# Geometric albedo

In astronomy, the geometric albedo of a celestial body is the ratio of its actual brightness as seen from the light source (i.e. at zero phase angle) to that of an idealized flat, fully reflecting, diffusively scattering (Lambertian) disk with the same cross-section. (This phase angle refers to the direction of the light paths and is not a phase angle in its normal meaning in optics or electronics.)

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.

## Airless bodies

The surface materials (regoliths) 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.[1] 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 or descending 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. A 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 albedo of the surface when the illumination is provided by a beam of radiation that comes in perpendicular to the surface.

## Examples

The geometric albedo may be greater or smaller than the Bond albedo, depending on surface and atmospheric properties of the body in question. Some examples:[2]

Name Bond albedo Visual geometric albedo
Mercury [3] [4] 0.088

0.142

Venus [5] [4] 0.76

0.689

Earth [6] [4] 0.306

0.434

Moon[7] [7] 0.11

0.12

Mars [8] [4] 0.25

0.17

Jupiter [9] [4] 0.503

0.538

Saturn [10] [4] 0.342

0.499

1.4

Uranus [12] [4] 0.300

0.488

Neptune [13] [4] 0.290

0.442

Pluto 0.4

0.44–0.61

Eris 0.96

## References

• NASA JPL glossary
• K.P. Seidelmann, Ed. (1992) Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, California.
1. ^ See for example this discussion of Lunar albedo Archived April 13, 2009, at the Wayback Machine by Jeff Medkeff.
2. ^ Albedo of the Earth
3. ^ Mallama, Anthony (2017). "The spherical bolometric albedo for planet Mercury". arXiv:1703.02670.
4. 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.
5. ^ 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.
6. ^ Williams, David R. (2004-09-01). "Earth Fact Sheet". NASA. Retrieved 2010-08-09.
7. ^ a b Williams, David R. (2014-04-25). "Moon Fact Sheet". NASA. Retrieved 2015-03-02.
8. ^ Mars Fact Sheet, NASA
9. ^ Li, Liming; et al. (2018). "Less absorbed solar energy and more internal heat for Jupiter". Nature Communications. doi:10.1038/s41467-018-06107-2.
10. ^ 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.
11. ^ See the discussion here for explanation of this unusual value above one.
12. ^ 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.
13. ^ 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.
(444030) 2004 NT33

(444030) 2004 NT33 is a classical trans-Neptunian object and possible dwarf planet of the Kuiper belt in the outermost region of the Solar System, approximately 450 kilometers in diameter. It was discovered on 13 July 2004, by astronomers at Palomar Observatory, California, United States.

(471288) 2011 GM27

(471288) 2011 GM27 is a trans-Neptunian object (TNO) in the Kuiper belt. It orbits slightly outside a 3:5 resonance with Neptune, taking 16 years (5.5% of its orbit) longer to orbit the Sun than a body in 3:5 resonance. It was discovered on 2 April 2011 at ESO's La Silla Observatory in Chile. With an absolute magnitude of 5.2, it is probably a dwarf planet, as its diameter has been roughly estimated to be about 450 kilometers based on an assumed geometric albedo of 0.06. It has a Tisserand's parameter relative to Jupiter of 5.771. Precovery observations exist dating back to 2006 in SDSS data.

103 Hera

Hera (minor planet designation: 103 Hera) is a moderately large main-belt asteroid that was discovered by Canadian-American astronomer James Craig Watson on September 7, 1868, and named after Hera, queen and fifth in power of the Olympian gods in Greek mythology. It is an S-type asteroid with a silicate surface composition.

Photometric observations made in 2010 at the Organ Mesa Observatory at Las Cruces, New Mexico, and the Hunters Hill Observatory at Ngunnawal, Australian Capital Territory, give a synodic rotation period of 23.740 ± 0.001 hours. The bimodal light curve shows a maximum brightness variation of 0.45 ± 0.03 in magnitude.Measurements made with the IRAS observatory give a diameter of 91.58 ± 4.14 km and a geometric albedo of 0.19 ± 0.02. By comparison, the MIPS photometer on the Spitzer Space Telescope gives a diameter of 88.30 ± 8.51 km and a geometric albedo of 0.20 ± 0.04. When the asteroid was observed occulting a star, the results showed a diameter of 89.1 ± 1.1 km.

106 Dione

Dione (minor planet designation: 106 Dione) is a large main-belt asteroid. It probably has a composition similar to 1 Ceres. It was discovered by J. C. Watson on October 10, 1868, and named after Dione, a Titaness in Greek mythology who was sometimes said to have been the mother of Aphrodite, the Greek goddess of love and beauty. It is listed as a member of the Hecuba group of asteroids that orbit near the 2:1 mean-motion resonance with Jupiter.Dione was observed to occult a dim star on January 19, 1983, by observers in Denmark, Germany and the Netherlands. A diameter of 147 ± 3 km was deduced, closely matching the value acquired by the IRAS satellite.Measurements made with the IRAS observatory give a diameter of 169.92 ± 7.86 km and a geometric albedo of 0.07 ± 0.01. By comparison, the MIPS photometer on the Spitzer Space Telescope gives a diameter of 168.72 ± 8.89 km and a geometric albedo of 0.07 ± 0.01. When the asteroid was observed occulting a star, the results showed a diameter of 176.7 ± 0.4 km.Photometric observations of this asteroid collected during 2004–2005 show a rotation period of 16.26 ± 0.02 hours with a brightness variation of 0.08 ± 0.02 magnitude.One of Saturn's satellites is also named Dione.

184 Dejopeja

Dejopeja (minor planet designation: 184 Dejopeja) is a large M-type Main belt asteroid. It was discovered by Johann Palisa on February 28, 1878, and was named after Deiopea, a Roman nymph.

This is an X-type asteroid with a diameter of 66 km and a geometric albedo of 0.190. Based upon Photometric observations taken during 2000, it has a synodic rotation period of 6.441 ± 0.001 h. The light curve is tri-modal, most likely due to an angular shape, with a peak-to-peak amplitude of 0.19 ± 0.01 in magnitude.

206 Hersilia

Hersilia (minor planet designation: 206 Hersilia) is a fairly large Main belt asteroid. It was discovered by C. H. F. Peters on October 13, 1879, in Clinton, New York. The asteroid was named after Hersilia, Roman wife of Romulus. It is classified as a primitive, dark carbon-rich C-type asteroid.

Measurements made with the IRAS observatory give a diameter of 101.72 ± 5.18 km and a geometric albedo of 0.06 ± 0.01. By comparison, the MIPS photometer on the Spitzer Space Telescope gives a diameter of 97.99 ± 7.40 km and a geometric albedo of 0.06 ± 0.02.The last close earth transit was in November and December 2002.

233 Asterope

Asterope ( ə-STERR-ə-pee; minor planet designation: 233 Asterope) is a main-belt asteroid that was discovered on 11 May 1883, by French astronomer Alphonse Borrelly at Marseille Observatory in Marseille, France. The asteroid was named after Asterope (or Sterope), one of the Pleiades. It is a rare T-type asteroid and has a relatively dark surface. The spectrum of 233 Asterope bears a resemblance to Troilite, a sulfurous iron mineral found in most iron meteorites.Photometric observations during 1995 show a rotation period of

19.743 hours. Measurements made with the IRAS observatory give a diameter of 109.56 ± 5.04 km and a geometric albedo of 0.08 ± 0.01. By comparison, the MIPS photometer on the Spitzer Space Telescope gives a diameter of 97.54 ± 10.32 km and a geometric albedo of 0.10 ± 0.01.

283 Emma

Emma (minor planet designation: 283 Emma) is a large asteroid of the asteroid belt and the namesake of the Emma family. It was discovered by Auguste Charlois on 8 February 1889, in Nice, France. The reason for its name is unknown.Measurements made with the IRAS observatory give a diameter of 145.70 ± 5.89 km and a geometric albedo of 0.03 ± 0.01. By comparison, the MIPS photometer on the Spitzer Space Telescope gives a diameter of 145.44 ± 7.72 km and a geometric albedo of 0.03 ± 0.01. When the asteroid was observed occulting a star, the results showed a diameter of 148.00 ± 16.26 km.

318 Magdalena

Magdalena (minor planet designation: 318 Magdalena) is a main belt asteroid orbiting the Sun. It was discovered by Auguste Charlois on 24 September 1891 in Nice.

On April 15, 2005 UT Magdalena occulted a 10.7 mag star in the constellation Scutum for observers along a path across Australia.

Measurements made with the IRAS observatory give a diameter of 106.08 ± 0.25 km and a geometric albedo of 0.03 ± 0.01. By comparison, the MIPS photometer on the Spitzer Space Telescope gives a diameter of 105.32 ± 11.11 km and a geometric albedo of 0.03 ± 0.01.Alternative Rock group The Pixies named one of their songs after the asteroid on their album Indie Cindy.

556 Phyllis

Phyllis (minor planet designation: 556 Phyllis) is a minor planet orbiting the Sun. It is an S-type asteroid with a diameter of 38 km and a geometric albedo of 0.185. Based on photometric observations between 1998 and 2006, it has a synodic rotation period of 4.293 ± 0.001 hours.

Belinda (moon)

Belinda ( bə-LIN-də) is an inner satellite of the planet Uranus. Belinda was discovered from the images taken by Voyager 2 on 13 January 1986 and was given the temporary designation S/1986 U 5. It is named after the heroine of Alexander Pope's The Rape of the Lock. It is also designated Uranus XIV.Belinda belongs to the Portia group of satellites, which also includes Bianca, Cressida, Desdemona, Portia, Juliet, Cupid, Rosalind and Perdita. These satellites have similar orbits and photometric properties. Other than its orbit, radius of 45 km and geometric albedo of 0.08 virtually nothing is known about it.

The Voyager 2 images show Belinda as an elongated object with its major axis pointing towards Uranus. The moon is very elongated, with its short axis 0.5 ± 0.1 times the long axis. Its surface is grey in color.

Bianca (moon)

There is also an asteroid called 218 Bianca.Bianca ( bee-AHNG-kə) is an inner satellite of Uranus. It was discovered from the images taken by Voyager 2 on January 23, 1986, and was given the temporary designation S/1986 U 9. It was named after the sister of Katherine in Shakespeare's play The Taming of the Shrew. It is also designated Uranus VIII.Bianca belongs to Portia Group of satellites, which also includes Cressida, Desdemona, Juliet, Portia, Rosalind, Cupid, Belinda and Perdita. These satellites have similar orbits and photometric properties. Other than its orbit, radius of 27 km, and geometric albedo of 0.08 virtually nothing is known about it.

At the Voyager 2 images Bianca appears as an elongated object, the major axis pointing towards Uranus. The ratio of axes of the Bianca's prolate spheroid is 0.7 ± 0.2. Its surface is grey in color.

Bond albedo

The Bond 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.

Cordelia (moon)

Cordelia ( kor-DEE-lee-ə) is the innermost known moon of Uranus. It was discovered from the images taken by Voyager 2 on January 20, 1986, and was given the temporary designation S/1986 U 7. It was not detected again until the Hubble Space Telescope observed it in 1997. Cordelia takes its name from the youngest daughter of Lear in William Shakespeare's King Lear. It is also designated Uranus VI.Other than its orbit, radius of 20 km and geometric albedo of 0.08 virtually nothing is known about it. In the Voyager 2 images Cordelia appears as an elongated object with its major axis pointing towards Uranus. The ratio of axes of Cordelia's prolate spheroid is 0.7 ± 0.2.Cordelia acts as the inner shepherd satellite for Uranus' ε ring. Cordelia's orbit is within Uranus' synchronous orbit radius, and is therefore slowly decaying due to tidal deceleration.Cordelia is very close to a 5:3 orbital resonance with Rosalind.

Desdemona (moon)

There is also a minor planet called 666 Desdemona.Desdemona ( DEZ-di-MOH-nə) is an inner satellite of Uranus. It was discovered from the images taken by Voyager 2 on 13 January 1986, and was given the temporary designation S/1986 U 6. Desdemona is named after the wife of Othello in William Shakespeare's play Othello. It is also designated Uranus X.Desdemona belongs to Portia Group of satellites, which also includes Bianca, Cressida, Juliet, Portia, Rosalind, Cupid, Belinda and Perdita. These satellites have similar orbits and photometric properties. Other than its orbit, radius of 32 km and geometric albedo of 0.08 virtually nothing is known about Desdemona.

At the Voyager 2 images Desdemona appears as an elongated object, the major axis pointing towards Uranus. The ratio of axes of Desdemona's prolate spheroid is 0.6 ± 0.3. Its surface is grey in color.Desdemona may collide with one of its neighboring moons Cressida or Juliet within the next 100 million years.

Juliet (moon)

There is also an asteroid called 1285 Julietta.Juliet ( JOO-lee-ət, JOO-lee-ET) is an inner satellite of Uranus. It was discovered from the images taken by Voyager 2 on 3 January 1986, and was given the temporary designation S/1986 U 2. It is named after the heroine of William Shakespeare's play Romeo and Juliet. It is also designated Uranus XI.Juliet belongs to Portia Group of satellites, which also includes Bianca, Cressida, Desdemona, Portia, Rosalind, Cupid, Belinda and Perdita. These satellites have similar orbits and photometric properties. Unfortunately, other than its orbit, radius of 53 km and geometric albedo of 0.08 virtually nothing is known about Juliet.

At the Voyager 2 images Juliet appears as an elongated object, the major axis pointing towards Uranus. The ratio of axes of Juliet's prolate spheroid is 0.5 ± 0.3, which is rather an extreme value. Its surface is grey in color.Juliet may collide with Desdemona within the next 100 million years.

Ophelia (moon)

Ophelia ( o-FEE-lee-ə) is a moon of Uranus. It was discovered from the images taken by Voyager 2 on January 20, 1986, and was given the temporary designation S/1986 U 8. It was not seen until the Hubble Space Telescope recovered it in 2003. Ophelia was named after the daughter of Polonius, Ophelia, in William Shakespeare's play Hamlet. It is also designated Uranus VII.Other than its orbit, radius of 21 km and geometric albedo of 0.08 virtually nothing is known about it. At the Voyager 2 images Ophelia appears as an elongated object, the major axis pointing towards Uranus. The ratio of axes of the Ophelia's prolate spheroid is 0.7 ± 0.3.Ophelia acts as the outer shepherd satellite for Uranus' ε ring. The orbit of Ophelia is within the synchronous orbit radius of Uranus, and is therefore slowly decaying due to tidal forces.

Portia (moon)

Portia ( POR-shə) is an inner satellite of Uranus. It was discovered from the images taken by Voyager 2 on 3 January 1986, and was given the temporary designation S/1986 U 1. The moon is named after Portia, the heroine of William Shakespeare's play The Merchant of Venice. It is also designated Uranus XII.Portia is the second-largest inner satellite of Uranus after Puck. The Portian orbit, which lies inside Uranus' synchronous orbital radius, is slowly decaying due to tidal deceleration. The moon will one day either break up into a planetary ring or hit Uranus.

It heads a group of satellites called the Portia Group, which includes Bianca, Cressida, Desdemona, Juliet, Rosalind, Cupid, Belinda and Perdita. These satellites have similar orbits and photometric properties.Little is known about Portia beyond its size of about 140 km, orbit, and geometric albedo of about 0.08.In the Voyager 2 images, Portia appears as an elongated object whose major axis points towards Uranus. The ratio of axes of the Portia's prolate spheroid is 0.8 ± 0.1. Its surface is grey in color. Observations with Hubble Space Telescope and large terrestrial telescopes found water ice absorption features in the spectrum of Portia.

Rosalind (moon)

There is also an asteroid called 900 Rosalinde.Rosalind ( ROZ-əl-ind) is an inner satellite of Uranus. It was discovered from the images taken by Voyager 2 on 13 January 1986, and was given the temporary designation S/1986 U 4. It was named after the daughter of the banished Duke in William Shakespeare's play As You Like It. It is also designated Uranus XIII.Rosalind belongs to Portia group of satellites, which also includes Bianca, Cressida, Desdemona, Portia, Juliet, Cupid, Belinda and Perdita. These satellites have similar orbits and photometric properties. Other than its orbit, radius of 36 km and geometric albedo of 0.08 virtually nothing is known about Rosalind.

In the Voyager 2 images Rosalind appears as an almost spherical object. The ratio of axes of Rosalind's prolate spheroid is 0.8-1.0. Its surface is grey in color.Rosalind is very close to a 3:5 orbital resonance with Cordelia.

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