<p>I refer to the book : Astronomical Algorithms (Second Edition) by Jean Meeus.</p>
<ol>
<li><p>To calculate the values of position angle of the bright limb and position angle you will need to calculate  the apparent RA and DEC of the Sun and the Moon.</p>
</li>
<li><p>Code the equations for the Sun RA and DEC using Chapter 25. Please note that L0 (equ. 28.2)  is in error To calculate T (Julian century you will need to compute Julian day (Chapter 7).</p>
</li>
<li><p>Code equations for the Moon RA and Dec from the equations given in Chapter 47.</p>
</li>
<li><p>For the calculation of Apparent RA and Dec you will need to compute Nutation and Obliquity - Equations in Chapter 22.</p>
</li>
</ol>
<p>BTW. For all my calculations I have &quot;standardized&quot; on using the equations on page 144 for the variables : D, M, Mdash, F, and Omega.
Fyi compare the equations for M given in this book ie. equations 25.2 and 47.3</p>
<ol start="5">
<li>Chapter 48 provides a formula (48.1) for the illuminated fraction of the moons disc.</li>
</ol>
<p>5.1 I used 48.2 and 48.3</p>
<p>Addition:</p>
<p>5.2 To use equation 48.5 you will need to obtain or write the atan code yourself to resolve the angle X in the correct quadrant - I wrote a routine: ATAN2(sin_tl,cos_bl).</p>
<p>I have coded all the above to run on my HP Prime graphing calculator and they have proved to be very, very accurate.</p>
<p>For the purpose of accurate determination of the moon phase angle you will need to calculate UTC(date and time) using your zone longitude or better still your local longitude.</p>

CC BY-SA 4.0
2020-06-22T21:41:40.743Z
2020-06-23T02:16:08.620Z
2020-06-23T02:16:08.620Z
Jeremy  Waller
<p>I need to calculate the exact moon phase angle for each our of a day. I have my position in lat and long and a unix timestamp. At the end i would like to be able to caluculate the moon brightness with this formula: <a href="https://patents.google.com/patent/DE10113295A1" rel="nofollow noreferrer">https://patents.google.com/patent/DE10113295A1</a></p>

<pre><code>const moonPhaseAngle = Math.cos(( 2 * ( ( phase * 100 ) / 100 ) -1));

const moonBrightness = 10 * Math.sin( altitude ) * ( .5 + ( .5 * Math.cos( moonPhaseAngle ) ) );
</code></pre>

<p>This is my actual progress through web search.
Thank you for helping me!</p>

CC BY-SA 4.0
2019-10-05T03:14:42.337Z
I suggest that you get the book "Astronomical Algorithms" by Jean Meeus in order to get the half dozen or so equations needed to calculate the phase angle. Note that the phase angle calculation can be performed without using the observer's location.
JohnHoltz
CC BY-SA 4.0
2019-10-07T09:10:10.553Z
Thank you for the responses! I have the observers position and calculate some values with the SunCalc Lib for JS. But I still can not get the angle ...
JKortmann
CC BY-SA 4.0
2020-06-22T22:43:10.113Z
I may add: the brightness is not simple geometric math alone. The scattered intensity varies by observation angle. Direct back-scatter as on full moon scatters a higher amount of light than at 90° scatter angle. The effect may not be gigantic, but definitely measurable.
planetmaker
<the-moon><moon-phases>
How to calculate the moon phase angle?
JKortmann
# How to calculate the moon phase angle?

(Asked by: username_0 on 2019-10-04)

I need to calculate the exact moon phase angle for each our of a day. I have my position in lat and long and a unix timestamp. At the end i would like to be able to caluculate the moon brightness with this formula: https://patents.google.com/patent/DE10113295A1
const moonPhaseAngle = Math.cos(( 2 * ( ( phase * 100 ) / 100 ) -1));

const moonBrightness = 10 * Math.sin( altitude ) * ( .5 + ( .5 * Math.cos( moonPhaseAngle ) ) );

This is my actual progress through web search.
Thank you for helping me!

**Tags:** the-moon, moon-phases
> **Comments:**
> **username_1**: I suggest that you get the book "Astronomical Algorithms" by Jean Meeus in order to get the half dozen or so equations needed to calculate the phase angle. Note that the phase angle calculation can be performed without using the observer's location.  
> **username_0**: Thank you for the responses! I have the observers position and calculate some values with the SunCalc Lib for JS. But I still can not get the angle ...  
> **username_2**: I may add: the brightness is not simple geometric math alone. The scattered intensity varies by observation angle. Direct back-scatter as on full moon scatters a higher amount of light than at 90° scatter angle. The effect may not be gigantic, but definitely measurable.  

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## 1 answers

### Answer by username_3 on 2020-06-22. Score: 2

I refer to the book : Astronomical Algorithms (Second Edition) by Jean Meeus.

1. To calculate the values of position angle of the bright limb and position angle you will need to calculate the apparent RA and DEC of the Sun and the Moon.
2. Code the equations for the Sun RA and DEC using Chapter 25. Please note that L0 (equ. 28.2) is in error To calculate T (Julian century you will need to compute Julian day (Chapter 7).
3. Code equations for the Moon RA and Dec from the equations given in Chapter 47.
4. For the calculation of Apparent RA and Dec you will need to compute Nutation and Obliquity - Equations in Chapter 22.

BTW. For all my calculations I have "standardized" on using the equations on page 144 for the variables : D, M, Mdash, F, and Omega.
Fyi compare the equations for M given in this book ie. equations 25.2 and 47.3

5. Chapter 48 provides a formula (48.1) for the illuminated fraction of the moons disc.

5.1 I used 48.2 and 48.3

Addition:

5.2 To use equation 48.5 you will need to obtain or write the atan code yourself to resolve the angle X in the correct quadrant - I wrote a routine: ATAN2(sin\_tl,cos\_bl).

I have coded all the above to run on my HP Prime graphing calculator and they have proved to be very, very accurate.

For the purpose of accurate determination of the moon phase angle you will need to calculate UTC(date and time) using your zone longitude or better still your local longitude.


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