On meteor masses and densities.

For a number of years the two-station photographic meteor data have been used in the determination of density, p, in the upper atmosphere. A comparison of the rocket determinations of pressures, densities, and temperatures in the region of the White Sands Proving Ground in New Mexico with the determinations by meteors made nearby at the Harvard stations now provides a completely independent check on the theory and numerical constants involved in the meteor theory. Tentative reductions by Dr. L. Jacchia compared with the combined upper atmospheric data by rocket techniques suggest a systematic correction of -0.1 in log p to the determinations by meteors. It is now possible to reverse the procedure and adopt the rocket determinations of p in order to establish the masses or densities of meteors. Basic is the drag equation: dv _ _ FA0 2 dl p~213 m'13 v p in which the meteoric velocity is given by v, the density of the meteoroid by p~, the mass of the meteroid by m, the drag coefficient by F, and the dimensionless shape coefficient by A0 (A, = 1.21 for a sphere). The quantities v, dv/dt and p may be considered as accurately determined statistically. The product F A0 has now been well established by the work of J. S. Rinehart, W A. Allen and W. C. White of the Naval Observatory Test Station at Inyokern, California. Their values for irregularly shaped iron and aluminum pellets to velocities of 6 km/sec are F = 0.42 and A0 = 1.70. There is every reason to believe that the drag coefficient will not change much in the range of observed meteoric velocities and that the shape factor will be typical for irregularly shaped masses such as meteoroids. With these constants one can then derive numerically the product p5213m'13 for individual meteors at various velocity ranges. From the photographic light curve of a meteor one can determine the total am.ount of photographic radiation from the phenomenon and, on the basis of a dimensionless luminous efficiency coefficient determined by E. Opik, one can calculate the original mass of an individual meteoroid. The meteoric data indicate that the luminous efficiency coefficient is closely proportional to the velocity, in agreement with ()pik's calculations. If the density of a meteoroid is taken as 3.5 gm/cm' and the corresponding mass is calculated by the two methods, a disparity of more than an order of magnitude is indicated, in the sense that the drag equation leads to a smaller mass than the luminosity relation. These two determinations may be reconciled by assuming an error in the luminous efficiency coefficient, which is not unlikely; a large error in the assumed atmospheric density, which is unlikely; errors in the other constants; an error in the drag equations; or a smaller value for the density of a meteoroid. A maximum density for the meteoroid can be derived on the assumption that the luminous efficiency coefficient is unity for the fastest meteors and proportional to the velocity for slower meteors. Unless there is reason to believe that atmospheric energy contributes appreciably to the observed luminosity of a meteor, the luminosity efficiency factor cannot exceed unity. The other constants and measured data in the equations are well established. The maximal meteoric density comes out to be approximately 1.7 gm/cm', over the velocity range from 20 to 72 km/sec. It appears difficult to increase the calculated density to 3 gm/cm' without making consistently extreme assumptions as to the various constants involved. This extremal density, however, is about that for average meteorites. The few laboratory experiments with relevant atoms and ions in the meteoric velocity range indicate that radiation by encounters is generally inefficient. It seems unlikely that the luminous efficiency factor can be very much greater than &pik's calculated values, which were the order of I per cent. Probably 10 per cent is a high value. The corresponding meteoroid densities on this basis are roughly 0.3 to 1.0 gm/cm', generally below the density of water. We are dealing here almost entirely with cometary debris, which appears to be entirely different from meteorites physically, but not chemically. A few very slow photographic meteors with asteroidal-type orbits suggest more normal densities. It is concluded tentatively that meteoroids of cometary origin are of very much lower density than those of the meteoritic type. Such a deduction would follow naturally from the writer's icy conglomerate model of comets. Here one would expect the original meteoroid to consist of a large fraction, perhaps 0.7 to o.8 by mass, of ices which have been sublimated by the sun S radiation. A resulting meteoroid would then be a porous fragile structure of meteoritic materials with an expected density in the range from 0.2 to 1.0 gm/cm'. Whether the structure should be porous at the microscopic or macroscopic level is not immediately obvious. For estimates of meteoroid energies and masses, the writer still recommends for use the results based upon O~pik's luminous efficiency coefficient. The corresponding energy for a meteor of visual magnitude zero is about 1.0 X 10" ergs and the mass 1.25 gms at a mean velocity of 40 km/sec. For other velocities the energy varies as the inverse velocity and the mass as the inverse-cube velocity; with magnitude, the energy and mass vary directly as the corresponding visual light intensity. An improved theory for the luminous efficiency factor is urgently needed.s1;0;69]This investigation was a part of research conducted under an Office of Naval Research contract. Harvard College Observatory, Cambridge, Mass.