Bond albedo#Examples

{{short description|Fraction of incident light reflected by an astronomical body}}

The Bond albedo (also called spheric albedo, planetary albedo, and 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

: $A = pq$

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

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

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 the surface and atmospheric properties of the body in question.

Some examples:[http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/albedo.html Albedo of the Earth]

Name	colspan="2"\|Bond albedo	colspan="2"\|Visual geometric albedo
class="wikitable sortable"
Mercury{{cite arXiv \|title=The spherical bolometric albedo for planet Mercury \|first1=Anthony \|last1=Mallama \|date=2017 \|class=astro-ph.EP \|eprint=1703.02670 }}{{cite journal \|title=Comprehensive wide-band magnitudes and albedos for the planets, with applications to exo-planets and Planet Nine \|journal=Icarus \|first1=Anthony \|last1=Mallama \|first2=Bruce \|last2=Krobusek \|first3=Hristo \|last3=Pavlov \|volume=282 \|pages=19–33 \|date=2017 \|doi=10.1016/j.icarus.2016.09.023 \|arxiv=1609.05048 \|bibcode=2017Icar..282...19M \|s2cid=119307693 }} \|{{bartable\|0.088	100}} \|{{bartable\|0.142	100}}
Venus{{cite journal \|title=Radiative energy balance of Venus based on improved models of the middle and lower atmosphere \|journal=Icarus \|first1=R. \|last1=Haus \|display-authors=etal \|volume=272 \|pages=178–205 \|date=July 2016 \|doi=10.1016/j.icarus.2016.02.048 \|bibcode=2016Icar..272..178H \|url=https://elib.dlr.de/107059/1/haus_improved_energybalance_icarus_2016_preprint.pdf }} \|{{bartable\|0.76	100}} \|{{bartable\|0.689	100}}
Earth{{cite web\|last1=Williams\|first1=David R.\|date=2004-09-01\|url=http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html\|title=Earth Fact Sheet\|publisher=NASA\|access-date=2010-08-09}} \|{{bartable\|0.306	100}} \|{{bartable\|0.434	100}}
Moon{{cite web\|last1=Williams\|first1=David R.\|date=2014-04-25\|url=http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html\|title=Moon Fact Sheet\|publisher=NASA\|access-date=2015-03-02}} \|{{bartable\|0.11	100}} \|{{bartable\|0.12	100}}
Mars [http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html Mars Fact Sheet, NASA] \|{{bartable\|0.25	100}} \|{{bartable\|0.17	100}}
Jupiter{{cite journal \|title=Less absorbed solar energy and more internal heat for Jupiter \|first1=Liming \|last1=Li \|display-authors=etal \|journal=Nature Communications \|date=2018 \|doi=10.1038/s41467-018-06107-2 \|pmid=30213944 \|volume=9 \|issue=1 \|pmc=6137063 \|page=3709 \|bibcode=2018NatCo...9.3709L}} \|{{bartable\|0.503	100}} \|{{bartable\|0.538	100}}
Saturn{{cite journal \|title=Albedo, internal heat flux, and energy balance of Saturn \|first1=R.A. \|last1=Hanel \|display-authors=etal \|journal=Icarus \|volume=53 \|pages=262–285 \|date=1983 \|issue=2 \|doi=10.1016/0019-1035(83)90147-1 \|bibcode=1983Icar...53..262H }} \|{{bartable\|0.342	100}} \|{{bartable\|0.499	100}}
Enceladus{{cite journal\| last1 = Verbiscer\| first1 = A.\| last2 = French\| first2 = R.\| last3 = Showalter\| first3 = M.\| last4 = Helfenstein\| first4 = P.\| title = Enceladus: Cosmic Graffiti Artist Caught in the Act\| journal = Science\| volume = 315\| issue = 5813\| page = 815\| date = February 9, 2007\| pmid = 17289992\| bibcode = 2007Sci...315..815V\| doi = 10.1126/science.1134681\| s2cid = 21932253\|ref = {{sfnRef\|Verbiscer French et al.\|2007}}}} (supporting online material, table S1){{cite journal \|title =Thermal inertia and bolometric Bond albedo values for Mimas, Enceladus, Tethys, Dione, Rhea and Iapetus as derived from Cassini/CIRS measurements \|last1=Howett \|first1=Carly J. A. \|last2=Spencer \|first2=John R. \|last3=Pearl \|first3=J. C. \|last4=Segura \|first4=M. \|date =2010 \|journal=Icarus \|volume =206 \|issue =2 \|pages =573–593 \|doi =10.1016/j.icarus.2009.07.016 \|bibcode=2010Icar..206..573H}} \|{{bartable\|0.81	100}} \|{{bartable\|1.375	100}}
Uranus{{cite journal \|title=The albedo, effective temperature, and energy balance of Uranus, as determined from Voyager IRIS data \|first1=J.C. \|last1=Pearl \|display-authors=etal \|journal=Icarus \|volume=84 \|pages=12–28 \|date=1990 \|issue=1 \|doi=10.1016/0019-1035(90)90155-3 \|bibcode=1990Icar...84...12P }} \|{{bartable\|0.300	100}} \|{{bartable\|0.488	100}}
Neptune{{cite journal \|title=The albedo, effective temperature, and energy balance of Neptune, as determined from Voyager data \|first1=J.C. \|last1=Pearl \|display-authors=etal \|journal=J. Geophys. Res. \|volume=96 \|pages=18,921-18,930 \|date=1991 \|doi=10.1029/91JA01087 \|bibcode=1991JGR....9618921P }} \|{{bartable\|0.290	100}} \|{{bartable\|0.442	100}}
Pluto{{cite journal \|display-authors = etal \|first1 = Anne J. \|last1 = Verbiscer \|first2 = Paul \|last2 = Helfenstein \|first3 = Simon B. \|last3 = Porter \|first4 = Susan D. \|last4 = Benecchi \|first5 = J. J. \|last5 = Kavelaars \|first6 = Tod R. \|last6 = Lauer \|title = The Diverse Shapes of Dwarf Planet and Large KBO Phase Curves Observed from New Horizons \|journal = The Planetary Science Journal \|date = April 2022 \|volume = 3 \|issue = 4 \|id = 95 \|pages = 31 \|doi-access = free \|doi = 10.3847/PSJ/ac63a6 \|bibcode = 2022PSJ.....3...95V}} \|{{bartable\|0.41	100}} \|{{bartable\|0.51	100}}
Charon{{Cite journal \|last1=Buratti \|first1=B. J. \|last2=Hicks \|first2=M. D. \|last3=Hillier \|first3=J. H. \|last4=Verbiscer \|first4=A. J. \|last5=Abgarian \|first5=M. \|last6=Hofgartner \|first6=J. D. \|last7=Lauer \|first7=T. R. \|last8=Grundy \|first8=W. M. \|last9=Stern \|first9=S. A. \|last10=Weaver \|first10=H. A. \|last11=Howett \|first11=C. J. A. \|date=2019-03-19 \|title=New Horizons Photometry of Pluto's Moon Charon \|journal=The Astrophysical Journal \|volume=874 \|issue=1 \|pages=L3 \|doi=10.3847/2041-8213/ab0bff \|bibcode=2019ApJ...874L...3B \|s2cid=127098911 \|issn=2041-8213\|doi-access=free }} \|{{bartable\|0.29	100}} \|{{bartable\|0.41	100}}
Haumea \|{{bartable\|0.33	100}} \|{{bartable\|0.66	100}}
Makemake \|{{bartable\|0.74	100}} \|{{bartable\|0.82	100}}
Eris \|{{bartable\|0.99	100}} \|{{bartable\|0.96	100}}

References

External links

[https://web.archive.org/web/20090413042346/http://jeff.medkeff.com/astro/lunar/obs_tech/albedo.htm discussion of Lunar albedo]

Category:Concepts in astrophysics

Category:Electromagnetic radiation

Category:Radiometry

Category:Scattering, absorption and radiative transfer (optics)

Name	colspan="2"\|Bond albedo	colspan="2"\|Visual geometric albedo
class="wikitable sortable"
Mercury{{cite arXiv \|title=The spherical bolometric albedo for planet Mercury \|first1=Anthony \|last1=Mallama \|date=2017 \|class=astro-ph.EP \|eprint=1703.02670 }}{{cite journal \|title=Comprehensive wide-band magnitudes and albedos for the planets, with applications to exo-planets and Planet Nine \|journal=Icarus \|first1=Anthony \|last1=Mallama \|first2=Bruce \|last2=Krobusek \|first3=Hristo \|last3=Pavlov \|volume=282 \|pages=19–33 \|date=2017 \|doi=10.1016/j.icarus.2016.09.023 \|arxiv=1609.05048 \|bibcode=2017Icar..282...19M \|s2cid=119307693 }} \|{{bartable\|0.088	100}} \|{{bartable\|0.142	100}}
Venus{{cite journal \|title=Radiative energy balance of Venus based on improved models of the middle and lower atmosphere \|journal=Icarus \|first1=R. \|last1=Haus \|display-authors=etal \|volume=272 \|pages=178–205 \|date=July 2016 \|doi=10.1016/j.icarus.2016.02.048 \|bibcode=2016Icar..272..178H \|url=https://elib.dlr.de/107059/1/haus_improved_energybalance_icarus_2016_preprint.pdf }} \|{{bartable\|0.76	100}} \|{{bartable\|0.689	100}}
Earth{{cite web\|last1=Williams\|first1=David R.\|date=2004-09-01\|url=http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html\|title=Earth Fact Sheet\|publisher=NASA\|access-date=2010-08-09}} \|{{bartable\|0.306	100}} \|{{bartable\|0.434	100}}
Moon{{cite web\|last1=Williams\|first1=David R.\|date=2014-04-25\|url=http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html\|title=Moon Fact Sheet\|publisher=NASA\|access-date=2015-03-02}} \|{{bartable\|0.11	100}} \|{{bartable\|0.12	100}}
Mars [http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html Mars Fact Sheet, NASA] \|{{bartable\|0.25	100}} \|{{bartable\|0.17	100}}
Jupiter{{cite journal \|title=Less absorbed solar energy and more internal heat for Jupiter \|first1=Liming \|last1=Li \|display-authors=etal \|journal=Nature Communications \|date=2018 \|doi=10.1038/s41467-018-06107-2 \|pmid=30213944 \|volume=9 \|issue=1 \|pmc=6137063 \|page=3709 \|bibcode=2018NatCo...9.3709L}} \|{{bartable\|0.503	100}} \|{{bartable\|0.538	100}}
Saturn{{cite journal \|title=Albedo, internal heat flux, and energy balance of Saturn \|first1=R.A. \|last1=Hanel \|display-authors=etal \|journal=Icarus \|volume=53 \|pages=262–285 \|date=1983 \|issue=2 \|doi=10.1016/0019-1035(83)90147-1 \|bibcode=1983Icar...53..262H }} \|{{bartable\|0.342	100}} \|{{bartable\|0.499	100}}
Enceladus{{cite journal\| last1 = Verbiscer\| first1 = A.\| last2 = French\| first2 = R.\| last3 = Showalter\| first3 = M.\| last4 = Helfenstein\| first4 = P.\| title = Enceladus: Cosmic Graffiti Artist Caught in the Act\| journal = Science\| volume = 315\| issue = 5813\| page = 815\| date = February 9, 2007\| pmid = 17289992\| bibcode = 2007Sci...315..815V\| doi = 10.1126/science.1134681\| s2cid = 21932253\|ref = {{sfnRef\|Verbiscer French et al.\|2007}}}} (supporting online material, table S1){{cite journal \|title =Thermal inertia and bolometric Bond albedo values for Mimas, Enceladus, Tethys, Dione, Rhea and Iapetus as derived from Cassini/CIRS measurements \|last1=Howett \|first1=Carly J. A. \|last2=Spencer \|first2=John R. \|last3=Pearl \|first3=J. C. \|last4=Segura \|first4=M. \|date =2010 \|journal=Icarus \|volume =206 \|issue =2 \|pages =573–593 \|doi =10.1016/j.icarus.2009.07.016 \|bibcode=2010Icar..206..573H}} \|{{bartable\|0.81	100}} \|{{bartable\|1.375	100}}
Uranus{{cite journal \|title=The albedo, effective temperature, and energy balance of Uranus, as determined from Voyager IRIS data \|first1=J.C. \|last1=Pearl \|display-authors=etal \|journal=Icarus \|volume=84 \|pages=12–28 \|date=1990 \|issue=1 \|doi=10.1016/0019-1035(90)90155-3 \|bibcode=1990Icar...84...12P }} \|{{bartable\|0.300	100}} \|{{bartable\|0.488	100}}
Neptune{{cite journal \|title=The albedo, effective temperature, and energy balance of Neptune, as determined from Voyager data \|first1=J.C. \|last1=Pearl \|display-authors=etal \|journal=J. Geophys. Res. \|volume=96 \|pages=18,921-18,930 \|date=1991 \|doi=10.1029/91JA01087 \|bibcode=1991JGR....9618921P }} \|{{bartable\|0.290	100}} \|{{bartable\|0.442	100}}
Pluto{{cite journal \|display-authors = etal \|first1 = Anne J. \|last1 = Verbiscer \|first2 = Paul \|last2 = Helfenstein \|first3 = Simon B. \|last3 = Porter \|first4 = Susan D. \|last4 = Benecchi \|first5 = J. J. \|last5 = Kavelaars \|first6 = Tod R. \|last6 = Lauer \|title = The Diverse Shapes of Dwarf Planet and Large KBO Phase Curves Observed from New Horizons \|journal = The Planetary Science Journal \|date = April 2022 \|volume = 3 \|issue = 4 \|id = 95 \|pages = 31 \|doi-access = free \|doi = 10.3847/PSJ/ac63a6 \|bibcode = 2022PSJ.....3...95V}} \|{{bartable\|0.41	100}} \|{{bartable\|0.51	100}}
Charon{{Cite journal \|last1=Buratti \|first1=B. J. \|last2=Hicks \|first2=M. D. \|last3=Hillier \|first3=J. H. \|last4=Verbiscer \|first4=A. J. \|last5=Abgarian \|first5=M. \|last6=Hofgartner \|first6=J. D. \|last7=Lauer \|first7=T. R. \|last8=Grundy \|first8=W. M. \|last9=Stern \|first9=S. A. \|last10=Weaver \|first10=H. A. \|last11=Howett \|first11=C. J. A. \|date=2019-03-19 \|title=New Horizons Photometry of Pluto's Moon Charon \|journal=The Astrophysical Journal \|volume=874 \|issue=1 \|pages=L3 \|doi=10.3847/2041-8213/ab0bff \|bibcode=2019ApJ...874L...3B \|s2cid=127098911 \|issn=2041-8213\|doi-access=free }} \|{{bartable\|0.29	100}} \|{{bartable\|0.41	100}}
Haumea \|{{bartable\|0.33	100}} \|{{bartable\|0.66	100}}
Makemake \|{{bartable\|0.74	100}} \|{{bartable\|0.82	100}}
Eris \|{{bartable\|0.99	100}} \|{{bartable\|0.96	100}}

Bond albedo#Examples

Phase integral

Examples

See also

References

External links