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Bond albedo

## Summary

The Bond albedo (or spheric albedo or planetary albedo or bolometric albedo), named after the American astronomer George Phillips Bond (1825–1865), 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.

Because the Bond albedo accounts for all of the light scattered from a body at all wavelengths and all phase angles, it is a necessary quantity for determining how much energy a body absorbs. This, in turn, is crucial for determining the equilibrium temperature of a body.

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.

## Phase integral

The Bond albedo (A) is related to the geometric albedo (p) by the expression

${\displaystyle A=pq}$

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

${\displaystyle q=2\int _{0}^{\pi }{\frac {I(\alpha )}{I(0)}}\sin \alpha \,d\alpha .}$

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 is a value strictly between 0 and 1, as it includes all possible scattered light (but not radiation from the body itself). This is in contrast to other definitions of albedo such as the geometric albedo, which can be above 1. In general, though, 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 Visual geometric albedo
Mercury[2][3] 0.088

0.142

Venus[4][3] 0.76

0.689

Earth[5][3] 0.306

0.434

Moon[6] 0.11

0.12

Mars [7][3] 0.25

0.17

Jupiter[8][3] 0.503

0.538

Saturn[9][3] 0.342

0.499

1.4

Uranus [11][3] 0.300

0.488

Neptune[12][3] 0.290

0.442

Pluto 0.4

0.44–0.61

Eris 0.96

## References

1. ^ Albedo of the Earth
2. ^ Mallama, Anthony (2017). "The spherical bolometric albedo for planet Mercury". arXiv:1703.02670.
3. Mallama, Anthony; Krobusek, Bruce; Pavlov, Hristo (2017). "Comprehensive wide-band magnitudes and albedos for the planets, with applications to exo-planets and Planet Nine". Icarus. 282: 19–33. Bibcode:2017Icar..282...19M. doi:10.1016/j.icarus.2016.09.023.
4. ^ Haus, R.; et al. (July 2016). "Radiative energy balance of Venus based on improved models of the middle and lower atmosphere". Icarus. 272: 178–205. Bibcode:2016Icar..272..178H. doi:10.1016/j.icarus.2016.02.048.
5. ^ Williams, David R. (2004-09-01). "Earth Fact Sheet". NASA. Retrieved 2010-08-09.
6. ^ Williams, David R. (2014-04-25). "Moon Fact Sheet". NASA. Retrieved 2015-03-02.
7. ^ Mars Fact Sheet, NASA
8. ^ Li, Liming; et al. (2018). "Less absorbed solar energy and more internal heat for Jupiter". Nature Communications. 9: 3709. Bibcode:2018NatCo...9.3709L. doi:10.1038/s41467-018-06107-2. PMC 6137063. PMID 30213944.
9. ^ Hanel, R.A.; et al. (1983). "Albedo, internal heat flux, and energy balance of Saturn". Icarus. 53: 262. Bibcode:1983Icar...53..262H. doi:10.1016/0019-1035(83)90147-1.
10. ^ See the discussion here for explanation of this unusual value above one.
11. ^ Pearl, J.C.; et al. (1990). "The albedo, effective temperature, and energy balance of Uranus, as determined from Voyager IRIS data". Icarus. 84: 12–28. Bibcode:1990Icar...84...12P. doi:10.1016/0019-1035(90)90155-3.
12. ^ Pearl, J.C.; et al. (1991). "The albedo, effective temperature, and energy balance of Neptune, as determined from Voyager data". J. Geophys. Res. 96: 18, 921–18, 930. Bibcode:1991JGR....9618921P. doi:10.1029/91JA01087.