The Poynting-Robertson effect ( Robertson , 1937 ; ;
Wyatt and Whipple , 1950 ) , which is a retardation of the orbital motion of particles by the relativistic aberration of the repulsive force of the impinging solar radiation , causes the dust to spiral into the sun in times much shorter than the age of the Earth .
The radial velocity varies inversely as the particle size -- a 1000-m-diameter particle near the orbit of Mars would reach the sun in about 60 million years .
Whipple ( 1955 ) extends the effects to include the solar-corpuscular-radiation pressure , which increases both the minimum particle size and the drag .
Further , the corpuscular radiation , i.e. , the solar-wind protons , must sputter away the surface atoms of the dust and cause a slow diminution in size , with a resultant increase in both the Poynting-Robertson effect and the ratio of the repulsive force to the gravitational force .
The Poynting-Robertson effect causes the semi-major axis of orbits to diminish more rapidly than the semi-minor axis , with a consequent tendency toward circular orbits as the particles move toward the sun .
Also , planetary gravitational attraction increases the dust concentration near the plane of the ecliptic as the sun is approached .
At one astronomical unit from the sun ( the Earth's distance ) the dust orbits are probably nearly circular .
If such is the case , the particles within a distance of about Af of the Earth will have , relative to the Earth , a kinetic energy less than their potential energy and they will be captured into orbits about the Earth .
De Jager ( 1955 ) has calculated the times required for these particles to reach the atmosphere under the influence of the Poynting-Robertson effect , which in this case causes the orbits to become more and more eccentric without changing the semi-major axis .
This effect can give rise to a blanket of micrometeorites around the Earth .
Since there is a continual loss of micrometeoritic material in space because of the radiation effects , there must be a continual replenishment : otherwise , micrometeorites would have disappeared from interplanetary space .
There are several possible sources .
According to Whipple ( 1955 ) , cometary debris is sufficient to replenish the material spiraling into the sun , maintaining a fairly steady state .
Asteroidal collisions are also thought to contribute material .
It is also possible that some of the dust in the vicinity of the Earth originated from meteoritic impacts upon the moon .
5.3 direct measurements of micrometeorite flux
One cannot make a very satisfactory guess about the micrometeorite flux in space .
Even in the neighborhood of the Earth , where information has been obtained both directly and indirectly , the derived flux values vary by at least four orders of magnitude .
This large discrepancy demonstrates the inadequacies of the experimental methods and the lack of understanding of the various phenomena involved .
Beyond a few million kilometers from the Earth , but still in the region of the Earth's orbit , a prediction of the flux of dust is even more unreliable .
At greater distances from the sun , the situation is still less certain .
There are several sources of evidence on the micrometeorite environment .
Direct information has been obtained from rockets and satellites equipped with impact sensors .
In addition , the size distribution obtained from visual and radar observations of meteors may be extrapolated to the micrometeorite domain .
From the brightness of the F component of the solar corona and the brightness of the zodiacal light , an estimate of the particle sizes , concentrations , and spatial distribution can be derived for regions of space near the ecliptic plane .
Another important source of evidence only recently receiving much attention is the analysis of atmospheric dust for a meteoritic component .
The cores of deep-sea sediments and content of collectors in remote regions are valuable in this category .
The data provide a measure of the total mass of cosmic material incident upon the Earth .
The direct evidence on the micrometeorite environment near the Earth is obtained from piezoelectric sensors ( essentially microphones ) and from wire gages ; ;
these instruments are installed on rockets , satellites , and space probes .
Statistically , the most significant data have been collected from the sensors on 1958 Alpha ( Explorer 1 ) , 1958 Delta 2 ( Sputnik 3 ) , and 1959 Eta ( Vanguard 3 ) .
These vehicles , with large sensitive areas , have collected data for long enough times to give reliable impact rates for the periods of exposure .
Many other vehicles with smaller sensitive-area exposure-time products contribute some information .
The impact rate on 1958 Alpha for 153 events was Af for particles of mass greater than Af ( Dubin , 1960 ) ; ;
this mass threshold was derived from the detector calibration and an assumed impact velocity of Af .
The data show daily and diurnal variations .
Ninety per cent of the 153 recorded impacts occurred between midnight and noon , and from day to day the variation of the rate was as much as an order of magnitude .
One may conclude that most of the detected micrometeoritic material is concentrated in orbital streams which intersect the Earth's orbit .
There have been contradictory reports from 1958 Delta 2 , and the data quoted here are believed to be the more reliable .
On May 15 , a very large increase occurred with Af of mass between Af and Af ; ;
for the next two days , the impact rate was Af ; ;
and for the next nine days , the impact rate was less than Af ( Nazarova , 1960 ) .
The data for the first day indicate a meteor stream with a very high concentration of particles and may have led to the high estimates of micrometeorite flux .
Preliminary data from 1959 Eta give an average impact rate of Af for masses larger than Af for about 1000 events in a 22-day period ( LaGow and Alexander , 1960 ) .
The day-to-day rate varied by less than a factor of 4.5 .
The data have not yet been analyzed for diurnal variations .
Note that the mass threshold is four times that of 1958 Alpha and that the flux is one fifth as large .
If one assumes that the average flux did not change between measurements , a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius .
Space probes have yielded little information .
Pioneer 1 , recorded a decrease in flux with distance from the Earth on the basis of 11 counts in 9 hours .
With detectors sensitive to three mass intervals and based on a few counts , the second and third Russian space probes indicate that the flux of the smallest particles detected is less than that of larger ones .
Being based on so few events , these results are of dubious validity .
The calibration of piezoelectric sensors in terms of the particle parameters is very uncertain .
Many workers believe that the response is proportional to the incident momentum of the particles , a relation deduced from laboratory results linearly extrapolated to meteoritic velocities .
However , one must expect that vaporization and ejection of material by hypervelocity impacts would cause a deviation from a linear relationship .
In the United States , most of the sensors are calibrated by dropping small spheres on their sensitive surfaces .
The Russian experimenters claim that only a small fraction of the impulse from the sensors is caused by the incident momentum with the remainder being momentum of ejected material from the sensor .
This `` ejection '' momentum is linearly related to the particle energy .
They quote about the same mass threshold as that of the U.S. apparatus , but a momentum threshold about 40 times greater .
There is a difference in the experimental arrangement , in that the U.S. microphones are attached directly to the vehicle skin while the Russian instruments are isolated from the skin .
The threshold mass is derived from the momentum threshold with the assumption of a mean impact velocity of Af in the U.S. work and Af in the U.S.S.R. work .
The threshold mass of about Af corresponds to a 10-M-diameter sphere of density Af .
However , the conversion from mass to size is unreliable , since many photographic meteors give evidence of a fluffy , loosely bound meteorite structure with densities as low as Af .
To what extent such low density applies to micrometeorites is unknown .
The velocity value used is also open to some question ; ;
if a substantial fraction of the dust is orbiting about the Earth , only about one third the above-mentioned average velocity should be used in deriving the mass .
Zodiacal light and the gegenschein give some evidence for such a dust blanket , a phenomenon also to be expected if the dust before capture is in circular orbits about the sun , as indicated by the trend of the smaller visible meteors .
The diurnal variation in the observed flux may be partly due to the dependence of the detector sensitivity on the incident velocity .
The flux of micrometeorites in the neighborhood of the Earth can be estimated by extrapolation from radar and visual meteor data .
A summary of meteorite data , prepared by Whipple ( 1958 ) on the basis of photographic , visual , and radar evidence , is given in Table 5-1 .
From an estimated mass of 25 g for a zero-magnitude meteorite , the other masses are derived with the assumption of a mass decrease by a factor of 2.512 for each unit increase in magnitude .
The radius is calculated from the mass by assuming spheres of density Af except for the smallest particles , which must have a higher mass density to remain in the solar system in the presence of solar-radiation pressure .
The flux values are for all particles with masses greater than the given mass and are based on an estimate of the numbers of visual meteors .
It is assumed that the flux values increase by a factor of 2.512 per magnitude , in accordance with the opinion that the total mass flux in each unit range in magnitude is constant .
The values agree with the data from 1958 Alpha and 1959 Eta .
The figures in the next-to-last column are derived with the assumption of 50 per cent shielding by the Earth ; ;
hence , these figures apply immediately above the Earth's atmosphere .
The unshielded flux is given in the last column ; ;
these figures constitute the best estimate for the flux in interplanetary space near the Earth .
Of course , if there is a dust blanket around the Earth , the fluxes in interplanetary space should be less than the figures given here .
Note that the mass scale is one to two orders of magnitude greater than some previously used ; ;
for example , Jacchia ( 1948 ) derived a scale of 0.15 g for a Af , zero-magnitude meteorite .
The older scales were based on theoretical estimates of the conversion efficiency of kinetic energy into light .
The mass scale used in Table 5-1 was derived on the assumption that the motion of the glowing trail is related to the momentum transfer to the trail by the meteorite , permitting the calculation of the mass if the velocity is known ( Cook and Whipple , 1958 ) .
A concentration distribution has been derived from radar observations sensitive to the fifteenth magnitude ( Manning and Eshleman , 1959 ) .
Extrapolation of this relationship through the thirtieth magnitude covers the range of micrometeorites .
The approximate equation is Af , where N is the number of Af with electron line-density greater than or equal to Af , and Q is proportional to the mass of the meteorite .
Therefore , N is inversely proportional to the radius cubed and in fair agreement with the inverse 7/2 power derived from 1958 Alpha and 1959 Eta data .
At the fifteenth magnitude , Af , and at the twenty-fifth magnitude , Af .
These extrapolated fluxes are about an order of magnitude less than the values from the satellite data and the figures in Whipple's table .
The extrapolation may be in error for several reasons .
The observational data determining the concentration distribution have a range of error which is magnified in the extension into the micrometeorite region .
The solar-electromagnetic- and corpuscular-radiation pressure and the associated Poynting-Robertson effect increase in effectiveness as the particle size decreases and modify the distribution and limit sizes to larger than a few microns .
Also , it has been suggested that the source of all or part of the dust may not be the same as that for visual or radar meteorites ( Best , 1960 ) , and the same distribution would not be expected .
Indirect indications of micrometeorite flux
A measure of the total mass accretion of meteoritic material by the Earth is obtained from analyses of deep-sea sediments and dust collected in remote regions ( Pettersson , 1960 ) .
Most meteoritic material , by the time it reaches the Earth's surface , has been reduced to dust or to spherules of ablated material in its passage through the atmosphere .
For all meteorites , the average nickel content is about 2.5 per cent .
This is much higher than the nickel content of terrestrial dusts and sediments and provides a basis for the determination of the meteoritic mass influx .
Present data indicate an accretion of about Af tons per year over the entire globe , or about Af .