<p>As the title suggests, I need a way to get the percentage of the Moon's disk which is illuminated as a function of time.</p>
<p>There are simple geometrical expressions for the fraction of a sphere illuminated by a collimated coplanar light source, but I need something more physically and geometrically representative of the Sun Earth Moon system.</p>

CC BY-SA 4.0
2021-05-25T18:29:52.960Z
When you say "brightness percentage", do you mean "percentage of the Moon illuminated" ? The actual brightness of the Moon is a more complicated function of the  distances, the phase angle and atmospheric conditions see e.g. [this](https://asterism.org/2019/04/12/how-bright-is-the-moon/)
astrosnapper
CC BY-SA 4.0
2021-05-25T20:08:42.593Z
Yes, I didn't explain well myself. I'm interested on the percentage of the moon illuminated
Arfmann
CC BY-SA 4.0
2021-05-25T23:03:05.733Z
I've made an edit to your question incorporating your response in comments. In the future, whenever there's a clarification in comments please go ahead and update your post to reflect it. Close voters and answerers often ignore comments and just view the post. I've made an edit now to reflect your comment and to try to clarify your question. Does this look okay? Please feel free to edit further.
uhoh
CC BY-SA 4.0
2021-05-25T23:04:47.373Z
Also, what kinds of solutions can you use? For example, could it be a free program you can download? Could it be an on-line website like [Horizons](https://ssd.jpl.nasa.gov/horizons.cgi) (with some explanation of course)? The more you can explain about what you need and what you are doing, the better and more helpful the answers will be to you. *Thanks!*
uhoh
CC BY-SA 4.0
2021-05-26T05:48:17.053Z
@uhoh I actually need those percentage to put them on a software that I've made. I have done the calculation to get the moon phase for a specific time, getting the days since new moon (so the age)
Arfmann
CC BY-SA 4.0
2021-05-26T06:04:27.310Z
@Arfmann Well there are different solutions depending on how precise you need it. I can write up a short script in Python *that you could rewrite into any other language* that should be pretty good for say +/- 100 years from now using only trigonometry, but you need library functions that convert normal dates to Julian dates. Does that sound useful?
uhoh
CC BY-SA 4.0
2021-05-26T06:19:13.857Z
@uhoh This seems to be fine. I already have a conversion from normal dates to Julian dates that I've made to get the Moon's age. Do you have any source where I could find the calculation to do to get the results? For the precision, let's say something like 2% between two dates ore something like that
Arfmann
CC BY-SA 4.0
2021-05-26T06:56:22.703Z
I think others may be better at finding something official, let's see what I can do, but **I hope others post answers as well!** :-)
uhoh
<moon-phases>
How to get the percentage of the Moon illuminated as a function of time?
Arfmann
# How to get the percentage of the Moon illuminated as a function of time?

(Asked by: username_0 on 2021-05-25)

As the title suggests, I need a way to get the percentage of the Moon's disk which is illuminated as a function of time.

There are simple geometrical expressions for the fraction of a sphere illuminated by a collimated coplanar light source, but I need something more physically and geometrically representative of the Sun Earth Moon system.

**Tags:** moon-phases
> **Comments:**
> **username_1**: When you say "brightness percentage", do you mean "percentage of the Moon illuminated" ? The actual brightness of the Moon is a more complicated function of the  distances, the phase angle and atmospheric conditions see e.g. [this](https://asterism.org/2019/04/12/how-bright-is-the-moon/)  
> **username_0**: Yes, I didn't explain well myself. I'm interested on the percentage of the moon illuminated  
> **username_2**: I've made an edit to your question incorporating your response in comments. In the future, whenever there's a clarification in comments please go ahead and update your post to reflect it. Close voters and answerers often ignore comments and just view the post. I've made an edit now to reflect your comment and to try to clarify your question. Does this look okay? Please feel free to edit further.  
> **username_2**: Also, what kinds of solutions can you use? For example, could it be a free program you can download? Could it be an on-line website like [Horizons](https://ssd.jpl.nasa.gov/horizons.cgi) (with some explanation of course)? The more you can explain about what you need and what you are doing, the better and more helpful the answers will be to you. *Thanks!*  
> **username_0**: @uhoh I actually need those percentage to put them on a software that I've made. I have done the calculation to get the moon phase for a specific time, getting the days since new moon (so the age)  
> **username_2**: @Arfmann Well there are different solutions depending on how precise you need it. I can write up a short script in Python *that you could rewrite into any other language* that should be pretty good for say +/- 100 years from now using only trigonometry, but you need library functions that convert normal dates to Julian dates. Does that sound useful?  
> **username_0**: @uhoh This seems to be fine. I already have a conversion from normal dates to Julian dates that I've made to get the Moon's age. Do you have any source where I could find the calculation to do to get the results? For the precision, let's say something like 2% between two dates ore something like that  
> **username_2**: I think others may be better at finding something official, let's see what I can do, but **I hope others post answers as well!** :-)  

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