Lunar Albedo

by Jeff Medkeff

A lot of confusing statements are made about the albedo of the moon. The moon is, according to various accounts, "darker than blacktop" or "darker than a black sheet of construction paper." These are oversimplifications - neither blacktop or construction paper have the special characteristics of the moon. Besides, both materials can be found in colors that actually range from light gray to nearly black, so unless you specify a brand of construction paper, or a particular mile of highway, the assertion is next to meaningless even if it weren't untrue.

Albedo is given in a variety of definitions, and the blacktop analogy is the result of the unwitting abuse of a couple of such definitions. Without knowing the definition that is used, its impossible to be sure you are comparing apples to apples. The simplest version of albedo is the Lambert albedo. A Lambert surface is one which scatters light isotropically - in other words, an equal intensity of light is scattered in all directions; it doesn't matter whether you measure it from directly above the surface or off to the side. The photometer will give you the same reading.

For a lambert planetary surface, the illumination effects are entirely geometric. The brightest illumination is directly below the sun, and the amount of light reflected diminishes the farther you get from this point, simply because the sunlight is played along a greater arc of the surface. The illumination isophotes will be round. Unfortunately, the moon is not a Lambert surface.

For one thing, the subsolar point does not provide the brightest reflection - the limb does. And the phase curve has a sharp peak in brightness during full moon - the moon is extra reflective at full compared to first quarter. Attempts were once made to explain this in terms of a Lambert surface with various kinds of topography, but this does not work out.

It is now known that this departure from a Lambert surface is caused by the very porous first few millimeters of the lunar regolith. Sunlight can penetrate the surface and illuminate subsurface grains, the scattered light from which can make its way back out in any direction. At full phase, all such grains cover their own shadows; the dark shadows being covered by bright grains, the surface is brighter than normal.

The picture is further complicated by the fact that the perfectly full moon is never visible from Earth (at such times, the moon is eclipsed). From the Apollo missions, we know that the exact subsolar point - in effect, the fullest possible moon - is some 30% brighter than the fullest moon seen from earth. It is thought that this is caused by glass beads formed by impact in the lunar regolith, which tend to reflect light in the direction from which it comes. This light is therefore reflected back toward the sun, bypassing earth.

The original definition of albedo, proposed by Bond, is the ratio of total solar radiation scattered from a body to the radiation incident upon it. The Bond albedo of the moon is 11%. But limiting this figure to V-band radiation produces quite a different value. The average visual Bond albedo of the earth-facing side of the moon is 7.2%.

This is what has led to the often repeated statement that the moon is blacker than even very black terrestrial materials. Flocked paper, often used in light traps and as telescope darkening material, has an albedo of about 6%, for example. But the low Bond albedo of 7.2% is the result of the porous upper layers, which cast shadows over a substantial percentage of the visible surface. No common terrestrial material has a similar layer, so it isn't useful for comparison purposes. So the black construction paper theory and the asphalt theory simply have to be abandoned.

Another definition is the visual geometric albedo, which is the proportion of visible light received from an illuminated body at zero phase angle to that which would be received by a Lambert surface in the same position. For the moon, the full moon problem again intrudes. The visual geometric albedo of the full moon is 12.5%, but much less at other phases.

Because it is very difficult to measure this value, the visual geometric albedo at 5% phase angle is often used instead. That should be self-explanatory; the value for the moon is about 8.4%. But it can't be used to compare with terrestrial materials for the same reason the Bond albedo cannot.

Yet another definition - and by far the most useful for observers - is the visual normal albedo. This is the ratio between the brightness of a given area of an illuminated body at zero phase angle and oriented normal to the incident light, to that of a plane white Lambert surface similarly oriented. But normal incidence is never seen from earth (remember, the moon would be eclipsed), so they've introduced the "normal albedo at 5% phase angle" instead - which is a contradiction in terms, but I suppose we know what it is supposed to mean.

The following is a list of the "visual normal albedo at 5% phase angle" of various lunar features. These numbers can be used to directly compare to terrestrial surfaces (reference cited below):

Darkest areas:  8.6%
Tranquillitatis south of Plinius: 9.1%
Plato's floor: 9.6%
Serenitatis east of Linne: 10%
Imbrium south of Plato: 10.4%
Nectaris: 11.4%
Ptolemaeus floor: 13.1%
Arzachel: 17%
Tycho ejecta: 20%
Aristarchus: 20%
Aristarchus interior: 22%
Bright spot in Deslandres: 24%
Proclus E wall: 28%
Stevinus A, Abulfeda E: 30%

These values are, as you can see, considerably higher than the other lunar albedos given. For comparison, the albedo of a green golf course is about 13%, roughly the same as that of the Cayley Formation which covers the floor of Ptolemaeus. So you see, the moon is not quite as dark as is often claimed - something about in the middle range of lunar brightnesses is just as bright as a grassy yard at noon.

Ref: British Astronomical Association, Guide to Observing the Moon, Enslow 1986

part of Jeff Medkeff's Notes on Lunar Features
Jeff Medkeff's home page.
Jeff's astronomy pages.
Copyright © Jeff Medkeff, 2002, All Rights Reserved.