeed collect many small particles but it is very difficult to avoid terrestrial contamination. Even in the absence of modern industrial fallout there has always been volcanic ash which, once it has reached the stratosphere will remain suspended for years, drifting slowly down again over the whole globe, although there is a bias toward the hemisphere of origin as transequatorial dust transport is limited. Collection of aerosols from high-flying aircraft also suffers from a similar problem of terrestrial contamination.
Sounding rockets have carried micrometeorite collection boxes through the deceleration altitudes of those particles, only exposing the boxes once an altitude of 80 km has been reached and closing them up again before descent through the contaminated lower atmosphere. One early experiment of this type was very descriptively titled the "Venus Flytrap" and was flown from White Sands in New Mexico in 1961.
Terrestrial contamination of this type of experiment is believed to be very small because of the high altitudes involved. When the contents of such collections are examined with an electron microscope under high magnification three main types of particles, believed to be of extraterrestrial origin, have been found. These types are:
These types agree quite nicely with our theories of meteoroid origin and with our ideas on spherule formation from deceleration temperatures just above melting point.
Not all collected micrometeorites necessarily have their origin as micron or sub-micron sized parent bodies. Some may have fragmented from a larger meteoroid before it became totally vapourised, and we then refer to these as secondary micrometeorites.
Although the high altitude rocket collection experiments provide the greatest unambiguous information on micrometeorite morphology, two other collection methods deserve mention. One is the occurrence of small particles found in deep-sea sediments. These are found either as black magnetic spherules rich in magnesium or nickel-iron alloy specimens. It is basically from a measurement of the concentration of these particles that a first estimate of several thousand tons for the daily influx of micrometeorites was made.
The second group of collection experiments worthy of note are those performed by examination of snow or ice core samples taken from the Antarctic continent. This work began during the International Geophysical Year (IGY 1957-8) and was supported heavily by the US Space Agency NASA. The most abundant spherules found in these ice samples was black metallic bodies of magnetite, and yellow translucent glassy spheres. Further work on ice core samples has been concerned with examining the relative concentrations of these particles with depth below the surface to throw light on how the micrometeorite influx has changed with time.
The images below show the collection of a metallic spherule from a dust collector set up at the Australian Space Academy site at Meckering. The collector (left) is a plastic tub raised above the ground to minimise the collection of local dust particles. The exit/collection device from the tub has a very fine filter. The allows water through but not dust particles. After six months the collector was removed and processed to look for metallic spherules one of which is shown in the micrograph to the right. It can be seen that it has a diameter of ~ 10 microns (0.01 mm - the thickness of the vertical lines).
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INTERPLANETARY DUST
The large cloud of dust in interplanetary space that provides our source of micrometeorites is a dynamic cloud. With a density of around 10-18 kg m-3 (or about 250 dust particles in each cubic kilometre of space) this cloud is constantly changing, losing some members and gaining some new members through the many forces acting in this arena. The forces that replenish the cloud include collisional encounters between larger bodies, grinding off small pieces, and repeated heat cycling of larger rotating meteoroids. Sputtering of small particles by the solar wind (a stream of atomic particles constantly flowing out from the Sun) will reduce their size even further. Evaporation of dust and gas from comets during perihelion passage is probably a major source of raw material. On the other hand, gravitational perturbations of the particle orbits by the planets, in the extreme, send the particles into the Sun or out of the solar system. The planets themselves will also sweep up and remove many particles as they travel around their orbits.
For interplanetary dust particles (IDP) smaller than 0.1 microns the actual pressure of sunlight on the particle is thought to be sufficient to drive the particle out of the solar system.
Another removal mechanism is the Poynting-Robertson effect. This is an effect whereby small bodies experience a drag force which causes them to spiral inward toward the Sun. This effect may be understood in a simplified form by reference to the diagram below.
In the same way that a car driver, driving through a vertical rain shower, sees the raindrops slanting toward his windshield, so a body in orbit around the Sun sees the photons of light approach from a slight forward angle. This causes a drag force to act on the body which will slowly spiral the particle toward the Sun. The exact effect involves an application of Einstein's theory of relativity and considers the total energy balance of the micrometeoroid, but the net result is the drag force described above.
Calculations have found that for meteoroids with a radius of less than 10 cm, the Poynting-Robertson effect will remove them from interplanetary space into the Sun in less than the presently accepted age of the solar system. The smaller the particle, the shorter the removal time. A 10 micron particle may be cleared in less than 10,000 years. On the other hand, particles less than 0.1 micron will tend to be blown the other way by solar radiation pressure.
Such an efficient clearing method (astronomically speaking) has had many physicists and astronomers worried, as the replenishment methods do not appear to be able to keep pace with the attrition rate. It thus becomes a concern to ask from where do all these dust particle arise?
Fundamental physical laws combined with a few simplifying assumptions
enable us to make an order of magnitude estimate for the maximum size of a micrometeoroid - the size above which the object completely vaporises in its passage through the Earth's atmosphere. The basic consideration is one of energy transfer. The net energy transferred to the particle must be sufficiently at a sufficiently low rate that its temperature does not exceed the vaporisation temperature of the constituent material. Melting of the particle is probably tolerable although a change of form will certainly result, and if too large, the melt may disperse into several droplets.
The energy of motion (kinetic energy) inherent in a particle of mass m moving at a velocity v is 1/2 m v2. To obtain a rate of energy gain we need to know the particle deceleration time. This further requires knowledge of the stopping distance d. We make the simplifying assumption that the micrometeoroid will be brought to rest when it has traversed or encountered a column of air equal to its own mass. This is something that can be readily computed from a knowledge of the upper atmosphere density. In essence all the momentum of the micrometeoroid has been transferred to the column of air molecules.
Thus
The stopping time is then given by:
The rate at which energy is input to the surface of the particle is:
If the body is a perfect radiator (a 'black' body) it can dissipate this energy at a rate given by the Stefan-Boltzman law:
where
For a spherical particle of radius r, A = 4 π r2
and then equating Pin to Pout gives:
Now the mass of a sphere of density ρ is
This equation can then be written with particle size as the subject:
Note that this is an iterative equation because d must first be calculated from r [ d = 4 ρm r / ( 3 ρ ) ] and then used to find the next approximation to r and so on until convergence is reached.
The final figure below shows how the temperature of the body changes with both radius and velocity.
From this graph we can see that 10 microns is the critical size for
a micrometeorite. Low velocity bodies below this size will make it through intact. High velocity bodies will probably totally vapourise.
The melting point of iron alloys is generally above 2000C. The vapourisation temperature for iron is 2700C at sea-level pressure but may drop to 1000 C in the rarefied atmosphere at 100km. The melting point of stony meteorites is probably around that of basalts which are around 1000 C but vary widely.
THE LIMITING SIZE OF MICROMETEORITES
mair = mmmd or
where
mmmd = ρ π r2 d
ρ is the air density at the entry altitude
r is the radius of the particle and
d is the stopping distance
t = d / (v/2) = 2 d / v
Pin = m v2 / ( 2 t )
= m v3 / ( 4 d )
Pout = σ A T4
σ is the Stefan-Boltzmann constant ( 5.67 x 10-8 SI )
A is the surface area of the particle
T is the absolute temperature of the particle
m v3 ( 4 d ) = 4 π σ r2 T4
m = 4 π r3 ρm / 3
r = 12 d σ T4 / ( ρm v3)
Australian Space Academy