<p>I'm trying to understand how albedo would be <em>calculated</em> for a body with well-characterized surface reflectance properties, so that it's absolute magnitude could be defined. One could argue that this is going backwards (one should measure apparent magnitude, correct for distances and phase angle to extract absolute magnitude, correct for radius to extract albedo) but consider if the body were not smooth and diffusely reflecting.</p>

<p>Imagine two identically sized spherical bodies; one diffuse or matte white and the other somehow covered in liquid mercury and exhibiting specular rather than diffuse reflectivity, with no wind or waves.</p>

<p>Would they both have albedo of unity?</p>

<p>If these two reflective bodies were very irregularly-shaped and had an extremely large, flattened (much larger radius of curvature) face, would its albedo be larger than unity at times?</p>

<p>Here I'm looking for how astronomers and planetary scientists <em>use the term albedo</em> and not just a mathematical hypothesis. There may be ways this is dealt with practically.</p>

CC BY-SA 4.0
2019-02-04T04:48:14.280Z
This question has the answers: https://astronomy.stackexchange.com/questions/20795/why-is-enceladuss-albedo-greater-than-1

There's Bond Albedo and geometric albedo. Bond albedo is a property intrinsic to a material and not necessarily an astronomy-only feature. Geometric albedo is about how bright a celestial body ought to be assuming certain properties, such as Lambertian scattering of light and a given bond albedo.
Ingolifs
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2019-02-04T04:56:53.090Z
I thought only stars had absolute magnitudes
Ingolifs
CC BY-SA 4.0
2019-02-04T05:03:57.077Z
@Ingolifs see [this](https://space.stackexchange.com/a/32065/12102) and [this](https://space.stackexchange.com/a/25121/12102) and links therein. Any database of asteroids will have their absolute magnitudes, either explicitly, or hidden in a reported size based on an assumed albedo. For cheezy pics see [here](https://astronomy.stackexchange.com/a/29458/7982).
uhoh
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2019-02-04T05:09:07.277Z
@Ingolifs I'm going to assume that it's [geometric albedo in zephyr's answer](https://astronomy.stackexchange.com/a/20803/7982) that's used in the relationship between absolute and apparent magnitudes and voting to close this as a duplicate to that. Thanks!
uhoh
CC BY-SA 4.0
2019-02-05T01:49:12.407Z
Not really. Apparent magnitude,m, for asteroids is given by $m=H+5log (r\Delta) - 2.5 log[(1-G)\Phi_1 + G\Phi_2]$ where $H$ is the (asteroid) absolute magnitude, $r$ is Sun-asteroid distance, $\Delta$ is Earth-asteroid distance and $\Phi_1,\Phi_2$ are "phase functions" which involve the "phase angle" (Sun-body-Earth). $G$ is "sort of" related to the albedo as it measures how much reflection happens as a function of incident to reflected light.
astrosnapper
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2019-02-05T01:59:32.013Z
@astrosnapper Thanks! I've been quoting something simpler all this time ([1](https://space.stackexchange.com/a/32065/12102), [2](https://space.stackexchange.com/a/25121/12102)) and I'd really love to see how $[(1-G) \Phi_1 +G \Phi_2]$ arises and what $G$ really is. If I modify this question to zero in on that, and start a reopen process, do you think you could write up a short answer and link to a source?
uhoh
CC BY-SA 4.0
2019-02-05T02:04:52.243Z
@astrosnapper actually the presence of both $(1-G)$ and $G$ makes me wonder if this is not related to absorption of visible light and radiation of thermal IR light, which would have both of those (in a simple approximation of emissivity independent of wavelength).
uhoh
CC BY-SA 4.0
2019-02-05T02:29:51.673Z
I don't think so as the apparent and absolute magnitude are always given as 'for a particular passband'. The most common one, used by the Minor Planet Center, is $m_V$ and $H_V$ for (Bessell) $V$ band. So the phase function is only taking into account changing geometry, not "physics" in the sense of absorption and re-radiation of light or shape,thermal inertia, surface roughness etc which all affect albedo
astrosnapper
CC BY-SA 4.0
2019-02-05T02:40:51.167Z
@astrosnapper I'd really like to track down the source of the expression in your [comment](https://astronomy.stackexchange.com/questions/29459/is-albedo-ever-greater-than-unity-how-is-it-calculated-for-various-surface-diff?noredirect=1#comment53115_29459) either by [rewording/reopening](https://astronomy.stackexchange.com/questions/29459/is-albedo-ever-greater-than-unity-how-is-it-calculated-for-various-surface-diff?noredirect=1#comment53116_29459) this question, or if you can just mention a source if you have a moment. Thanks!
uhoh
CC BY-SA 4.0
2019-02-05T19:54:16.750Z
My source was Meeus' _Astronomical Algorithms_ which cited IAU Commission 20 in 1985. I think the best source of explanation is the [Muinonen et al 2010](https://wiki.helsinki.fi/display/PSR/HG1G2+tools?preview=/93719612/94699735/Muinonen-2010-Icarus.pdf) discussing improving the $H,G$ system. There they state $\log_{10}D=3.1236−0.2H−0.5\log_{10}p_V$ where $D$ is equivalent diameter, $H$ is absolute mag (at 0 phase angle) and $p_V$ is the geometric albedo (in V band). It then explains why the $H,G$ formalism is used since asteroid obs. at phase angles <10 degrees are rare
astrosnapper
CC BY-SA 4.0
2019-02-06T00:12:27.023Z
@astrosnapper I'm going to read that today, *thank you!!!*
uhoh
<apparent-magnitude><magnitude><absolute-magnitude><albedo>
Is albedo ever greater than unity? How is it calculated for various surface diffusivities and specular reflection?
uhoh
# Is albedo ever greater than unity? How is it calculated for various surface diffusivities and specular reflection?

(Asked by: username_0 on 2019-02-04)

I'm trying to understand how albedo would be *calculated* for a body with well-characterized surface reflectance properties, so that it's absolute magnitude could be defined. One could argue that this is going backwards (one should measure apparent magnitude, correct for distances and phase angle to extract absolute magnitude, correct for radius to extract albedo) but consider if the body were not smooth and diffusely reflecting.

Imagine two identically sized spherical bodies; one diffuse or matte white and the other somehow covered in liquid mercury and exhibiting specular rather than diffuse reflectivity, with no wind or waves.

Would they both have albedo of unity?

If these two reflective bodies were very irregularly-shaped and had an extremely large, flattened (much larger radius of curvature) face, would its albedo be larger than unity at times?

Here I'm looking for how astronomers and planetary scientists *use the term albedo* and not just a mathematical hypothesis. There may be ways this is dealt with practically.

**Tags:** apparent-magnitude, magnitude, absolute-magnitude, albedo
> **Comments:**
> **username_1**: This question has the answers: https://astronomy.stackexchange.com/questions/20795/why-is-enceladuss-albedo-greater-than-1  There's Bond Albedo and geometric albedo. Bond albedo is a property intrinsic to a material and not necessarily an astronomy-only feature. Geometric albedo is about how bright a celestial body ought to be assuming certain properties, such as Lambertian scattering of light and a given bond albedo.  
> **username_1**: I thought only stars had absolute magnitudes  
> **username_0**: @Ingolifs see [this](https://space.stackexchange.com/a/32065/12102) and [this](https://space.stackexchange.com/a/25121/12102) and links therein. Any database of asteroids will have their absolute magnitudes, either explicitly, or hidden in a reported size based on an assumed albedo. For cheezy pics see [here](https://astronomy.stackexchange.com/a/29458/7982).  
> **username_0**: @Ingolifs I'm going to assume that it's [geometric albedo in zephyr's answer](https://astronomy.stackexchange.com/a/20803/7982) that's used in the relationship between absolute and apparent magnitudes and voting to close this as a duplicate to that. Thanks!  
> **username_2**: Not really. Apparent magnitude,m, for asteroids is given by $m=H+5log (r\Delta) - 2.5 log[(1-G)\Phi_1 + G\Phi_2]$ where $H$ is the (asteroid) absolute magnitude, $r$ is Sun-asteroid distance, $\Delta$ is Earth-asteroid distance and $\Phi_1,\Phi_2$ are "phase functions" which involve the "phase angle" (Sun-body-Earth). $G$ is "sort of" related to the albedo as it measures how much reflection happens as a function of incident to reflected light.  
> **username_0**: @astrosnapper Thanks! I've been quoting something simpler all this time ([1](https://space.stackexchange.com/a/32065/12102), [2](https://space.stackexchange.com/a/25121/12102)) and I'd really love to see how $[(1-G) \Phi_1 +G \Phi_2]$ arises and what $G$ really is. If I modify this question to zero in on that, and start a reopen process, do you think you could write up a short answer and link to a source?  
> **username_0**: @astrosnapper actually the presence of both $(1-G)$ and $G$ makes me wonder if this is not related to absorption of visible light and radiation of thermal IR light, which would have both of those (in a simple approximation of emissivity independent of wavelength).  
> **username_2**: I don't think so as the apparent and absolute magnitude are always given as 'for a particular passband'. The most common one, used by the Minor Planet Center, is $m_V$ and $H_V$ for (Bessell) $V$ band. So the phase function is only taking into account changing geometry, not "physics" in the sense of absorption and re-radiation of light or shape,thermal inertia, surface roughness etc which all affect albedo  
> **username_0**: @astrosnapper I'd really like to track down the source of the expression in your [comment](https://astronomy.stackexchange.com/questions/29459/is-albedo-ever-greater-than-unity-how-is-it-calculated-for-various-surface-diff?noredirect=1#comment53115_29459) either by [rewording/reopening](https://astronomy.stackexchange.com/questions/29459/is-albedo-ever-greater-than-unity-how-is-it-calculated-for-various-surface-diff?noredirect=1#comment53116_29459) this question, or if you can just mention a source if you have a moment. Thanks!  
> **username_2**: My source was Meeus' _Astronomical Algorithms_ which cited IAU Commission 20 in 1985. I think the best source of explanation is the [Muinonen et al 2010](https://wiki.helsinki.fi/display/PSR/HG1G2+tools?preview=/93719612/94699735/Muinonen-2010-Icarus.pdf) discussing improving the $H,G$ system. There they state $\log_{10}D=3.1236−0.2H−0.5\log_{10}p_V$ where $D$ is equivalent diameter, $H$ is absolute mag (at 0 phase angle) and $p_V$ is the geometric albedo (in V band). It then explains why the $H,G$ formalism is used since asteroid obs. at phase angles <10 degrees are rare  
> **username_0**: @astrosnapper I'm going to read that today, *thank you!!!*  

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