Bond albedo

Bond albedo

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The Bond albedo, named after the American astronomer George Phillips Bond
George Phillips Bond
George Phillips Bond was an American astronomer. He was the son of William Cranch Bond. Some sources give his year of birth as 1826....

 (1825–1865), who originally proposed it, is the fraction of power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

 in the total electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

 incident on an astronomical body that is scattered back out into space. It takes into account all wavelengths at all phase angles
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...


It is an important quantity for characterizing a planetary body's energy balance.

For objects in the Solar System, the relevant weighting of each wavelength is proportional to the solar-power spectrum
Sunlight, in the broad sense, is the total frequency spectrum of electromagnetic radiation given off by the Sun. On Earth, sunlight is filtered through the Earth's atmosphere, and solar radiation is obvious as daylight when the Sun is above the horizon.When the direct solar radiation is not blocked...

. Visible light is a major contribution because over 40% of solar output is in this range.

Like most albedo
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...

s, the Bond albedo is a value between 0 and 1.

Because bodies in the outer Solar System are always observed at very low phase angles from the Earth, the only reliable data for measuring their Bond albedo comes from spacecraft.

The Bond albedo was originally defined for spherical bodies, but is also applicable for irregular objects.

Phase integral

The Bond albedo (A) is related to the geometric albedo
Geometric albedo
The geometric albedo of an astronomical body is the ratio of its actual brightness at zero phase angle to that of an idealized flat, fully reflecting, diffusively scattering disk with the same cross-section....

 (p) by the expression

where q is termed the phase integral and is given in terms of the directional scattered flux I(α) into phase angle α (averaged over all wavelengths and azimuthal angles) as

The phase angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

α is the angle between the source of the radiation (usually the Sun) and the observing direction, and varies from zero for light scattered back towards the source, to 180° for observations looking towards the source. For example, during opposition or looking at the full moon, α is very small, while backlit objects or the new moon have α close to 180°.


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

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