The geometric albedo of an astronomical body is the ratio of its actual brightness at zero phase angle (i. Phase angle in astronomical observations is the angle between the light incident onto an observed object and the light reflected from the object 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 reflection is the reflection of Light from an uneven or granular surface such that an incident ray is seemingly reflected at a number of angles See also Lambert's cosine law If a surface exhibits Lambertian reflectance, light falling on it is scattered such that the apparent brightness of the surface to an observer
Diffuse scattering implies that radiation is reflected isotropically with no memory of the location of the incident light source. Diffuse reflection is the reflection of Light from an uneven or granular surface such that an incident ray is seemingly reflected at a number of angles 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. Opposition is a term used in Positional astronomy and Astrology to indicate when one celestial body is on the opposite side of the sky when viewed from The ecliptic is the apparent path that the Sun traces out in the sky during the year
The visual geometric albedo refers to the geometric albedo quantity when accounting for only electromagnetic radiation in the visible spectrum. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter.
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Airless bodies
The 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 diffusively. Regolith ( Greek: "blanket rock" is a layer of loose Heterogeneous material covering solid rock. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. The opposition effect (also opposition spike, or opposition surge) is the brightening of a rough surface or an object with many particles when illuminated from directly
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 bidirectional reflectance distribution function ( BRDF; {f_r(\omega_i, \omega_o\ } is a 4-dimensional function that defines how light is reflected at 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 node of their orbit and hence lie on the ecliptic. Opposition is a term used in Positional astronomy and Astrology to indicate when one celestial body is on the opposite side of the sky when viewed from An orbital node is one of the two points where an Orbit crosses a Plane of reference which it is inclined to The ecliptic is the apparent path that the Sun traces out in the sky during the year In practice, measurements at small nonzero phase angles are used to derive the Hapke parameters for the body. The Hapke parameters are a set of parameters for a quasi-experimental model that are commonly used to describe the directional reflectance properties of the airless Regolith 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 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. TemplateInfobox Planet.--> This article is about the moon of TemplateInfobox Planet.--> Tethys (ˈtiːθɨs, /ˈtɛθɨs/, or The Bond albedo is the fraction of power in the total electromagnetic radiation incident on an astronomical body that is scattered back out into space The opposition effect (also opposition spike, or opposition surge) is the brightening of a rough surface or an object with many particles when illuminated from directly 4 in the case of Enceladus) [2]. 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. Angle of incidence is a measure of deviation of something from "straight on" for example in the approach of a ray to a surface or the angle The geometric albedo above unity means that the intensity of light scattered back 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. The albedo of an object is the extent to which it diffusely reflects light from the sun In Geometry, two lines or planes (or a line and a plane are considered perpendicular (or orthogonal) to each other if they form congruent
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 [3]:
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Name Bond Albedo Geometric albedo Mercury 0. 119 0. 138 Venus 0. The VENUS ( V ictoria E xperimental N etwork U nder the S ea project is a cabled sea floor observatory operated by the University 75 0. 84 Earth 0. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 29 0. 367 Moon 0. 123 0. 113 Mars 0. 16 0. 15 Enceladus 0. TemplateInfobox Planet.--> This article is about the moon of 99 1. 4 [4] Pluto 0. 4 0. 44-0. 61
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See also
References
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- NASA JPL glossary
- K. Anisotropy (pronounced with stress on the third syllable ˌænaɪˈsɒtrəpi is the property of being directionally dependent as opposed to Isotropy, which means homogeneity In the world of 3D computer graphics and visualisation there exist many methods of representing how light sources interact with other objects in a virtual scene P. Seidelmann, Ed. (1992) Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, California.
- ^ See for example this discussion of Lunar albedo by Jeff Medkeff.
- ^ See the discussion here for an explanation of this unusual value.
- ^ Albedo of the Earth
- ^ See the discussion here for explanation of this unusual value above one.
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