# Geometric albedo

The geometric albedo of an astronomical body is the ratio of its actual brightness at zero phase angle (i.e. as seen from the light source) to that of an idealized flat, fully reflecting, diffusively scattering (Lambertian) disk with the same cross-section.

Diffuse scattering implies that radiation is reflected isotropically with no memory of the location of the incident light source. Zero phase angle corresponds to looking along the direction of illumination. For Earth-bound observers this occurs when the body in question is at opposition and on the ecliptic.

The visual geometric albedo refers to the geometric albedo quantity when accounting for only electromagnetic radiation in the visible spectrum.

## Airless bodies

The surface materials (regoliths) of airless bodies (in fact, the majority of bodies in the Solar System) are strongly non-Lambertian and exhibit the opposition effect, which is a strong tendency to reflect light straight back to its source, rather than scattering light diffusely.

The geometric albedo of these bodies can be difficult to determine because of this, as their reflectance is strongly peaked for a small range of phase angles near zero.[1] The strength of this peak differs markedly between bodies, and can only be found by making measurements at small enough phase angles. Such measurements are usually difficult due to the necessary precise placement of the observer very close to the incident light. For example, the Moon is never seen from the Earth at exactly zero phase angle, because then it is being eclipsed. Other Solar System bodies are not in general seen at exactly zero phase angle even at opposition, unless they are also simultaneously located at the ascending or descending node of their orbit, and hence lie on the ecliptic. In practice, measurements at small nonzero phase angles are used to derive the parameters which characterize the directional reflectance properties for the body Hapke parameters. The reflectance function described by these can then be extrapolated to zero phase angle to obtain an estimate of the geometric albedo.

For very bright, solid, airless objects such as Saturn's moons Enceladus and Tethys, whose total reflectance (Bond albedo) is close to one, a strong opposition effect combines with the high Bond albedo to give them a geometric albedo above unity (1.4 in the case of Enceladus). Light is preferentially reflected straight back to its source even at low angle of incidence such as on the limb or from a slope, whereas a Lambertian surface would scatter the radiation much more broadly. The geometric albedo above unity means that the intensity of light scattered back per unit solid angle towards the source is higher than is possible for any Lambertian surface.

## Equivalent definitions

For the hypothetical case of a plane surface, the geometric albedo is the albedo of the surface when the illumination is provided by a beam of radiation that comes in perpendicular to the surface.

## Examples

The geometric albedo may be greater or smaller than the Bond albedo, depending on surface and atmospheric properties of the body in question. Some examples:[2]

Name Bond albedo Visual geometric albedo
Mercury 0.119

0.138

Venus[3] 0.90

0.67

Earth[4] 0.306

0.367

Moon 0.123

0.113

Mars[5] 0.25

0.15

Jupiter[6] 0.343

0.52

Saturn[7] 0.342

0.47

1.4

Uranus[9] 0.300

0.51

Neptune[10] 0.290

0.41

Pluto 0.4

0.44–0.61

Eris 0.96

## References

• NASA JPL glossary
• K.P. Seidelmann, Ed. (1992) Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, California.
1. ^ See for example this discussion of Lunar albedo by Jeff Medkeff.
2. ^ Albedo of the Earth
3. ^ Mallama, A.; Wang, D.; Howard, R.A. (2006). "Venus phase function and forward scattering from H2SO4". Icarus 182: 10–22. Bibcode:2006Icar..182...10M. doi:10.1016/j.icarus.2005.12.014.
4. ^ Williams, David R. (2004-09-01). "Earth Fact Sheet". NASA. Retrieved 2010-08-09.
5. ^ Mars Fact Sheet, NASA
6. ^ Jupiter Fact Sheet, NASA
7. ^ Saturn Fact Sheet, NASA
8. ^ See the discussion here for explanation of this unusual value above one.
9. ^ Uranus Fact Sheet, NASA
10. ^ Neptune Fact Sheet, NASA