Lunar Phase Angle Research Articles

Polarization images of the Moon as a function of the lunar phase

Moonlight has a partial polarization state that varies with the lunar phase angle. This needs to be characterized for the Moon to be used as a calibration source for polarization-sensitive instruments or as the illumination source in nighttime passive remote sensing. To contribute to this characterization, a pixelated polarization imager was calibrated with a telescope and with a telephoto lens and used to record images of the Moon at 40 phase angles from -138° to 125°. High-resolution images of relative intensity, degree of linear polarization (DoLP), and angle of polarization (AoP) were recorded in a spectral band from 400-1000 nm and were used to calculate disk-averaged DoLP values. These images are made available to readers. Results showed higher DoLP in regions of lower reflectivity (the Umov effect), higher DoLP for waning phases (maximum DoLP of 8.3%) than for waxing (maximum DoLP of 6.8%), and consistent DoLP to disk-averaged values published previously for wavelengths contained within our broader band.

Applicability Analysis of Three Atmospheric Radiative Transfer Models in Nighttime

The relatively stable lunar illumination may be used to realize radiometric calibration under low light. However, there is still an insufficient understanding of the accuracy of models and the influence of parameters when conducting research on low-light radiometric calibration. Therefore, this study explores the applicability of three atmospheric radiative transfer models under different nighttime conditions. The simulation accuracies of three nighttime atmospheric radiative transfer models (Night-SCIATRAN, Night-MODTRAN, and Night-6SV) were evaluated using the visible-infrared imaging radiometer suite day/night band (VIIRS/DNB) data. The results indicate that Night-MODTRAN has the highest simulation accuracy under DNB. The consistency between simulated top-of-atmosphere (TOA) radiance and DNB radiance is approximately 3.1%, and uncertainty is 2.5%. This study used Night-MODTRAN for parameter sensitivity analysis. The results indicate that for the lunar phase angle, aerosol optical depth, surface reflectance, lunar zenith angle, satellite zenith angle, and relative azimuth angle, the average change rates are 68%, 100%, 2561%, 75%, 20%, and 0%. This paper can help better understand the performance of models under different atmospheric and geographical conditions, as well as whether existing models can simulate the complex processes of atmospheric radiation.

Fast Calculation on Atmospheric Rayleigh Scattering Extinction Optical Depth for Day/Night Band Radiative Transfer Model With Periodic Lunar Illumination

AbstractRayleigh scattering effect inspired by tiny atmospheric molecules generates significant extinction at relatively short wavelength, such as Day/Night Band (DNB) covering visible (VIS, 0.4–0.76 μm) and near‐infrared (NIR, 0.76–1.0 μm) wavelengths. This salient extinction effect coupled with periodic changes in lunar illumination and wide DNB will further lead to increased complexity in nocturnal fast radiative transfer model (RTM) calculation of DNB. For these reasons, this study is aimed at developing a precise and robust fast calculation method on Rayleigh scattering extinction optical depth (RayOD) for pertinent fast RTM calculation of DNB. Firstly, we coupled the lunar spectral irradiance model and the parameterized Rayleigh scattering extinction calculation module into a RTM for forward simulations. Moreover, we find that the errors in DNB‐averaged RayOD calculated from the classical fast algorithm from RTTOV (Radiative Transfer for TOVS) of training the DNB instrument coefficients (about 20% of relative error in reflectance) and the parameterization method using the central wavelength of DNB (about 5%) are too large to be tolerable in fast RTM. Finally, to address this issue, we skillfully conceptualize a new equivalent optimal central wavelength algorithm to retrieve a dynamically wavelength in DNB using observation scattering and lunar phase angles for rapidly calculating DNB‐averaged RayOD. The relative errors in simulated reflectance from coupled RTM aforementioned are subtle nuances, which are about 10−5∼10−6 order of magnitude. Besides, this robust algorithm can also correct the relative error of about 1% at dark surface caused by periodic changes in lunar illumination.

Measurements of absolute, SI-traceable lunar irradiance with the airborne lunar spectral irradiance (air-LUSI) instrument

The airborne lunar spectral irradiance (air-LUSI) instrument is designed to make low uncertainty measurements of the lunar spectral irradiance from an ER-2 aircraft from altitudes above 95% of the atmosphere. Measurements cover the visible and near infrared spectral region (350 nm to 1050 nm) and are traceable to the international system of units. Five demonstration flights were conducted in November 2019 at NASA’s Armstrong Flight Research Center. During that campaign, air-LUSI measured the spectral irradiance at lunar phase angles ranging from 10° to 60°. This work provides an overview of the air-LUSI instrument, the lunar irradiance measurements made during demonstration flights, a description of our calibration approach, and summary of the uncertainty budget. Based on the flight results and laboratory measurements, we estimate the instrument is capable of measuring lunar irradiance, propagated to the top-of-the atmosphere, with combined standard uncertainty of 1% (k = 1) or less over the spectral region from 450 nm to 980 nm. An examination of the uncertainty budget leads to a path forward toward potentially achieving uncertainties of 0.6% in lunar irradiance over much of the spectral range for future flights.

The irradiance instrument subsystem (IRIS) on the airborne-lunar spectral irradiance (air-LUSI) instrument

The objective of the airborne lunar spectral irradiance (air-LUSI) project is to make low uncertainty, SI-traceable measurements of the LUSI in the visible to near-infrared region from an aircraft above most of the optically absorbing components of the atmosphere. The measurements are made from a NASA ER-2 aircraft, which can fly at altitudes of approximately 20 km above sea level. Air-LUSI measurements, corrected for residual atmospheric attenuation, are designed to provide a matrix of low uncertainty top-of-the-atmosphere lunar irradiances at known lunar phase and libration angles to be compared and combined with other lunar irradiance data sets to constrain the uncertainties in models of lunar irradiance and reflectance. The measurements are also expected to provide insight into the differences between models and satellite sensor measurements of lunar irradiance. This paper describes the development and characterization of the air-LUSI subsystem for acquiring lunar measurements, called the irradiance instrument subsystem, prior to flight.

Calibration of the space-borne microwave humidity sounder based on real-time thermal emission from lunar surface

Calibration is a key issue for quantitative application of meteorological satellite data. The complex space environment may cause many uncertainties in data calibration. A highly stable and reliable calibrator in flight is needed. Because the Moon has no atmosphere and no environmental variation, the physical and chemical properties of its surface are stable in the long term. The Moon might be an ideal candidate for in-flight thermal calibration. In advanced satellite-borne microwave remote sensing such as NOAA-18, the deep space view (DSV) of the microwave humidity sounder (MHS) has viewed the Moon many times every year. Using the thermal-physical properties of the lunar regolith derived from the Diviner infrared (IR) brightness temperature (TB) data, we solve the one-dimensional heat conduction equation to obtain the temperature profile of the near side of the lunar regolith medium. The loss tangents of the regolith medium are retrieved from microwave TB data of the Chinese satellite Chang’e-2. The integrated radiative transfer equation is used to simulate the weighted disk-average TB of the lunar surface for the MHS channels at 89, 157, and 183 GHz for the year 2011. The Moon is taken as an extended circular target. The simulated TBs are used to correct the full width at half maximum (FWHM) fitted with the MHS counts. We analyze the influences of the distance between the satellite and the Moon, the lunar phase angle, and the FWHM of the radiometer on the inverted FWHM. The corrected TB data are compared with the simulation. This paper presents a new method for thermal calibration of spaceborne in-flight microwave and millimeter-wave radiometers with the weighted disk-average TB of the lunar surface.

Improved Lunar Irradiance Model Using Multiyear MODIS Lunar Observations

The Moderate Resolution Imaging Spectroradiometer (MODIS) instruments on board the Terra and Aqua spacecrafts were launched on December 18, 1999, and May 4, 2002, respectively. One of the features of the MODIS instruments is the ability to perform observations of the lunar surface from its space view (SV) port. This event is scheduled approximately once a month via a spacecraft roll maneuver, which enables the lunar phase to be confined to within 1° for each instrument. The Moon is considered to be an extremely stable reference to monitor the long-term radiometric stability of the reflective solar bands (RSB). Each MODIS instrument can also view the Moon for about four months in a year without a roll maneuver. This is caused by the intrusion of the Moon in the SV. The lunar phase angles of these unscheduled lunar observations are distributed over a wide range varying from approximately 50° to 80° for Terra MODIS and from about -80° to -50° for Aqua MODIS, where the positive phase angle refers to a waning Moon, while the negative phase angle corresponds to a waxing Moon. Together, the scheduled and unscheduled lunar observations are used to monitor the long-term radiometric stability of the RSB. Of the several challenges involved in the modeling of the lunar optical properties, such as its absolute brightness, a number of optical and view geometry effects need to be considered. These effects are much easier to characterize for the scheduled observations due to confinement of the lunar phase angles compared to those for the unscheduled intrusions of the Moon in the SV. Nevertheless, it is still a challenge to remove the view geometry effect in the calibration coefficients derived from the scheduled lunar observations and even more challenging for the unscheduled lunar intrusions. In this work, the lunar absolute irradiance is modeled using known attributes and from the lunar observations by the two MODIS instruments from the time period between the years 2005 and 2012. The model developed here attempts to mitigate for the deficiencies in the lunar irradiance measurements by the RObotic Lunar Observatory (ROLO) model, developed by the United States Geological Survey. Overall, the relative uncertainty of the ROLO model for MODIS calibration has been assessed to be about 4% for the shortest wavelength (a center wavelength of 412 nm) in the phase angle range mentioned above. With our new established lunar model, the calibration coefficients derived from the lunar observations, especially those from the unscheduled lunar observations, for the RSB of the two MODIS instruments are significantly improved for the entire mission. A good agreement is observed between the calibration coefficients derived from the scheduled and unscheduled lunar observations. Both the absolute uncertainty of the new lunar irradiance model and its relative uncertainty due to view geometry variation are much smaller than those of the current ROLO model which has been widely used for most remote sensors' lunar calibrations. Our newly developed lunar irradiance model can be applied to other remote sensors for their lunar calibrations as well. Finally, the significant improvement in the measurement of the lunar irradiance led to a polarization effect in the Moon response for MODIS to be identified. In this article, the impact of the polarization of the moonlight for the MODIS RSB is quantified. This is extremely vital as polarization effect for remote sensors such as MODIS and the follow-on suite of the Joint Polar Satellite System Visible Infrared Imaging Radiometer Suite has been found to significantly increase the calibration uncertainty, especially at short wavelengths.

A low-light radiative transfer model for satellite observations of moonlight and earth surface light at night

Lunar sun-reflected light can be effectively measured through a low-light band or a day/night band (DNB) implemented on space-based optical sensors. Based on moonlight, nocturnal observations for artificial light sources at night can be achieved. However, to date, an open-sourced and mature Low-Light Radiative Transfer Model (LLRTM) for the further understanding of the radiative transfer problem at night is still unavailable. Therefore, this study develops a new LLRTM at night with the correction of the lunar and active surface light sources. First, the radiative transfer equations with an active surface light source are derived for the calculation based on the lunar spectral irradiance (LSI) model. The simulation from this new LLRTM shows a minimal bias when compared with the discrete ordinates radiative transfer (DISORT) model. The simulated results of radiance and reflectance at the top of the atmosphere (TOA) also show that the surface light source has a remarkable impact on the radiative transfer process. In contrast, the change in the lunar phase angle has minimal influence. Also, comparing with space-based DNB radiance observations, LLRTM shows the potential to simulate space-based low-light imager observations under an effective surface light source condition during the night.

Radiometric Inter-Consistency of VIIRS DNB on Suomi NPP and NOAA-20 from Observations of Reflected Lunar Lights over Deep Convective Clouds

The Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) is capable of observing reflected lunar radiances at night with its high gain stage (HGS), and the radiometric calibration is traceable to the sun through gain transfer from the low gain stage (LGS) calibrated near the terminator with the solar diffuser. Meanwhile, deep convective clouds (DCC) are known to have a stable reflectance in the visible spectral range. Therefore, the reflected lunar radiance at night from the DCC provides a unique dataset for the inter-calibration of VIIRS DNB on different satellites such as Suomi National Polar-orbiting Partnership (NPP) and NOAA-20, as well as quantifying the lunar radiance as a function of lunar phase angle. This study demonstrates a methodology for comparing nighttime Suomi NPP and NOAA-20 VIIRS DNB measured DCC reflected lunar radiance at various phase angles using data from July 2018 to March 2019 with an 86 second sampling interval and comparing Suomi NPP VIIRS DNB measured lunar radiances with those from lunar model predictions. The result shows good consistency between these two instruments on the two satellites, although a low bias in the NOAA-20 VIIRS DNB of ~5% is found. Also, observed lunar radiance from VIIRS DNB on Suomi NPP is found to be consistent with model predictions within 3% ± 5% (1σ) for a large range of lunar phase angles. However, discrepancies are significant near full moon, due to lunar opposition effects, and limitations of the lunar models. This study is useful not only for monitoring the DNB calibration stability and consistency across satellites, but also may help validate lunar models independently.

An investigation of the implications of lunar illumination spectral changes for Day/Night Band‐based cloud property retrieval due to lunar phase transition

AbstractThe Moon reflects sunlight like a huge mirror hanging in the sky at night, which presents the obviously periodical changes in its luminance or irradiance due to Sun‐Earth‐Moon geometry variation. The potential effect of the periodical changes in lunar phase angle on nighttime Day/Night Band (DNB) radiative transfer simulation in the presence of cloud has seldom been reported thus far. In this study, a radiative transfer model is developed by coupling the lunar light source with various Sun‐Earth‐Moon geometries. To elucidate the stability of DNB‐averaged cloud bulk scattering properties, we simulate nighttime reflectance and radiances under four typical lunar phase angles (0°, 45°, 90°, and 135°) from 7 April 2016 to 8 May 2016 (e.g., two lunar cycles). Explicit simulation analyses indicated that DNB‐averaged cloud bulk scattering properties exhibit weak sensitivity to lunar phase angles. The maximum DNB reflectance differences between any and 90° lunar phase angles are less than 0.05% (0.01%) in the presence of water (ice) clouds, indicating a negligible effect of periodically changes on lunar spectral irradiances. Our findings suggest that the differences of reflectance at lunar phase angle = 90° are less than approximately 0.05% (water cloud)/0.01% (ice cloud), much smaller than 11% radiometric calibration uncertainties of DNB. This means that these differences could be ignored in both nighttime cloud property retrieval and DNB radiative transfer modeling.

On the measurements of the moon’s infrared temperature and its relation to the phase angle

Radiometric measurements of the thermal radiation originating from the moon’s surface were obtained using an infrared detector operating at wavelengths between 8 and 14μm. The measurements cover a full moon cycle. The variation of the moon’s temperature with the lunar phase angle was established. The lunar temperatures were 391±2.0K for the full moon, 240±3.5K for the first quarter, and 236±3K for the last quarter. For the rest of the phase angles, the lunar temperature varied between 170 and 380K. Our results are comparable with those obtained previously at these phase angles. For the new moon phase, the obtained temperature was between 120 and 133K. With the exception of the new moon phase, our measurements at all the phase angles were consistent with those obtained using Earth-based data and those obtained by the Diviner experiment and the Clementine spacecraft. At the new phase, our measurements were comparable with those obtained from the ground but were significantly higher than those obtained by the Diviner and Clementine data. We attribute this inconsistency to either the calibration curve of our detector, which does not perform well at very low temperatures, or to infrared emission from the atmosphere. A simple linear model to predict the lunar temperature as a function of the phase angle was proposed. The experimental errors that affect the measured temperatures are discussed.

Variation in lunar sodium exosphere measured from lunar orbiter SELENE (Kaguya)

Resonant scattering of the lunar sodium exosphere was measured from the lunar orbiter SELENE (Kaguya) from December 2008 to June 2009. Variations in line-of-sight integrated intensity measured on the night-side hemisphere of the Moon could be described as a spherical symmetric distribution of the sodium exosphere with a temperature of 2400–6000 K. Average surface density of sodium atoms in February is well above that in the other months by about 30%. A clear variation in surface density related to the Moon’s passage across the Earth’s magnetotail could not be seen, although sodium density gradually decreased (by 20±8%) during periods from the first through the last quarter of two lunar cycles. These results suggest that the supra-thermal components of the sodium exosphere are not mainly produced by classical sputtering of solar wind. The variation in sodium density (which depends on lunar-phase angle) is possibly explained by the presence of an inhomogeneous source distribution of photon-stimulated desorption (PSD) on the surface.

Probable swirls detected as photometric anomalies in Oceanus Procellarum

Images of the lunar nearside obtained by telescopes of Maidanak Observatory (Uzbekistan) and Simeiz Observatory (Crimea, Ukraine) equipped with Canon CMOS cameras and Sony CCD LineScan camera were used to study photometric properties of the lunar nearside in several spectral bands. A wide range of lunar phase angles was covered, and the method of phase ratios to assess the steepness of the phase function at different phase angles is applied. We found several areas with photometric anomalies in the south-west portion of the lunar disk that we refer to as Oceanus Procellarum anomalies. The areas being unique on the lunar nearside do not obey the inverse correlation between albedo and phase-curve slope, demonstrating high phase-curve slopes at intermediate albedo. Low-Sun images acquired with Lunar Orbiter IV and Apollo-16 cameras do not reveal anomalous topography of the regions, at least for scales larger than several tens of meters. The areas also do not have any thermal inertia, radar (70 and 3.8 cm), magnetic, or chemical/mineral peculiarities. On the other hand they exhibit a polarimetric signature that we interpret to be due to the presence of a porous regolith upper layer consisting of dust particles. The anomalies may be interpreted as regions of very fresh shallow regolith disturbances caused by impacts of meteoroid swarms consisting of rather small impactors. This origin is similar to one of the hypotheses for the origin of lunar swirls like the Reiner-γ formation. The photometric difference between the shallow and pervasive (Reiner-γ class) swirls is that the latter appear to have a significant amount of immature soils in the upper surface layers.

Sources of sodium in the lunar exosphere: Modeling using ground-based observations of sodium emission and spacecraft data of the plasma

Observations of the equatorial lunar sodium emission are examined to quantify the effect of precipitating ions on source rates for the Moon’s exospheric volatile species. Using a model of exospheric sodium transport under lunar gravity forces, the measured emission intensity is normalized to a constant lunar phase angle to minimize the effect of different viewing geometries. Daily averages of the solar Lyman α flux and ion flux are used as the input variables for photon-stimulated desorption (PSD) and ion sputtering, respectively, while impact vaporization due to the micrometeoritic influx is assumed constant. Additionally, a proxy term proportional to both the Lyman α and to the ion flux is introduced to assess the importance of ion-enhanced diffusion and/or chemical sputtering. The combination of particle transport and constrained regression models demonstrates that, assuming sputtering yields that are typical of protons incident on lunar soils, the primary effect of ion impact on the surface of the Moon is not direct sputtering but rather an enhancement of the PSD efficiency. It is inferred that the ion-induced effects must double the PSD efficiency for flux typical of the solar wind at 1 AU. The enhancement in relative efficiency of PSD due to the bombardment of the lunar surface by the plasma sheet ions during passages through the Earth’s magnetotail is shown to be approximately two times higher than when it is due to solar wind ions. This leads to the conclusion that the priming of the surface is more efficiently carried out by the energetic plasma sheet ions.

Celestial body irradiance determination from an underfilled satellite radiometer: application to albedo and thermal emission measurements of the Moon using CERES

The Clouds and the Earth's Radiant Energy System (CERES) is a program that measures the Earth radiation budget (ERB) from two polar orbiting satellite platforms. CERES radiometers are designed to make stable broadband measurements of scattered solar and emitted thermal radiative flux leaving Earth with an accuracy of 1% or better. Using versatile and programmable scan modes, it is also possible for every CERES instrument to view the Moon on each orbit. However, until now, it has not been possible to derive absolute measurements of lunar irradiance using CERES because the Moon's disk fills only 10% of the telescope field of view. This work presents a method of integrating CERES raster-scan data in order to obtain a measurement of the average scattered solar and emitted thermal radiance from the entire lunar disk. The technique results in excellent agreement between CERES instruments on different satellites as to lunar albedo and emitted thermal flux. The average broadband Moon albedo is measured by CERES at a value of 0.1362 (+/-2-3%) when normalized to a static lunar phase angle of 7 degrees using the U.S. Geological Survey lunar irradiance Robotic Lunar Observatory model. The method for the first time also yields very accurate measurements of the thermal irradiance emitted from the Moon. These suggest an average long-wave flux of 977 Wm(-2) (+/-2-3% at 7 degrees phase), implying an approximate mean surface temperature of around 92 degrees C. Statistical analysis on available data suggests that a CERES instrument performing monthly lunar measurements could utilize the Moon as a stability target and reduce calibration drifts to 0.3% per decade or less within an instrument's lifetime. Given the success of the technique, a solar calibration system is proposed that will allow precise tracking of an ERB instrument's optical degradation using the Sun.

Observing the Moon at Microwave Frequencies Using a Large-Diameter Deep Space Network Antenna

The Moon radiates energy at infrared and microwave wavelengths, in addition to reflecting sunlight at optical wavelengths. As a result, an antenna pointed at or near the Moon will result in an increase in system operating noise temperature, which needs to be accounted for in RF telecommunications, radio science or radiometric link calculations. The NASA Deep Space Network (DSN) may use its large-diameter antennas in future lunar robotic or human missions, and thus it is important to understand the nature of this temperature increase as a function of observing frequency, lunar phase, and angular position of the antenna beam on the lunar disk. This paper reports on a comprehensive lunar noise temperature measurement campaign and associated theoretical treatment for a 34-m diameter Deep Space Network antenna observing an extended source such as the Moon. A set of measurements over a wide range of lunar phase angles was acquired at DSS-13, a 34-m diameter beam waveguide antenna (BWG) located at Goldstone, California at 2.3 GHz (S-band), 8.4 GHz (X-band) and 32 GHz (Ka-band). For validation purposes, independent predictions of noise temperature increase were derived using a physical optics characterization of the 34-m diameter antenna gain patterns and Apollo model-based brightness temperature maps of the Moon as input. The model-based predictions of noise temperature increase were compared with the measurements at all three frequencies. In addition, a methodology is presented that relates noise temperature increase due to the Moon to disk-centered or disk-averaged brightness temperature of the Moon at the microwave frequencies of interest. Comparisons were made between the measurements and models in the domain of lunar disk-centered and disk-averaged brightness temperatures. It is anticipated that the measurements and associated theoretical development will be useful in developing telecommunications strategies for future high-rate Ka-band communications where large diameter DSN antennas will be required.

Lunar numerical theory and determination of parametersk2, $\delta_M$ from analysis of LLR data

Analysis of lunar ranging data of 1970–2001 was carried out to estimate values of the lunar phase angle and Love's number . The Moon's dynamic theory has been constructed by simultaneous numerical integration of equations of motion of the major and minor planets and the Moon with equations of lunar librations. Partial derivatives with respect to estimated parameters were obtained following the method of arbitrary constant varying.

Precise relative calibration of Earth-orbiting remote sensors, using the Moon

An observation strategy is described that uses the Moon to monitor the radiometric stability of Earthorbiting remote-sensing instruments without requiring precise lunar-radiance measurements over the full range of lunar cycles. The Moon can be used as a constant irradiance reference for monitoring on-orbit shifts in instrument responsivity if (i) the Moon is observed at equivalent phase angles, (ii) the Moon is observed at equivalent sensorMoon libration angles, (iii) the Moon is observed at equivalent Sun-Moon libration angles, and (iv) the Moon is observed at equivalent scan rates and aspect angles. Irradiance changes due to changes in Sun-to-Moon and Moon-to-sensor distance can be precisely computed from ephemerides using inverse square scaling. A preliminary model of libration effects being developed by the United States Geological Survey from Clementine lunar-orbiter measurements was used to evaluate the effects of lunar libration in the 400 nm to 1000 nm spectral region. If the satellite platform can be rotated to view the Moon from a position in the orbit that exactly provides the required lunar phase angle, lunar-irradiance levels for 48 of the 75 lunar cycles in the 1994-1999 epoch examined can be matched to within 0.1 %. All lunar cycles in the epoch have at least one match to within 0.27 %. A pixel integration procedure that minimizes calibration uncertainties due to sensor pointing and optics contamination is presented and evaluated for the NASA Earth Observing System (EOS) Moderate Resolution Imaging Spectroradiometer (MODIS). The total combined relative uncertainties between suitable lunar reference pairs are expected to be less than 1 %.

Submicron lunar ejecta in the magnetosphere associated with meteor showers

Recent studies of the lunar ejecta from lunar impacts of interplanetary dust particles indicate that during favorable lunar phases, over 80% of the submicron ejecta enters the earth's magnetosphere. This “pulse” of lunar ejecta produced by the sporadic meteor background will follow the random variations of the sporadic flux. An additional enhancement of this flux can be related to major meteor showers. Since the annual periods of these showers occur during varying lunar phase angles, magnetosphere ejecta flux associated with major showers will vary depending on the coincidence of shower periods and favorable lunar phase angles. The results of an analysis of the “pulse” of ejecta flux in the magnetosphere during the Quadrantids, Geminids, Leonids, and Perseids meteor showers are presented. These results are compared to the satellite measurements of 1959 Eta and HEOS II.

Polarization–Albedo Relationship for Selected Lunar Regions

I HAVE tested the accepted theory that there is a strong inverse relationship between brightness and polarization on the lunar surface, by measuring the polarization of several examples of “pure” maria (dark and light), highlands and mountains in five passbands with a photoelectric Wollaston polarimeter. The effective central wavelengths were 3360 A, 3640 A, 3830 A, 4500 A and 5340 A and the bandwidths (half-response points) ranged from 330 to 560 A. The short wavelengths are uncertain (± 30 A) because of unknown atmospheric extinction. Observations of the 30 s of arc diameter regions were made within a sufficiently short period of time during each observing session that the lunar phase angle (−107°) did not change by more than ±1.5°. The probable error was ±0.06 per cent in polarization. The observations were made on June 14, 1967, and May 4, 1968, UT. Some of the regions were measured on both dates.