81.1162L THE ASTRONOMICAL JOURNAL VOLUME 81, NUMBER 12 DECEMBER 1976 Far-ultraviolet albedo of the Moon 1976AJ R. L. Lucke, R. C. Henry, and W. G. Fastie Department of Physics, Johns Hopkins University, Baltimore, Maryland 21218 (Received 28 May 1976; revised 21 September 1976) The albedo and photometric function of the Moon have been measured between 121.6 and 168.0 nm by comparing the brightness of the Moon, observed with an orbiting far-ultraviolet spectrometer during the Apollo 17 mission, to the solar brightness observed simultaneously from a sounding rocket. The instruments were carefully cross calibrated. In contrast to what is found in the visible and the near ultraviolet, the brightness of the Moon is found to increase toward shorter wavelengths; the Moon is “blue” in the far ultraviolet. This is confirmed by new laboratory study of lunar samples. A brief review of lunar albedo measurements in the 120-600-nm range is given. INTRODUCTION Moon’s surface is adequately described by the photo- metric functions of Hapke (1963), later modified for LUCKE, Henry, and Fastie (1973) have improved accuracy near grazing incidence (Hapke l reported in these pages laboratory measurements of 1966). Since the observations of the present experiment the far-ultraviolet reflectivity of lunar fines (dust) ob- did not come close to grazing incidence (the observation tained during the Apollo 11,12, and 14 missions. They angle was always close to 30° from the vertical), the deduced, by comparing their result with existing direct 1963 version of the photometric function is quite ade- measurements of the lunar brightness, that most pre- quate: The amount of light (e.g., in photons/sec) received viously reported far-ultraviolet lunar albedo determi- by a detector of area a from a patch of the Moon’s sur- nations had given much too low a value. face subtending a solid angle du is (Hapke 1963): In the present paper, a direct measurement of the lunar far-ultraviolet albedo obtained during the Apollo /(/, 6, a) = hadub — ^ ; 2(a)B(a, g), (1) 17 mission is presented, and more accurate results on 1 + cos 6/ cos i lunar samples, now including samples from Apollo 17, are described. Both types of new data support the pre- where vious conclusion: If anything, the lunar far-ultraviolet i = angle between surface normal and direction of light albedo is somewhat higher than we have previously source, 0° < / < 90°. claimed. e = angle between surface normal and direction to de- tector, 0° < € < 90°. I. LUNAR ORBITAL OBSERVATIONS a = angle between directions of incidence and observa- tion, 0° < a < 180°. The lunar observations discussed here were made using a scanning far-ultraviolet spectrometer, sensitive /o = intensity of incident radiation (e.g., photons/sec per unit area normal to direction of incidence). in the 118-168-nm range, which was mounted in the b = total average reflectivity of the individual dust Service Module of the Apollo 17 spacecraft on the lunar grains, i.e., ratio of light reflected to light incident av- mission of December 1972. The instrument has been eraged over many grains. described in detail by Fastie (1973). The prime objective 2(a) = average scattering law of the individual grains. of this experiment was detection of lunar atmospheric It is assumed that the grains have random orientations species by observing resonant reradiation of sunlight. No so that, on the average, this is a function of a only. 2(a) lunar atmosphere was detected (Fastie et al. 1973), but is normalized so that during the period in lunar orbit, the instrument spent many hours (approximately 1 h on each of 37 different orbits over a span of five days), observing the sunlit r 7T sin ad a = 1, (2) hemisphere of the Moon with precisely known viewing geometry. The instrumental line of sight was directed toward the Moon, and made an angle of about 30° with and the differential cross section is therefore èS(a). the local vertical. The 11.°65 square field of view inter- g = the “compaction parameter,” a measure of the cepted, roughly, a 30 X 30-km2 patch (about Io X Io in looseness of the packing of the soil. Small g implies lunar latitude and longitude) on the lunar surface. low-density packing. The scattering of visible light from a patch of the B(a, g) = the “retrodirective function,” which describes 1162 © American Astronomical Society • Provided by the NASA Astrophysics Data System 81.1162L FAR-ULTRAVIOLET ALBEDO OF THE MOON 1163 the Moon’s well-known backscattering properties. Ex- (3) and (5), and the relevant values for /, 6, and a ob- plicitly, tained from aspect data, normalizing for best fit. 1976AJ The displacement of the peak of the theoretical curve an tan slightly to the east of the experimental curve does not B{a, g) = 2~ (1 - e-?/‘ “)(3 - e-?/ “), 2g represent a failure of the theoretical photometric func- tion, which is intended only to describe the Moon’s av- “"7 erage reflection properties. The peak of the light curve (3) on orbit 29 occurs just as the field of view crosses onto Mare Crisium from the highlands to the east. Since, in far-ultraviolet light, maria reflect about 5%-10% more than terrae (Henry et al 1976; Lucke 1975; Lucke et al Most of the Moon’s surface can be characterized by 1974), this enhances the experimental curve to the west g — 0.7 in the visible and this value also works well in the of the peak of the theoretical curve, and relatively, de- far ultraviolet. presses it to the east. The slight crook in the theoretical The 2(a) that must be used in Eq. (1) to give a good curve at about 79° E is a result of a small maneuver of fit to optical photometric data is (Hapke 1963) the spacecraft. The rapid local variations in the experi- mental curve are caused by differences in the complex index of refraction of the surface (e.g., a mare-terra . 30 f sin a + (tt — a) cos a 2,(a) - TT- difference) and, especially near the terminators, by oItt L tt shadowing. This index-of-refraction dependence has 2 been discussed elsewhere (references above, especially + 0.1(1-cos a) J, (4) Henryk a/. 1976). The overall fit of the theoretical to the experimental curve (excluding local albedo variations) is seen to be where the 30/6 Itt factor is inserted to satisfy the nor- quite good: The most serious difference occurs eastward malization condition of Eq. (2). of about 120° E where the theoretical curve falls a little The only modification that is required in Eq. (1) to low. The theoretical photometric function has not been obtain a photometric function that gives a good fit to the adjusted to improve the fit, partly because this would far-ultraviolet reflectance data gathered in this experi- spoil the relative simplicity of the single-particle scat- ment is the substitution of a different “single-particle” tering law given in Eq. (5), but also because there are average scattering law 2(a) in Eq. (1). No modification other difficulties that make such a comparatively fine is required in the retrodirective function Æ(a, 0.7) (Eq. adjustment unjustified. The most serious of these is the 3). This should certainly be the case, because Moon dust limited range of the photometric function’s independent grains are generally ä; 10 in size and this is considerably variables—i, e, and a—that were covered in these ob- larger than a wavelength of either ultraviolet or visible servations. The situation is not too bad for /, which varied light. Therefore, both kinds of radiation should “see” the over the range 5° ;S / ;S 75° (larger values of i were ob- same surface microstructure, and this is what determines served, but were too heavily contaminated by near-ter- 5(a, g). The single-particle scattering law that was minator shadowing to be useful), and a (10° ;S a ;S found to fit the ultraviolet data is 100°), but, as already noted, e — 30° always. Also, the values of i and a were related by the spacecraft’s orbit, 22(a) = — so that only a single line in the /, a plane was covered on OTT each orbit. Furthermore, the locus of points on this line sin a + (tt — a) cos a 2 in the /, a plane remained nearly constant throughout X (1-0.32 sin a) , (5) the mission because precession of the orbital plane of the P ]• spacecraft very nearly matched the apparent motion of where again the S/ött factor is for normalization. the Sun in the lunar sky, so that orientation of the Sun An example of the fit provided to the ultraviolet data relative to the orbital plane of the spacecraft changed by substituting Eqs. (5) and (3) into Eq. (1) is given in only slightly. All this constitutes an important caveat in Fig. 1, which shows the light curve obtained during one the use of the far-ultraviolet photometric function given orbit (orbit 29) in the wavelength interval 146-148 nm. here, but the fit shown in Fig. 1 indicates that it should The instrument’s response, shown by the jagged line, rose be accurate enough to be useful. from, effectively, zero as it was carried across the sunrise The photometric functions may be used to write the terminator (here at about 180° E), reached a maximum expression for the total amount of light received by a at about 68° E, where the angle a, as defined above, had wide-angle detector (e.g., the human eye) from the entire its minimum value (a — 10° in this case), and then fell Moon.