Editing Albedo (section)

== Astronomical albedo ==
[[File:Titan and Saturn - May 6 2012 - combined (35516187116).jpg|thumb|upright=1.2|The moon [[Titan (moon)|Titan]] is darker than [[Saturn]] even though they receive the same amount of sunlight. This is due to a difference in albedo (0.22 versus 0.499 in [[geometric albedo]]).]]In astronomy, the term '''albedo''' can be defined in several different ways, depending upon the application and the wavelength of electromagnetic radiation involved.

===Optical or visual albedo===
The albedos of [[planet]]s, [[Natural satellite|satellites]] and [[minor planet]]s such as [[asteroid]]s can be used to infer much about their properties. The study of albedos, their dependence on wavelength, lighting angle ("phase angle"), and variation in time composes a major part of the astronomical field of [[photometry (astronomy)|photometry]]. For small and far objects that cannot be resolved by telescopes, much of what we know comes from the study of their albedos. For example, the absolute albedo can indicate the surface ice content of outer [[Solar System]] objects, the variation of albedo with phase angle gives information about [[regolith]] properties, whereas unusually high radar albedo is indicative of high metal content in [[asteroid]]s.

[[Enceladus]], a moon of Saturn, has one of the highest known optical albedos of any body in the Solar System, with an albedo of 0.99. Another notable high-albedo body is [[Eris (dwarf planet)|Eris]], with an albedo of 0.96.<ref name="sicardy">
{{cite journal
| title = Size, density, albedo and atmosphere limit of dwarf planet Eris from a stellar occultation
| journal = European Planetary Science Congress Abstracts
| volume = 6
| date = 2011
| url = http://meetingorganizer.copernicus.org/EPSC-DPS2011/EPSC-DPS2011-137-8.pdf
| access-date = 14 September 2011
| bibcode = 2011epsc.conf..137S
| last1 = Sicardy
| first1 = B.
| last2 = Ortiz
| first2 = J. L.
| last3 = Assafin
| first3 = M.
| last4 = Jehin
| first4 = E.
| last5 = Maury
| first5 = A.
| last6 = Lellouch
| first6 = E.
| last7 = Gil-Hutton
| first7 = R.
| last8 = Braga-Ribas
| first8 = F.
| last9 = Colas
| first9 = F.
| page = 137
| display-authors=8
}}
</ref> Many small objects in the outer Solar System<ref name="tnoalbedo">{{cite web
  |date=17 September 2008
  |title=TNO/Centaur diameters and albedos
  |publisher=Johnston's Archive
  |author=Wm. Robert Johnston
  |url=http://www.johnstonsarchive.net/astro/tnodiam.html
  |access-date=17 October 2008| archive-url= https://web.archive.org/web/20081022223827/http://www.johnstonsarchive.net/astro/tnodiam.html| archive-date= 22 October 2008<!--Added by DASHBot-->}}</ref> and [[asteroid belt]] have low albedos down to about 0.05.<ref name="astalbedo">{{cite web
  |date=28 June 2003
  |title=Asteroid albedos: graphs of data
  |publisher=Johnston's Archive
  |author=Wm. Robert Johnston
  |url=http://www.johnstonsarchive.net/astro/astalbedo.html
  |access-date=16 June 2008| archive-url= https://web.archive.org/web/20080517100307/http://www.johnstonsarchive.net/astro/astalbedo.html| archive-date= 17 May 2008<!--Added by DASHBot-->}}</ref> A typical [[comet nucleus]] has an albedo of 0.04.<ref name="dark">{{cite news
  |date=29 November 2001
  |title=Comet Borrelly Puzzle: Darkest Object in the Solar System
  |work=Space.com
  |author=Robert Roy Britt
  |url=http://www.space.com/scienceastronomy/solarsystem/borrelly_dark_011129.html
  |access-date=1 September 2012| archive-url= https://web.archive.org/web/20090122074028/http://www.space.com/scienceastronomy/solarsystem/borrelly_dark_011129.html| archive-date= 22 January 2009}}</ref> Such a dark surface is thought to be indicative of a primitive and heavily [[space weathering|space weathered]] surface containing some [[organic compound]]s.

The overall albedo of the [[Moon]] is measured to be around 0.14,<ref name="CERESmoon">
{{cite journal
| title = Celestial body irradiance determination from an underfilled satellite radiometer: application to albedo and thermal emission measurements of the Moon using CERES
| journal = Applied Optics
| volume = 47 | issue = 27
| date = 2008
| bibcode = 2008ApOpt..47.4981M
| last1 = Matthews
| first1 = G.
| pages = 4981–4993
|doi = 10.1364/AO.47.004981
| pmid=18806861}}
</ref> but it is strongly directional and non-[[Lambertian reflectance|Lambertian]], displaying also a strong [[opposition effect]].<ref name="medkeff" /> Although such reflectance properties are different from those of any terrestrial terrains, they are typical of the [[regolith]] surfaces of airless Solar System bodies.

Two common optical albedos that are used in astronomy are the (V-band) [[geometric albedo]] (measuring brightness when illumination comes from directly behind the observer) and the [[Bond albedo]] (measuring total proportion of electromagnetic energy reflected). Their values can differ significantly, which is a common source of confusion.

{| class="wikitable"
|-
! Planet
! Geometric
! Bond
|-
| Mercury
| 0.142 <ref name="Mallama_et_al"/>
| 0.088 <ref name="Mallama"/> or 0.068
|-
| Venus
| 0.689 <ref name="Mallama_et_al"/>
| 0.76  <ref name="Haus_et_al"/> or 0.77
|-
| Earth
| 0.434 <ref name="Mallama_et_al"/>
| 0.294 <ref>{{cite web|url =http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html |title =Earth Fact Sheet|website = NASA|first = David R.|last = Williams |date = 11 January 2024}}</ref>
|-
| Mars
| 0.170 <ref name="Mallama_et_al"/>
| 0.250 <ref>{{cite web|url = http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html |title =Mars Fact Sheet|website = NASA|first = David R.|last = Williams |date = 25 November 2020}}</ref>
|-
| Jupiter
| 0.538 <ref name="Mallama_et_al"/>
| 0.343±0.032 <ref>{{cite web|url = http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html |title =Jupiter Fact Sheet|website = NASA|first = David R.|last = Williams |date = 11 January 2024}}</ref> and also 0.503±0.012 <ref name="Li_et_al"/>
|-
| Saturn
| 0.499 <ref name="Mallama_et_al"/>
| 0.342 <ref name="Hanel_et_al"/>
|-
| Uranus
| 0.488 <ref name="Mallama_et_al"/>
| 0.300 <ref name="Pearl_et_al_Uranus"/>
|-
| Neptune
| 0.442 <ref name="Mallama_et_al"/>
| 0.290 <ref name="Pearl_et_al_Neptune"/>
|}

In detailed studies, the directional reflectance properties of astronomical bodies are often expressed in terms of the five [[Hapke parameters]] which semi-empirically describe the variation of albedo with [[phase angle (astronomy)|phase angle]], including a characterization of the opposition effect of [[regolith]] surfaces. One of these five parameters is yet another type of albedo called the [[single-scattering albedo]]. It is used to define scattering of electromagnetic waves on small particles. It depends on properties of the material ([[refractive index]]), the size of the particle, and the wavelength of the incoming radiation.

An important relationship between an object's astronomical (geometric) albedo, [[Absolute magnitude#Absolute magnitude for planets (H)|absolute magnitude]] and diameter is given by:<ref name="bruton">{{cite web
 |title=Conversion of Absolute Magnitude to Diameter for Minor Planets
 |publisher=Department of Physics & Astronomy (Stephen F. Austin State University)
 |author=Dan Bruton
 |url=http://www.physics.sfasu.edu/astro/asteroids/sizemagnitude.html
 |access-date=7 October 2008
 |archive-url=https://web.archive.org/web/20081210190134/http://www.physics.sfasu.edu/astro/asteroids/sizemagnitude.html
 |archive-date=10 December 2008
 |url-status=dead
}}</ref>
<math display="block">A =\left ( \frac{1329\times10^{-H/5}}{D} \right ) ^2,</math>
where <math>A</math> is the astronomical albedo, <math>D</math> is the diameter in kilometers, and <math>H</math> is the absolute magnitude.

===Radar albedo===
In planetary [[radar astronomy]], a microwave (or radar) pulse is transmitted toward a planetary target (e.g. Moon, asteroid, etc.) and the echo from the target is measured. In most instances, the transmitted pulse is [[circular polarization|circularly polarized]] and the received pulse is measured in the same sense of polarization as the transmitted pulse (SC) and the opposite sense (OC).<ref name="Ostro_Planetary_Radar">{{cite book |last1=Ostro |first1=S. J. |editor1-last=McFadden |editor1-first=L. |editor2-last=Weissman |editor2-first=P. R. |editor3-last=Johnson |editor3-first=T. V. |title=Planetary Radar in Encyclopedia of the Solar System |date=2007 |publisher=Academic Press |isbn=978-0-12-088589-3 |pages=735–764 |edition=2nd}}</ref><ref name="Ostro_Asteroid_Radar">{{cite book |last1=Ostro |first1=S. J. |display-authors=etal |editor1-last=Bottke |editor1-first=W. |editor2-last=Cellino |editor2-first=A. |editor3-last=Paolicchi |editor3-first=P. |editor4-last=Binzel |editor4-first=R. P. |title=Asteroid Radar Astronomy in Asteroids III |date=2002 |publisher=University of Arizona Press |isbn=9780816522811 |pages=151–168}}</ref> The echo power is measured in terms of [[radar cross-section]], <math>{\sigma}_{OC}</math>, <math>{\sigma}_{SC}</math>, or <math>{\sigma}_{T}</math> (total power, SC + OC) and is equal to the cross-sectional area of a metallic sphere (perfect reflector) at the same distance as the target that would return the same echo power.<ref name="Ostro_Planetary_Radar" />

Those components of the received echo that return from first-surface reflections (as from a smooth or mirror-like surface) are dominated by the OC component as there is a reversal in polarization upon reflection. If the surface is rough at the wavelength scale or there is significant penetration into the regolith, there will be a significant SC component in the echo caused by multiple scattering.<ref name="Ostro_Asteroid_Radar" />

For most objects in the solar system, the OC echo dominates and the most commonly reported radar albedo parameter is the (normalized) OC radar albedo (often shortened to radar albedo):<ref name="Ostro_Planetary_Radar" />
<math display="block"> \hat{\sigma}_\text{OC} = \frac{{\sigma}_\text{OC}}{\pi r^2} </math>

where the denominator is the effective cross-sectional area of the target object with mean radius, <math>r</math>. A smooth metallic sphere would have <math>\hat{\sigma}_\text{OC} = 1</math>.

====Radar albedos of Solar System objects====

{| class="wikitable"
|-
! Object
! <math>\hat{\sigma}_\text{OC}</math>
|-
| Moon
| 0.06 <ref name="Ostro_Planetary_Radar" />
|-
| Mercury
| 0.05 <ref name="Ostro_Planetary_Radar" />
|-
| Venus
| 0.10 <ref name="Ostro_Planetary_Radar" />
|-
| Mars
| 0.06 <ref name="Ostro_Planetary_Radar" />
|-
| Avg. S-type asteroid
| 0.14 <ref name="Magri2007">{{cite journal |last1=Magri |first1=C | display-authors=etal |title=A radar survey of main-belt asteroids: Arecibo observations of 55 objects during 1999-2004 |journal=Icarus |date=2007 |volume=186 |issue=1 |pages=126–151 |doi=10.1016/j.icarus.2006.08.018|bibcode=2007Icar..186..126M }}</ref>
|-
| Avg. C-type asteroid
| 0.13 <ref name="Magri2007"/>
|-
| Avg. M-type asteroid
| 0.26 <ref name="Shepard et al 2015">{{cite journal |last1=Shepard |first1=M. K. | display-authors= etal |title=A radar survey of M- and X-class asteroids: III. Insights into their composition, hydration state, and structure. |journal=Icarus |date=2015 |volume=245 |pages=38–55 | doi=10.1016/j.icarus.2014.09.016|bibcode=2015Icar..245...38S }}</ref>
|-
| Comet P/2005 JQ5
| 0.02 <ref>{{cite journal |last1=Harmon |first1=J. K. |display-authors=etal |title=Radar observations of Comet P/2005 JQ5 (Catalina) |journal=Icarus |date=2006 |volume=184 |issue=1 |pages=285–288 |doi=10.1016/j.icarus.2006.05.014|bibcode=2006Icar..184..285H }}</ref>
|}
The values reported for the Moon, Mercury, Mars, Venus, and Comet P/2005 JQ5 are derived from the total (OC+SC) radar albedo reported in those references.

====Relationship to surface [[bulk density]]====
In the event that most of the echo is from first surface reflections (<math>\hat{\sigma}_\text{OC} < 0.1</math> or so), the OC radar albedo is a first-order approximation of the Fresnel reflection coefficient (aka reflectivity)<ref name="Ostro_Asteroid_Radar" /> and can be used to estimate the bulk density of a planetary surface to a depth of a meter or so (a few wavelengths of the radar wavelength which is typically at the decimeter scale) using the following empirical relationships:<ref name="Shepard_M2">{{cite journal |last1=Shepard |first1=M. K. |display-authors=etal |title=A radar survey of M- and X-class asteroids II. Summary and synthesis |journal=Icarus |date=2010 |volume=208 |issue=1 |pages=221–237 |doi=10.1016/j.icarus.2010.01.017|bibcode=2010Icar..208..221S }}</ref>

:<math>\rho = \begin{cases}
   3.20 \text{ g cm}^{-3} \ln \left( \frac{1 + \sqrt{0.83 \hat{\sigma}_\text{OC}}}{1 - \sqrt{0.83 \hat{\sigma}_\text{OC}}} \right) & \text{for } \hat{\sigma}_\text{OC} \le 0.07 \\
  (6.944 \hat{\sigma}_\text{OC} + 1.083) \text{ g cm}^{-3} & \text{for } \hat{\sigma}_\text{OC} > 0.07
\end{cases}</math>.