Two Tricks of Light Make the Full Moon Brighter Than It Should Be

Follow the Moon through a month and its brightness does something that simple arithmetic cannot account for. It climbs as the lit crescent fattens, roughly in step with the growing area of sunlit ground. Then, in the last few degrees before the Sun, Earth, and Moon fall into line, it jumps. A full Moon is brighter than its own geometry allows. Astronomers call that jump the opposition effect, and it appears on every airless, dusty surface they have looked at.

Why it happens has been argued over for decades, and the argument is about proportions rather than kinds. Two effects are known to be at work. The first is shadow hiding. Soil grains cast shadows on one another, and those shadows are much of what makes a rough surface look dark. As the illumination swings around to sit directly behind the observer, each shadow slips out of sight behind the grain that cast it, and the surface brightens. The second is coherent backscatter, a wave effect rather than a geometric one. Light that threads a tangled path through the dust and light that runs the identical path backward emerge in step with each other. They interfere constructively, piling up a narrow spike of brightness aimed straight back at the source.

Bruce Hapke argued the case for the second in Science in 1993, and his scattering model has been the standard tool for the problem ever since. Telling the two apart in real data has been harder. They overlap in angle: coherent backscatter narrowly, shadow hiding across a broader span. Phase curves assembled from the ground carry the atmosphere's own variability, and curves stitched together from different instruments carry each instrument's calibration.

One exposure, the whole Moon, no atmosphere in the way

A team led from the Chinese Academy of Sciences has now pulled the two apart from an unusual vantage point. Siyuan Li, Yunzhao Wu and colleagues took full-disk images of the Moon recorded by GaoFen-4, China's first high-resolution optical Earth-observation satellite in geostationary orbit. It is a civil remote-sensing spacecraft, not a weather satellite. Their paper appeared online Aug. 28 in The Planetary Science Journal, and the analysis fits those images within a regularized version of Hapke's framework, using both Bayesian sampling and conventional optimization. The group has measured the Moon's brightness with GaoFen-4 before; what is new here is the partition between the two mechanisms, and what it implies about the soil.

Geostationary orbit buys two things here. The satellite sits above the atmosphere, so the haze and water vapor that distort brightness measurements from the ground are simply absent. And its camera catches the whole lunar disk in a single exposure, which puts bright highlands and dark maria on one radiometric scale at one instant. That beats building a comparison out of frames taken at different times through different air. The images run from within 3.7 degrees of exact opposition out past quarter phase, in four bands from green through the near-infrared. The Moon repays the attention: it is also used the other way around, as a calibration target for GaoFen-4's own camera.

Physically admissible fits require both mechanisms, the authors report; neither on its own reproduces the curves. Then come the shares. From the visible to the near-infrared, the fraction of the zero-phase peak attributed to coherent backscatter rises from about 52 percent to about 64 percent, and the angular window in which it dominates widens from roughly 2.5 degrees to 17.7.

Those are inferences, not readings. Nobody observes the Moon at exactly zero phase (that alignment is a lunar eclipse), so the zero-phase values are extrapolated from the fitted curves and then corrected for the Sun being a disk rather than a point. Fitted Hapke parameters are slippery besides, and this paper's own reference list carries studies devoted to how much uncertainty one really holds. What the work delivers is a well-constrained partition inside a standard model, which is a different kind of claim from a direct measurement.

What the widths say about the dust

The widths of the two components are where the geology enters. How wide the shadow-hiding peak is depends on how densely the grains are packed; how wide the coherent-backscatter peak is depends on the size of the structures doing the scattering. Put through the fits, the uppermost optically active layer of lunar soil, the thin skin the light actually samples, comes out about 69 percent empty space, give or take four points. That is well above the value usually quoted for lunar regolith in bulk, which is nearer half. The gap is the finding rather than a discrepancy: the very top of the soil is a far more open structure than anything a core sample brings up.

The structures themselves come out smaller than the grains. The fits give coherent-backscatter length scales of roughly 280 to 460 nanometers, below the wavelengths being observed, which is the regime the mechanism requires. The authors take that to favor sub-grain heterogeneity over the spacing between particles: the interference is happening on texture inside individual grains, not in the gaps between them.

The two great lunar terrains behave differently. Highlands are brighter and scatter light more strongly back toward its source, while the dark maria show a narrower but relatively stronger opposition surge. The authors read that as consistent with the iron-rich basalts of the maria producing more agglutinitic glass and nanophase iron: soil welded together by micrometeorite impacts, speckled with iron grains far too small to see. Consistent with, they write, not demonstrated by.

A place where somebody has already been

The strongest check sits in Mare Imbrium, where China's Chang'e-3 lander set down and measured the soil's optical behavior from a few steps away. At that site the phase curve derived from geostationary orbit, and a relative coherent-backscatter share of about 79 percent, line up with what the lander's instruments found on the less disturbed ground nearby. A camera in Earth orbit and an instrument standing on the Moon, describing the same dust in the same terms, is the sort of agreement that makes the remote version worth carrying elsewhere.

That is what the paper is finally offering: a lunar reference for opposition photometry of airless bodies. The Moon is the one such surface where orbiters, landers and returned samples can all be aimed at the same patch of ground. That makes it the yardstick for everything that cannot be visited: an asteroid brightening as a spacecraft swings toward opposition, or a small outer moon that is never more than a point of light. Read against a curve whose two mechanisms have been separated, and whose wavelength dependence has been written down, those brightenings become statements about soil. The wavelength trend is also the part of this result standing most nearly alone: no independent dataset has tested it yet, and it is exactly the kind of claim another instrument can go and check.