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At least 289 records · Page 16

The Role of KREEP in the Production of Mg-Suite Magmas and Its Influence on the Extent of Mg-Suite Magmatism in the Lunar Crust

The lunar magnesian-suite, or Mg-suite, is a series of ancient plutonic rocks from the lunar crust. They have received a considerable amount of attention from lunar scientists since their discovery for three primary reasons: 1) their ages and geochemistry indicate they represent pristine magmatic samples that crystallized very soon after the formation of the Moon; 2) their ages often overlap with ages of the ferroan anorthosite (FAN) crust; and 3) planetary-scale processes are needed in formation models to account for their unique geochemical features. Taken as a whole, the Mg-suite samples, as magmatic cumulate rocks, approximate a fractional crystallization sequence in the low-pressure forsterite-anorthite-silica system, and thus these samples are generally thought to be derived from layered mafic intrusions which crystallized very slowly from magmas that intruded the anorthositic crust. However, no direct linkages have been established between different Mg-suite samples based either on field relationships or geochemistry.The model for the origin of the Mg-suite, which best fits the limited available data, is one where Mg-suite magmas form from melting of a hybrid cumulate package consisting of deep mantle dunite, crustal anorthosite, and KREEP (potassium-rare earth elements-phosphorus) at the base of the crust under the Procellarum KREEP Terrane (PKT). In this model, these three LMO (Lunar Magma Ocean) cumulate components are brought into close proximity by the cumulate overturn process. Deep mantle dunitic cumulates with an Mg number of approximately 90 rise to the base of the anorthositic crust due to their buoyancy relative to colder, more dense Fe- and Ti-rich cumulates. This hybridized source rock melts to form Mg-suite magmas, saturated in Mg-rich olivine and anorthitic plagioclase, that have a substantial KREEP component.

Elardo, S. M.↗

Petrogenesis of lunar troctolites

Models of petrogenesis for lunar troctolites are severely constrained by the high Mg(*) (greater than 88) values of the most primitive members of the Mg-rich suite. Melts derived by partial melting of olivine cumulates to the lunar magma ocean have high Mg(*) but are strongly undersaturated with respect to plagioclase. Assimilation of lunar crust cannot bring these melts to the plagioclase liquious without unduly reducing the Mg(*) values of olivine. Partial melts derived by melting a lherzolite primitive interior have higher normative plagioclase contents but require sources with Mg(*) greater than 90. More terrestrial-like Mg(*) (approximately 88) values are permitted if rising thermal plumes are capable of entraining the most Mg-rich cumulates of the magma ocean. The Mg(*) values of lunar troctolites may, therfore, reflect a hybrid source composed of primitive mantle and Mr-rich cumulates of the magma ocean. Higher Mg(*) values may also arise from the reducction of small amounts of FeO to Fe. Alternatively, the parent magmas to lunar troctolites may be impact melts of the anorthositic crust and the Mg-rich dunites cumulates of the magma ocean; the latter were brought to the upper mantle during the overturn of the unstable cumulate pile of the magma ocean.

Hess, Paul C.↗

Assessing precipitation, evapotranspiration, and NDVI as controls of US Great Plains plant production

Productivity throughout the North American Great Plains grasslands is generally considered to be water limited, with the strength of this limitation increasing as precipitation decreases. We hypothesize that cumulative actual evapotranspiration water loss (AET) from April to July is the precipitation-related variable most correlated to aboveground net primary production (ANPP) in the U.S. Great Plains (GP). We tested this by evaluating the relationship of ANPP to AET, precipitation, and plant transpiration (Tr). We used multi-year ANPP data from five sites ranging from semiarid grasslands in Colorado and Wyoming to mesic grasslands in Nebraska and Kansas, mean annual NRCS ANPP, and satellite-derived normalized difference vegetation index (NDVI) data. Results from the five sites showed that cumulative April-to-July AET, precipitation, and Tr were well correlated (R2: 0.54–0.70) to annual changes in ANPP for all but the wettest site. AET and Tr were better correlated to annual changes in ANPP compared to precipitation for the drier sites, and precipitation in August and September had little impact on productivity in drier sites. April-to-July cumulative precipitation was best correlated (R2 = 0.63) with interannual variability in ANPP in the most mesic site, while AET and Tr were poorly correlated with ANPP at this site. Cumulative growing season (May-to-September) NDVI (iNDVI) was strongly correlated with annual ANPP at the five sites (R2 = 0.90). Using iNDVI as a surrogate for ANPP, we found that county-level cumulative April–July AET was more strongly correlated to ANPP than precipitation for more than 80% of the GP counties, with precipitation tending to perform better in the eastern more mesic portion of the GP. Including the ratio of AET to potential evapotranspiration (PET) improved the correlation of AET to both iNDVI and mean county-level NRCS ANPP. Accounting for how different precipitation-related variables control ANPP (AET in drier portion, precipitation in wetter portion) provides opportunity to develop spatially explicit forecasting of ANPP across the GP for enhancing decision-making by land managers and use of grassland ANPP for biofuels.

Maosi Chen↗

Spectral estimators of absorbed photosynthetically active radiation in corn canopies

Most models of crop growth and yield require an estimate of canopy leaf area index (LAI) or absorption of radiation. Relationships between photosynthetically active radiation (PAR) absorbed by corn canopies and the spectral reflectance of the canopies were investigated. Reflectance factor data were acquired with a LANDSAT MSS band radiometer. From planting to silking, the three spectrally predicted vegetation indices examined were associated with more than 95% of the variability in absorbed PAR. The relationships developed between absorbed PAR and the three indices were evaluated with reflectance factor data acquired from corn canopies planted in 1979 through 1982. Seasonal cumulations of measured LAI and each of the three indices were associated with greater than 50% of the variation in final grain yields from the test years. Seasonal cumulations of daily absorbed PAR were associated with up to 73% of the variation in final grain yields. Absorbed PAR, cumulated through the growing season, is a better indicator of yield than cumulated leaf area index. Absorbed PAR may be estimated reliably from spectral reflectance data of crop canopies.

Gallo, K. P.↗

Spectral estimators of absorbed photosynthetically active radiation in corn canopies

Most models of crop growth and yield require an estimate of canopy leaf area index (LAI) or absorption of radiation. Relationships between photosynthetically active radiation (PAR) absorbed by corn canopies and the spectral reflectance of the canopies were investigated. Reflectance factor data were acquired with a Landsat MSS band radiometer. From planting to silking, the three spectrally predicted vegetation indices examined were associated with more than 95 percent of the variability in absorbed PAR. The relationships developed between absorbed PAR and the three indices were evaluated with reflectance factor data acquired from corn canopies planted in 1979 through 1982. Seasonal cumulations of measured LAI and each of the three indices were associated with greater than 50 percent of the variation in final grain yields from the test years. Seasonal cumulations of daily absorbed PAR were associated with up to 73 percent of the variation in final grain yields. Absorbed PAR, cumulated through the growing season, is a better indicator of yield than cumulated leaf area index. Absorbed PAR may be estimated reliably from spectral reflectance data of crop canopies.

Gallo, K. P.↗

Spatial scales of cirrus cloud properties

Research in studying the spatial scales of the cirrus, used data collected during the flight legs of the NCAR Sabreliner aircraft on four days during the FIRE Cirrus IFO to study the spatial scales of the cirrus, and will concentrate on the scales of horizontal wind. The spatial scales of the cloud features can be described by power spectra (or spectral density graphs) and cumulative variance graphs. The cumulative variance graphs were created by first using a Fast Fourier Transform (FFT) to create variance spectra. The variances were then summed in a cumulative fashion from the largest scalelengths (wavelengths) to the smallest. No detrending was done to the original data, and no smoothing or averaging was done to the spectral points. All the spectral points were included. This means that the values of the first five to ten spectral points of the large scalelengths should only be considered to be qualitatively correct. The cumulative variance at smaller scalelengths should be correct because a more accurate representation of the variance at the larger scalelengths should only redistribute the energy amongst the larger scalelengths.

Hein, Paul F.↗

Site diversity for satellite earth terminals and measurements at 28 GHz

This paper reviews site diversity concepts and models and presents the results of a site diversity experiment, in which radiometers were used to measure attenuation on earth-space paths, performed at Columbus, Ohio, for a period of one year. Attenuation statistics are presented first in the form of the joint probability density function of attenuation at the two sites. From these are derived the cumulative two-dimensional distribution of attenuation at both sites, the cumulative distribution of attenuation at each site, the effective cumulative distribution of attenuation for a diversity system that always switches to the better of two signals, and the effective cumulative distribution of attenuation for a system with maximal-ratio signal combining. The switched-system diversity gain is compared with Hodge's predictive model, and the diversity improvement is compared with Boithias' model. Fade-duration and interfade-interval statistics are also presented for each site and for systems that employ switching and maximal-ratio combining. Rain-rate and interrainfall interval statistics are also included.

Lin, Kuan-Ting↗

Power-law confusion: You say incremental, I say differential

Power-law distributions are commonly used to describe the frequency of occurrences of crater diameters, stellar masses, ring particle sizes, planetesimal sizes, and meteoroid masses to name a few. The distributions are simple, and this simplicity has led to a number of misstatements in the literature about the kind of power-law that is being used: differential, cumulative, or incremental. Although differential and cumulative power-laws are mathematically trivial, it is a hybrid incremental distribution that is often used and the relationship between the incremental distribution and the differential or cumulative distributions is not trivial. In many cases the slope of an incremental power-law will be nearly identical to the slope of the cumulative power-law of the same distribution, not the differential slope. The discussion that follows argues for a consistent usage of these terms and against the oft-made implicit claim that incremental and differential distributions are indistinguishable.

Colwell, Joshua E.↗

Basalt generation at the Apollo 12 site. Part 2: Source heterogeneity, multiple melts, and crustal contamination

The petrogenesis of Apollo 12 mare basalts has been examined with emphasis on trace-element ratios and abundances. Vitrophyric basalts were used as parental compositions for the modeling, and proportions of fractionating phases were determined using the MAGFOX prograqm of Longhi (1991). Crystal fractionation processes within crustal and sub-crustal magma chambers are evaluated as a function of pressure. Knowledge of the fractionating phases allows trace-element variations to be considered as either source related or as a product of post-magma-generation processes. For the ilmenite and olivine basalts, trace-element variations are inherited from the source, but the pigeonite basalt data have been interpreted with open-system evolution processes through crustal assimilation. Three groups of basalts have been examined: (1) Pigeonite basalts-produced by the assimilation of lunar crustal material by a parental melt (up to 3% assimilation and 10% crystal fractionation, with an 'r' value of 0.3). (2) Ilmenite basalts-produced by variable degrees of partial melting (4-8%) of a source of olivine, pigeonite, augite, and plagioclase, brought together by overturn of the Lunar Magma Ocean (LMO) cumulate pile. After generation, which did not exhaust any of the minerals in the source, these melts experienced closed-system crystal fractionation/accumulation. (3) Olivine basalts-produced by variable degrees of partial melting (5-10%) of a source of olivine, pigeonite, and augite. After generation, again without exhausting any of the minerals in the source, these melts evolved through crystal accumulation. The evolved liquid counterparts of these cumulates have not been sampled. The source compositions for the ilmenite and olivine basalts were calculated by assuming that the vitrophyric compositions were primary and the magmas were produced by non-modal batch melting. Although the magnitude is unclear, evaluation of these source regions indicates that both be composed of early- and late-stage Lunar Magma Ocean (LMO) cumulates, requiring an overturn of the cumulate pile.

Neal, Clive R.↗

REE Partition Coefficients from Synthetic Diogenite-Like Enstatite and the Implications of Petrogenetic Modeling

Determining the petrogenesis of eucrites (basaltic achondrites) and diogenites (orthopyroxenites) and the possible links between the meteorite types was initiated 30 years ago by Mason. Since then, most investigators have worked on this question. A few contrasting theories have emerged, with the important distinction being whether or not there is a direct genetic link between eucrites and diogenites. One theory suggests that diogenites are cumulates resulting from the fractional crystallization of a parent magma with the eucrites crystallizing, from the residual magma after separation from the diogenite cumulates. Another model proposes that diogenites are cumulates formed from partial melts derived from a source region depleted by the prior generation of eucrite melts. It has also been proposed that the diogenites may not be directly linked to the eucrites and that they are cumulates derived from melts that are more orthopyroxene normative than the eucrites. This last theory has recently received more analytical and experimental support. One of the difficulties with petrogenetic modeling is that it requires appropriate partition coefficients for modeling because they are dependent on temperature, pressure, and composition. For this reason, we set out to determine minor- and trace-element partition coefficients for diogenite-like orthopyroxene. We have accomplished this task and now have enstatite/melt partition coefficients for Al, Cr, Ti, La, Ce, Nd, Sm, Eu, Dy, Er, Yb, and La.

Schwandt, C. S.↗

The Response of African Land Surface Phenology to Large Scale Climate Oscillations

Variations in agricultural production due to rainfall and temperature fluctuations are a primary cause of food insecurity on the African continent. Analysis of changes in phenology can provide quantitative information on the effect of climate variability on growing seasons in agricultural regions. Using a robust statistical methodology, we describe the relationship between phenology metrics derived from the 26 year AVHRR NDVI record and the North Atlantic Oscillation index (NAO), the Indian Ocean Dipole (IOD), the Pacific Decadal Oscillation (PDO), and the Multivariate ENSO Index (MEI). We map the most significant positive and negative correlation for the four climate indices in Eastern, Western and Southern Africa between two phenological metrics and the climate indices. Our objective is to provide evidence of whether climate variability captured in the four indices has had a significant impact on the vegetative productivity of Africa during the past quarter century. We found that the start of season and cumulative NDVI were significantly affected by large scale variations in climate. The particular climate index and the timing showing highest correlation depended heavily on the region examined. In Western Africa the cumulative NDVI correlates with PDO in September-November. In Eastern Africa the start of the June-October season strongly correlates with PDO in March-May, while the PDO in December-February correlates with the start of the February-June season. The cumulative NDVI over this last season relates to the MEI of March-May. For Southern Africa, high correlations exist between SOS and NAO of September-November, and cumulative NDVI and MEI of March-May. The research shows that climate indices can be used to anticipate late start and variable vigor in the growing season of sensitive agricultural regions in Africa.

Brown, Molly E.↗

Automated ISS Flight Utilities

During my internship at NASA Johnson Space Center, I worked in the Space Radiation Analysis Group (SRAG), where I was tasked with a number of projects focused on the automation of tasks and activities related to the operation of the International Space Station (ISS). As I worked on a number of projects, I have written short sections below to give a description for each, followed by more general remarks on the internship experience. My first project is titled "General Exposure Representation EVADOSE", also known as "GEnEVADOSE". This project involved the design and development of a C++/ ROOT framework focused on radiation exposure for extravehicular activity (EVA) planning for the ISS. The utility helps mission managers plan EVAs by displaying information on the cumulative radiation doses that crew will receive during an EVA as a function of the egress time and duration of the activity. SRAG uses a utility called EVADOSE, employing a model of the space radiation environment in low Earth orbit to predict these doses, as while outside the ISS the astronauts will have less shielding from charged particles such as electrons and protons. However, EVADOSE output is cumbersome to work with, and prior to GEnEVADOSE, querying data and producing graphs of ISS trajectories and cumulative doses versus egress time required manual work in Microsoft Excel. GEnEVADOSE automates all this work, reading in EVADOSE output file(s) along with a plaintext file input by the user providing input parameters. GEnEVADOSE will output a text file containing all the necessary dosimetry for each proposed EVA egress time, for each specified EVADOSE file. It also plots cumulative dose versus egress time and the ISS trajectory, and displays all of this information in an auto-generated presentation made in LaTeX. New features have also been added, such as best-case scenarios (egress times corresponding to the least dose), interpolated curves for trajectories, and the ability to query any time in the EVADES output. As mentioned above, GEnEVADOSE makes extensive use of ROOT version 6, the data analysis framework developed at the European Organization for Nuclear Research (CERN), and the code is written to the C++11 standard (as are the other projects). My second project is the Automated Mission Reference Exposure Utility (AMREU).Unlike GEnEVADOSE, AMREU is a combination of three frameworks written in both Python and C++, also making use of ROOT (and PyROOT). Run as a combination of daily and weekly cron jobs, these macros query the SRAG database system to determine the active ISS missions, and query minute-by-minute radiation dose information from ISS-TEPC (Tissue Equivalent Proportional Counter), one of the radiation detectors onboard the ISS. Using this information, AMREU creates a corrected data set of daily radiation doses, addressing situations where TEPC may be offline or locked up by correcting doses for days with less than 95% live time (the total amount time the instrument acquires data) by averaging the past 7 days. As not all errors may be automatically detectable, AMREU also allows for manual corrections, checking an updated plaintext file each time it runs. With the corrected data, AMREU generates cumulative dose plots for each mission, and uses a Python script to generate a flight note file (.docx format) containing these plots, as well as information sections to be filled in and modified by the space weather environment officers with information specific to the week. AMREU is set up to run without requiring any user input, and it automatically archives old flight notes and information files for missions that are no longer active. My other projects involve cleaning up a large data set from the Charged Particle Directional Spectrometer (CPDS), joining together many different data sets in order to clean up information in SRAG SQL databases, and developing other automated utilities for displaying information on active solar regions, that may be used by the space weather environment officers to monitor solar activity. I consulted my mentor Dr. Ryan Rios and Dr. Kerry Lee for project requirements and added features, and ROOT developer Edmond Offermann for advice on using the ROOT library. I also received advice and feedback from Dr. Janet Barzilla of SRAG, who tested my code. Besides these inputs, I worked independently, writing all of the code by myself. The code for all these projects is documented throughout, and I have attempted to write it in a modular format. Assuming that ROOT is updated accordingly, these codes are also Y2038-compliant (and Y10K-compliant). This allows the code to be easily referenced, modified and possibly repurposed for non-ISS missions in the future, should the necessary inputs exist. These projects have taught me a lot about coding and software design - I have become a much more skilled C++ programmer and ROOT user, and I also learned to code in Python and PyROOT (and its advantages and disadvantages compared to C++/ ROOT). Furthermore, I have learned about space radiation and radiation modeling, topics that greatly interest me as I pursue a degree in physics. Working alongside experimental physicists like Dr. Rios, I have developed a greater understanding and appreciation for experimental science, something I have always leaned towards but to which I lacked significant exposure. My work in SRAG has also given me the invaluable opportunity to witness the work environment for physicists at NASA, and what a career in academia may look like at a government laboratory such as NASA Johnson Space Center. As I continue my studies and look forward to graduate school and a future career, this experience at NASA has given me a meaningful and enjoyable opportunity to put my skills to use and see what my future career path might hold.

Offermann, Jan Tuzlic↗

Statistical Hypothesis Testing in Wavelet Analysis: Theoretical Developments and Applications to Indian Rainfall

Statistical hypothesis tests in wavelet analysis are methods that assess the degree to which a wavelet quantity(e.g., power and coherence) exceeds background noise. Commonly, a point-wise approach is adopted in which a wavelet quantity at every point in a wavelet spectrum is individually compared to the critical level of the point-wise test. However, because adjacent wavelet coefficients are correlated and wavelet spectra often contain many wavelet quantities, the point-wise test can produce many false positive results that occur in clusters or patches. To circumvent the point-wise test drawbacks, it is necessary to implement the recently developed area-wise, geometric, cumulative area-wise, and topological significance tests, which are reviewed and developed in this paper. To improve the computational efficiency of the cumulative area-wise test, a simplified version of the testing procedure is created based on the idea that its output is the mean of individual estimates of statistical significance calculated from the geometric test applied at a set of point-wise significance levels. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate wavelet spectral features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to strictly test for periodicities by using normalized arc length, which is defined as the number of points composing a cross section of a patch divided by the wavelet scale in question. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of Indian rainfall is also provided. An R software package has been written by the author to implement the various testing procedures.

Wind speed↗

Plagioclase Compositions of Eucrites and Eucrite-Type Achondrites

Eucrites are basalts, diabases and gabbros composed of ferroan pigeonite and augite, calcic plagioclase, and a silica phase, with accessory amounts of ilmenite, chromite, Ca-phosphate, troilite, metal and olivine. Many of the gabbroic-textured eucrites are cumulates from a mafic magma, while most other eucrites are close to melt compositions. These are referred to as cumulate and basaltic eucrites. Petrologic, compositional and isotopic studies have identified several mafic achondrites with eucritic mineralogy that have anomalous properties, and some of these are considered to have been derived from different parent asteroids than normal eucrites. These are referred to as eucrite-type achondrites, and they include cumulate and basaltic types. Petrologic studies of eucrites often concentrate on pyroxene compositions to reveal the petrogenetic history of the rocks and plagioclase compositions are less utilized. Here I examine Na and K variations of a suite of basaltic and cumulate eucrites and eucrite-type achondrites.

Mittlefehldt, David W.↗

The Abundances of F, Cl, and H2O in 4Vesta from Eucrites

The abundance and distribution of magmatic volatiles (i.e., H, C, N, F, S, and Cl) within the silicate portion of a differentiated planetary body has important consequences on its thermochemical evolution. However, the abundances of magmatic volatiles within differentiated bodies are difficult to quantify, and they are often depleted by varying degrees relative to CI chondrites. The mechanisms of depletion are not well constrained and could relate to intrinsic volatile depletion of the building blocks that formed the bodies, high temperature processes that result from accretion, post-accretion loss through parent body geological processes and large-scale impacts, and/or redistribution within a parent body through processes like core formation [1–4]. In the present study, we aim to constrain the abundances of F, Cl, and H2O in eucrites to better understand the magnitude of volatile depletion on 4Vesta. To accomplish this objective, we report electron microprobe analyses of apatite from seven unbrecciated, non-cumulate eucrites (i.e., CMS 04049,GRA 98098, LEW 88010, MAC 02522, MAC 041169,QUE 94484, and QUE 97053) and two monomict, non-cumulate eucrites (i.e., Berthoud and Stannern). In combination with previously published data on eucrite-hosted apatite, we determine Cl/F and H2O/F ratios in bulk rock eucrites through the application of apatite-based melt hygrometry and chlorometry [e.g., 5–7].Additionally, we estimate the bulk rock abundances of F in six non-cumulate eucrites (i.e., GRA 98098, MAC041169, PCA 91078, QUE 97053, Stannern, and Berthoud), which we combine with previously published bulk rock F data on non-cumulate eucrites[8] to constrain the abundances of F, Cl, and H2O in 4Vesta using appropriately paired volatile/refractory element ratios for F, followed by Cl/F and H2O/F ratios for Cl and H2O, respectively.

F M McCubbin↗

Experiment S012: Micrometeorite collection

The micrometeorite activity in a near-earth environment and the effect of the environment on microorganisms were studied by exposure of polished metal and plastic surfaces to the environment outside the Gemini spacecraft. Preliminary results are summarized as follows: (1) The cumulative influx rate in the size ranges from 10 to the minus 15th power to 10 to the minus 14th power gram was approximately 2 particles/ sq m/sec, as determined on the Gemini 12 mission; (2) The cumulative influx rate in the same mass range, as determined by the data from the Gemini 9 mission was almost 200 particles/ sq m/sec; and (3) The large particle cumulative influx rate was about 3 x 0.00001 particle/ sq m/sec, with a mass of the order of 10 to the minus 7th power gram. No living organisms could be found on the sterile collecting surfaces after recovery and handling.

Hemenway, C. L.↗

Probability of stress-corrosion fracture under random loading.

A method is developed for predicting the probability of stress-corrosion fracture of structures under random loadings. The formulation is based on the cumulative damage hypothesis and the experimentally determined stress-corrosion characteristics. Under both stationary and nonstationary random loadings, the mean value and the variance of the cumulative damage are obtained. The probability of stress-corrosion fracture is then evaluated using the principle of maximum entropy. It is shown that, under stationary random loadings, the standard deviation of the cumulative damage increases in proportion to the square root of time, while the coefficient of variation (dispersion) decreases in inversed proportion to the square root of time. Numerical examples are worked out to illustrate the general results.

Yang, J.-N.↗

Flux of optical meteors down to M sub pg = +12

Observations of the flux of optical meteors down to photographic magnitudes of +12 are reported. The meteors were detected by photometry using a 10-m optical reflector from December 12-15, 1974, during the Geminid shower. A total of 2222 light pulses is identified as coming from meteors within the 1 deg field of view of the detector, most of which correspond to sporadic meteors traversing the detector beam at various angles and velocities and do not differ with the date, indicating that the Geminid contribution at faint luminosities is small compared to the sporadic contribution. A rate of 1.1 to 3.3 x 10 to the -12th meteors/sq cm per sec is obtained together with a power law meteor spectrum which is used to derive a relationship between cumulative meteor flux and magnitude which is linear for magnitudes from -2.4 through +12. Expressions for the cumulative flux upon the earth's atmosphere and at a test surface at 1 AU far from the earth as a function of magnitude are also obtained along with an estimate of the cumulative number density of particles.

Cook, A. F.↗