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The upper limit for asteroidal particles of this size is about five impacts per square meter. Near the Earth, the flux of cometary meteoroids of 10-6 g or larger is about three impacts per square meter per year (NASA SP-8013, 1969), with an average velocity relative to the spacecraft of 20 km/s. Thus, for meteoroids in this size range, the asteroid belt is not likely to be more hazardous than the meteoroid environment near Earth.

However, assume that it is desired to insure that a spacecraft having 100 m” of surface area has at least a 0.99 probability of not being penetrated by a meteoroid. The spacecraft must then be designed to withstand (from eq. (9)) an impact by a particle of 10-4” g with a relative velocity of 15 km/s. (This compares with a cometary particle mass of 107* g for a similar spacecraft near Earth for 1 yr.) If the spacecraft were designed to withstand an impact from a 10-4” g meteoroid (which could add hundreds of kilograms to the spacecraft weight), and the upper limit to the asteroid flux were encountered, then the probability of no penetration would be reduced to 0.72. To design a spacecraft using the upper limit would require protection against a 10 g asteroidal meteoroid, which would severely increase the weight of the spacecraft.

REFERENCES

Baldwin, Ralph B. 1964, Lunar Crater Counts. Astron. J. 69(5), 377-392.
Brown, Harrison. 1960, The Density and Mass Distribution of Meteoritic Bodies in the
Neighborhood of the Earth's Orbit. J. Geophys. Res.65(6), 1679-1683.
Dohnanyi, J. S. 1969, Collisional Model of Asteroids and Their Debris. J. Geophys. Res.
74(10), 2531-2554.
Hartmann, William K. 1965, Secular Changes in Meteoritic Flux Through the History of
the Solar System. Icarus 4(2), 207-213.
Hartmann, William K. 1968, Lunar Crater Counts—VI: The Young Craters Tycho,
Aristarchus, and Copernicus. Communications of the Lunar and Planetary Lab., vol. 7,
no. 119, pp. 145-156. Univ. of Arizona Press. Tucson.
Hawkins, Gerald S. 1960, Asteroidal Fragments. Astron. J. 65(5), 318-322.
Hawkins, G. S. 1964, Interplanetary Debris Near the Earth. Ann. Rev. Astron. Astrophys.
2, 149-164.
Kessler, Donald J. 1968, Upper Limit on the Spatial Density of Asteroidal Debris. AIAA. J.
6(12), 2450.
Kessler, D. J. 1969, Spatial Density of the Known Asteroids in the Ecliptic Plane. NASA
TM X-58026.
Kuiper, G. P., Fujita, Y., Gehrels, T., Groeneveld, I., Kent, J., Van Biesbroeck, G., and
Houten, C. J. van. 1958, Survey of Asteroids. Astrophys. J. Suppl. Ser. 32, vol. III, pp.
289-335.
Marcus, A. H. 1966, A Stochastic Model for the Formation and Survival of Lunar Craters.
Icarus 5, 165-200.
Marcus, A. H. 1968, Number Density of Martian Craters. Bellcomm Rept. TR-68-710-1.
NASA SP-8013. 1969, Meteoroid Environment Model—1969 (Near Earth to Lunar
Surface).
NASA SP-8038. 1970, Meteoroid Environment Model-1970 (Interplanetary and
Planetary).
Piotrowski, S. 1953, Collisions of Asteroids. Acta Astron. 5, (Oct.), 115-138.
Wetherill, G. W. 1967, Collisions in the Asteroid Belt. J. Geophys. Res. 72(9), 2429-2444.

Whipple, Fred L. 1967, On Maintaining the Meteoritic Complex. Smithson. Astrophys. Observ. Special Rept. 239. (Also available in NASA SP-150, 1967, pp. 409-426.)

DISCUSSION

p ALFVEN: Have you made any estimates on how much danger a space mission to a comet might have, considering the fact that comets are associated with meteor streams? KESSLER: No.

DESCRIPTION OF PIONEER F AND G ASTEROID BELT
PENETRATION EXPERIMENT

WILL/AM. H. KINARD AWD ROBERT L. O'NEAL
NASA Langley Research Center

A NASA Langley Research Center meteoroid detection experiment will be performed on both the Pioneer F and G missions. The objective of this experiment is to obtain data that will indicate the population of meteoroids in the 10-9 to 10-8 g mass range in interplanetary space and, in particular, the region of the asteroid belt, and establish a first indication of the meteoroid penetration hazard to spacecraft in the asteroid belt. Specifically, the experiment will detect meteoroid penetrations of stainless steel targets 25 and 50 pm (1 and 2 mils) thick as the Pioneer spacecraft travel in interplanetary space through the asteroid belt to Jupiter and beyond.

The large asteroids that are visible from Earth are, of course, much too sparse to present a hazard to spacecraft. The spacecraft designer is concerned about the population of the more numerous smaller mass particles in the asteroid belt. The environmental model (NASA SP-8038, 1970), which is generally used in spacecraft design, for the distribution of these smaller mass asteroidal particles is presented in figure 1. In this model, the concentration of asteroidal meteoroids as a function of mass is based on an extrapolation of the data of number and mass for visible asteroids, with the number of smaller asteroids being limited to the estimated number that will reflect no more sunlight than is observed in the counterglow. The variation of the number of asteroidal meteoroids of all masses as a function of radial distance from the Sun, space longitude, etc., is assumed to vary as the asteroids are observed to vary.

The possibility of large errors existing in this model is recognized. The model represents an extrapolation of some 20 to 30 orders of magnitude from the asteroid data, which have intrinsic uncertainties resulting from the unknown albedo, density, and shape. There are also uncertainties in the limits placed on the model by the observed intensity of the counterglow. If a pessimistic view of all of these uncertainties is taken in spacecraft design considerations, the meteoroid shielding requirements would inflict severe weight penalties. It is therefore important to better define the population of

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the smaller asteroidal particles, and flight experiments are necessary to generate the required environment definition.

APPROACH

The asteroid belt penetration experiment objectives, as previously stated, will be accomplished by measuring the time, and thus the frequency, of meteoroid penetrations in stainless steel targets during interplanetary flight. The pressurized cell type of detector is being used to detect penetrations. In principle, the detector consists of a cavity that is gas pressurized and is equipped with a pressure monitoring device. If and when a meteoroid penetrates the test material, the gas in the cavity will leak out and the loss in pressure will be detected. The number of cells that have been punctured will be determined at each interrogation of the spacecraft.

Impact tests have shown that cell penetrations can be expected from impacts of meteoroids of approximately 107* g mass or larger. These tests indicate that each 25 pm (1 mil) cell penetration could be interpreted as an impact of approximately a 10-”g mass meteoroid or larger and each 50 um cell penetration could be interpreted as an impact of 107* g mass meteoroid or larger. Additional impact tests are being conducted to better define the requirements for detector penetration.

The pressure cells to be flown on the Pioneer F spacecraft will all have 25 pum (1 mil) thick target material. The decision on the target thickness for the pressure cells on the Pioneer G spacecraft will be dependent on the data from Pioneer F. If the expected number of 25 pm penetrations is detected on the Pioneer F mission, then 50 pum thick test material will be flown on Pioneer G. If the 25 pm penetrations detected by Pioneer F are fewer than expected, and if additional data are needed to form a reasonable 25 pm data sample, then the Pioneer G spacecraft will also fly 25 pm target material.

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