<p>I'm having a problem for a couple of days where I'm trying to accurately calculate the phase angle of the moon at any given Coordinates (lon,lat).If I know my current Coordinates, Moon and sun topocentric right ascension, declination, altitude and zenith Coordinates.</p>

<p>Given all of that data, how do I achieve that ? The result I'm looking for preferable in degrees where 0 degrees means the crescent moon pointing directly towards me, 180 degrees means the crescent moon pointing at the other direction and so on..</p>

<p>I have tried a formula where I measured the angle between the sun zenith and a certain coordinate in relation to the moon zenith, on paper this could work, the results were decent but not to the accuracy I'm looking for. Any help would be much appreciated.</p>

CC BY-SA 4.0
2020-02-04T14:42:52.500Z
It will be easier to answer if you can more clearly show what it is you tried and exactly what about it you feel is inadequate or inaccurate. Is the problem that most formula are based on the Sun-Moon-Earth angle using the center of the Earth, and you want to find that angle for a specific location on Earth's surface instead? It's about a 1 degree difference at most, but is that what you need?
uhoh
CC BY-SA 4.0
2020-02-04T20:31:00.063Z
If you are trying to calculate the phase angle, this post gives the formula for k (the phase angle) based on the elongation, i. If you use the topocentric coordinates instead of the geocentric coordinates to calculate i, then you will have your answer. See https://astronomy.stackexchange.com/questions/26200/implementation-of-formulae-for-meeus-for-the-moon and  https://astronomy.stackexchange.com/questions/19287/angle-from-2-point-on-celestial-sphere/19292 for the angle between two objects (that is, the elongation).
JohnHoltz
CC BY-SA 4.0
2020-02-05T03:49:29.427Z
uhoh: what I'm doing is very simple actually. I'm taking the direction vector from the moon to the sun normalized, and from the moon to my coordinate normalized, and then I take the Dot product between these two vectors. The result will be in ArcCos() to produce an angle.  So lets assume Moon at zenith (-15,20), Sun(-15,40) and my coordinate (24,20). Using my method, I will get an angle of 90 which is correct, but the further the moon from your location, the greater the Error.
The Oathman
CC BY-SA 4.0
2020-02-05T03:54:33.127Z
JohnHoltz: That's exactly what I'm looking for, I got the data for Hour angle, declination and My latitude. Your method should be much more accurate than what i'm currently using. I assume using the Moon geocentric declination will not make much different ?
The Oathman
CC BY-SA 4.0
2022-03-17T18:18:48.500Z
It sounds like you're using the wrong terms, what it sounds like you're looking for is the Parallactic Angle, the the first answer JohnHoltz gave shows how to compute that.  The "phase angle" is quite different, and more akin to describing "first quarter", "full", etc. which does not change with a person's position on Earth.
Greg Miller
<the-sun><the-moon><moon-phases>
How do I calculate moon phase orientation at any Coordinates given all the necessary data?
The Oathman
# How do I calculate moon phase orientation at any Coordinates given all the necessary data?

(Asked by: username_0 on 2020-02-04)

I'm having a problem for a couple of days where I'm trying to accurately calculate the phase angle of the moon at any given Coordinates (lon,lat).If I know my current Coordinates, Moon and sun topocentric right ascension, declination, altitude and zenith Coordinates.

Given all of that data, how do I achieve that ? The result I'm looking for preferable in degrees where 0 degrees means the crescent moon pointing directly towards me, 180 degrees means the crescent moon pointing at the other direction and so on..

I have tried a formula where I measured the angle between the sun zenith and a certain coordinate in relation to the moon zenith, on paper this could work, the results were decent but not to the accuracy I'm looking for. Any help would be much appreciated.

**Tags:** the-sun, the-moon, moon-phases

> **Comments:**
> **username_1**: It will be easier to answer if you can more clearly show what it is you tried and exactly what about it you feel is inadequate or inaccurate. Is the problem that most formula are based on the Sun-Moon-Earth angle using the center of the Earth, and you want to find that angle for a specific location on Earth's surface instead? It's about a 1 degree difference at most, but is that what you need?  
> **username_2**: If you are trying to calculate the phase angle, this post gives the formula for k (the phase angle) based on the elongation, i. If you use the topocentric coordinates instead of the geocentric coordinates to calculate i, then you will have your answer. See https://astronomy.stackexchange.com/questions/26200/implementation-of-formulae-for-meeus-for-the-moon and  https://astronomy.stackexchange.com/questions/19287/angle-from-2-point-on-celestial-sphere/19292 for the angle between two objects (that is, the elongation).  
> **username_0**: username_1: what I'm doing is very simple actually. I'm taking the direction vector from the moon to the sun normalized, and from the moon to my coordinate normalized, and then I take the Dot product between these two vectors. The result will be in ArcCos() to produce an angle.  So lets assume Moon at zenith (-15,20), Sun(-15,40) and my coordinate (24,20). Using my method, I will get an angle of 90 which is correct, but the further the moon from your location, the greater the Error.  
> **username_0**: username_2: That's exactly what I'm looking for, I got the data for Hour angle, declination and My latitude. Your method should be much more accurate than what i'm currently using. I assume using the Moon geocentric declination will not make much different ?  
> **username_3**: It sounds like you're using the wrong terms, what it sounds like you're looking for is the Parallactic Angle, the the first answer username_2 gave shows how to compute that.  The "phase angle" is quite different, and more akin to describing "first quarter", "full", etc. which does not change with a person's position on Earth.  

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