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# Bond albedo

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. It takes into account all wavelengths.

It is an important quantity for characterising 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. The strongest contribution is from visible light because the majority of solar output is in this range.

Like most albedos 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 is named for the American astronomer George Phillips Bond (1825-1865), who originally proposed it. It 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 (p) by the expression

$A = p q \frac{}{}$

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

$q = 2\int_0^{\pi}\frac{I(\alpha)}{I(0)} \sin \alpha d\alpha.$

The phase angle 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°.

## Examples

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 [1]:

Name Bond Albedo Geometric albedo
Mercury 0.119 0.138
Venus 0.75 0.84
Earth 0.29 0.367
Moon 0.123 0.113
Mars 0.16 0.15