Geometric albedo
Encyclopedia
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
.
s) 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. 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
. 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.
of the surface when the illumination is provided by a beam of radiation that comes in perpendicular
to the surface.
Phase angle (astronomy)
Phase angle in astronomical observations is the angle between the light incident onto an observed object and the light reflected from the object...
(i.e., as seen from the light source) to that of an idealized flat, fully reflecting, diffusively scattering
Diffuse reflection
Diffuse reflection is the reflection of light from a surface such that an incident ray is reflected at many angles rather than at just one angle as in the case of specular reflection...
(Lambertian) disk with the same cross-section.
Diffuse scattering
Diffuse reflection
Diffuse reflection is the reflection of light from a surface such that an incident ray is reflected at many angles rather than at just one angle as in the case of specular reflection...
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
Opposition (astronomy)
In positional astronomy, two celestial bodies are said to be in opposition when they are on opposite sides of the sky, viewed from a given place . In particular, two planets are in opposition to each other when their ecliptic longitudes differ by 180°.The astronomical symbol for opposition is ☍...
and on the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
.
The visual geometric albedo refers to the geometric albedo quantity when accounting for only electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
in the visible spectrum
Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
.
Airless bodies
The surface materials (regolithRegolith
Regolith is a layer of loose, heterogeneous material covering solid rock. It includes dust, soil, broken rock, and other related materials and is present on Earth, the Moon, some asteroids, and other terrestrial planets and moons.-Etymology:...
s) of airless bodies (in fact, the majority of bodies in the Solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
) 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
Bidirectional reflectance distribution function
The bidirectional reflectance distribution function is a four-dimensional function that defines how light is reflected at an opaque surface...
is strongly peaked for a small range of phase angles near zero. 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
Opposition (astronomy)
In positional astronomy, two celestial bodies are said to be in opposition when they are on opposite sides of the sky, viewed from a given place . In particular, two planets are in opposition to each other when their ecliptic longitudes differ by 180°.The astronomical symbol for opposition is ☍...
, unless they are also simultaneously located at the ascending node of their orbit and hence lie on the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
. 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
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...
's moons Enceladus
Enceladus (moon)
Enceladus is the sixth-largest of the moons of Saturn. It was discovered in 1789 by William Herschel. Until the two Voyager spacecraft passed near it in the early 1980s very little was known about this small moon besides the identification of water ice on its surface...
and Tethys
Tethys (moon)
Tethys or Saturn III is a mid-sized moon of Saturn about across. It was discovered by G. D. Cassini in 1684 and is named after titan Tethys of Greek mythology. Tethys is pronounced |Odysseus]] is about 400 km in diameter, while the largest graben—Ithaca Chasma is about 100 km wide and...
, whose total reflectance (Bond albedo
Bond albedo
The Bond albedo, named after the American astronomer George Phillips Bond , who originally proposed it, is the fraction of power in the total electromagnetic radiation incident on an astronomical body that is scattered back out into space...
) 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
Angle of incidence
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 at which the wing or horizontal tail of an airplane is installed on the fuselage, measured relative to the axis of the fuselage.-Optics:In geometric...
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 albedoAlbedo
Albedo , or reflection coefficient, is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it...
of the surface when the illumination is provided by a beam of radiation that comes in perpendicular
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...
to the surface.