<p>In general, you'd have to project the light from the sun (Assuming we're talking about objects in our solar system) onto the 3D surface and project it onto a 2D surface. This can be accomplished via a ray tracing algorithm. </p>

<p>This procedure will give you the fraction of the surface illuminated.</p>

<p>Now if you are concerned about the fraction of the illuminated surface that is reflected in a specific directly -- so that it is "viewable" from that direction -- you have to do the ray tracing in 3D from the source (Sun) to the object and on to the viewer. There packages you can google that will do this type of ray tracing if you can model the objects in 3D... </p>

CC BY-SA 4.0
2019-06-25T16:49:37.123Z
True you'd have to model specular reflection to model accurately, but just attenuating your solution to the above procedure will get you there. There are attenuating values you can use for your best guess as to surface composition.
earnric
CC BY-SA 4.0
2019-06-25T16:49:52.977Z
If folks have a better way of doing this modeling I'd like to hear it...
earnric
CC BY-SA 4.0
2019-06-21T20:21:44.653Z
2019-06-21T20:21:44.653Z
earnric
<p>Given the phase of a planet or satellite, I can find the area illuminated visible to us, <strong>if</strong> we consider a 2D surface. But how do I find the percentage of illuminated area visible considering it a 3D surface and thus finding the magnitude of the partially illuminated planet/satellite.</p>

CC BY-SA 4.0
2019-06-22T03:03:39.423Z
There is some helpful math in [this answer](https://space.stackexchange.com/a/36742/12102). See also [1](https://astronomy.stackexchange.com/a/26021/7982), [2](https://astronomy.stackexchange.com/a/28778/7982), [3](https://astronomy.stackexchange.com/q/29459/7982), [4](https://astronomy.stackexchange.com/a/29973/7982), [5](https://astronomy.stackexchange.com/a/20803/7982)
uhoh
<moon-phases><apparent-magnitude><magnitude>
Relation between phase and magnitude
Arnab Chowdhury
# Relation between phase and magnitude

(Asked by: username_0 on 2019-06-21)

Given the phase of a planet or satellite, I can find the area illuminated visible to us, **if** we consider a 2D surface. But how do I find the percentage of illuminated area visible considering it a 3D surface and thus finding the magnitude of the partially illuminated planet/satellite.

**Tags:** moon-phases, apparent-magnitude, magnitude

> **Comments:**
> **username_1**: There is some helpful math in [this answer](https://space.stackexchange.com/a/36742/12102). See also [1](https://astronomy.stackexchange.com/a/26021/7982), [2](https://astronomy.stackexchange.com/a/28778/7982), [3](https://astronomy.stackexchange.com/q/29459/7982), [4](https://astronomy.stackexchange.com/a/29973/7982), [5](https://astronomy.stackexchange.com/a/20803/7982)  

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## 1 answers

### Answer by username_2 on 2019-06-21. Score: -1

In general, you'd have to project the light from the sun (Assuming we're talking about objects in our solar system) onto the 3D surface and project it onto a 2D surface. This can be accomplished via a ray tracing algorithm.

This procedure will give you the fraction of the surface illuminated.

Now if you are concerned about the fraction of the illuminated surface that is reflected in a specific directly -- so that it is "viewable" from that direction -- you have to do the ray tracing in 3D from the source (Sun) to the object and on to the viewer. There packages you can google that will do this type of ray tracing if you can model the objects in 3D...

> **Comments:**
> **username_2**: True you'd have to model specular reflection to model accurately, but just attenuating your solution to the above procedure will get you there. There are attenuating values you can use for your best guess as to surface composition.  
> **username_2**: If folks have a better way of doing this modeling I'd like to hear it...  

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