<p>I'm trying to make a game with high accuracy moon position so I followed some equations on <a href="http://www.geoastro.de/elevazmoon/basics/meeus.htm#jd" rel="nofollow noreferrer">geoastro.de Basics of Positional Astronomy and Ephemerides</a> and with some help from the questions answers, I get the same result which they explained in <a href="http://www.geoastro.de/elevazmoon/basics/index.htm" rel="nofollow noreferrer">the example</a>.</p>
<p>but there is problem that is I calculate <strong>declination</strong> and <strong>right ascension</strong> by Pre-calculated values of <strong>ecliptic latitude and longitude</strong> and they didn't explain their equations or any thing about them.</p>
<p>I tried to search and ask, but I did not find anything, or I found very complex equations, and I don't think I will need this complexity.</p>
<p>So is there equation or resource that can help me to calculate <strong>declination</strong> and <strong>right ascension</strong> with limited information (<strong>Julian day</strong> and <strong>(T) number of Julian centuries since 2000/01/01 at 12 UT</strong>) or to calculate <strong>ecliptic latitude and longitude</strong> without very complex equations?</p>
<p><strong>Equations of the moon altitude and azimuth:</strong></p>
<pre><code>1- Julian day = (365.25 * year) + (30.6001 * (month + 1)) - 15 + 1720996.5 + day + hour/24.0


2- T (number of Julian centuries since 2000/01/01 at 12 UT) = (JD - 2451545.0) / 36525.0


3- eps (obliquity of the ecliptic) = 23.0 + 26.0 / 60.0 + 21.448 / 3600.0 - (46.8150 * T + 0.00059 * T * T - 0.001813 * T * T * T) / 3600

Ecliptic latitude (B) = -1.87° (pre-calculated value)
Ecliptic longitude (L) = 131.52° (pre-calculated value)

4- delta (declination) = (180/PI) * arcsin[sin(eps) * cos(Ecliptic latitude) * sin(Ecliptic longitude) + cos(eps) * sin(Ecliptic latitude)]

5- RA (right ascension) = (180/PI) * arctan[(sin(Ecliptic longitude) * cos(eps) - tan(Ecliptic latitude) * sin(eps)) / cos(Ecliptic longitude)]
if arctan result is lower than zero add (PI) to arctan.


6- theta0 (sidereal time (degrees) at Greenwich) = 280.46061837 + 360.98564736629 * (JD - 2451545.0) + 0.000387933 * T * T - T * T * T / 38710000.0


7- theta (local sidereal time at longitude 10° E) = theta0 + longitude (eastern longitudes positive, western negative).


8- tau (local hour angle) = theta - RA


9- altitude = (180/PI) * arcsin[sin(latitude) * sin(delta) + cos(latitude) * cos(delta) * cos(tau)]


10- azimuth = (180/PI) * arctan2[- sin(tau) / (cos(latitude) * tan(delta) - sin(latitude) * cos(tau))]
</code></pre>
<p>Thanks for reading.</p>

CC BY-SA 4.0
2024-06-10T13:06:35.583Z
No but it helped me to get the right way to calculate alt & az and  as I mentioned **"and with some help from the questions, I get the same result which they explained in the example."** But this time I have a problem with **declination** and **right ascension** and **ecliptic latitude and longitude**.
Ahmed Dyaa
CC BY-SA 4.0
2024-06-10T14:23:37.900Z
If you don't need high accuracy, why not just pre-generate the positions of the moon for say, every week for 100 years (using JPL Horizons), and linearly interpolate positions between the two?  High accuracy algorithms are going to have a lot of terms.
Greg Miller
CC BY-SA 4.0
2024-06-10T16:02:54.097Z
I don't understand the question. lots of that is constants, like obliquity of the ecliptic. The others are either precalculated or a function of time, which you know. You say they give the right answer.  Do you want to know how the equations are derived?
Miss Understands
CC BY-SA 4.0
2024-06-10T16:39:21.977Z
They used in example (that I put it's link) a pre-calculated values for **ecliptic latitude and longitude** to calculate **declination** and **right ascension**, **what I want** in my game is to calculate the position of the moon at specific date and time to do that, I **must** have equation for **ecliptic latitude and longitude** to calculate them at the specific date and time that I want **OR** to calculate**declination** and **right ascension** without **ecliptic latitude and longitude**, because I don't have them equation.
Ahmed Dyaa
CC BY-SA 4.0
2024-06-11T09:53:34.380Z
I *think* you are looking for simple analytical equations to predict where the Moon is but unfortunately you're going to be out of luck - the motion of the Moon is sufficiently complex that it has defied many attempts to make a simple, accurate theory. There are relatively simple [low precision methods](http://stjarnhimlen.se/comp/tutorial.html#7) or much more complex high precision methods with hundreds of terms; you will need to decide what precision is acceptable for your use. Take a look at the link above which gives ecliptic lat & long and the sec. 8 after it and see if it meets the needs
astrosnapper
CC BY-SA 4.0
2024-07-02T05:28:21.780Z
I tried to find out any thing but I failed. is there a formulas for **declination** and **right ascension** without **ecliptic latitude and longitude**? or is it impossible?.
Ahmed Dyaa
CC BY-SA 4.0
2024-07-02T15:02:50.637Z
Did you look at Paul Schlyter's site, http://stjarnhimlen.se/ that astrosnapper linked?
PM 2Ring
<the-moon><mathematics><declination><right-ascension><algorithm>
calculate declination and right ascension with limited information
Ahmed Dyaa
# calculate declination and right ascension with limited information

(Asked by: username_0 on 2024-06-10)

I'm trying to make a game with high accuracy moon position so I followed some equations on [geoastro.de Basics of Positional Astronomy and Ephemerides](http://www.geoastro.de/elevazmoon/basics/meeus.htm#jd) and with some help from the questions answers, I get the same result which they explained in [the example](http://www.geoastro.de/elevazmoon/basics/index.htm).

but there is problem that is I calculate **declination** and **right ascension** by Pre-calculated values of **ecliptic latitude and longitude** and they didn't explain their equations or any thing about them.

I tried to search and ask, but I did not find anything, or I found very complex equations, and I don't think I will need this complexity.

So is there equation or resource that can help me to calculate **declination** and **right ascension** with limited information (**Julian day** and **(T) number of Julian centuries since 2000/01/01 at 12 UT**) or to calculate **ecliptic latitude and longitude** without very complex equations?

**Equations of the moon altitude and azimuth:**

```
1- Julian day = (365.25 * year) + (30.6001 * (month + 1)) - 15 + 1720996.5 + day + hour/24.0

2- T (number of Julian centuries since 2000/01/01 at 12 UT) = (JD - 2451545.0) / 36525.0

3- eps (obliquity of the ecliptic) = 23.0 + 26.0 / 60.0 + 21.448 / 3600.0 - (46.8150 * T + 0.00059 * T * T - 0.001813 * T * T * T) / 3600

Ecliptic latitude (B) = -1.87° (pre-calculated value)
Ecliptic longitude (L) = 131.52° (pre-calculated value)

4- delta (declination) = (180/PI) * arcsin[sin(eps) * cos(Ecliptic latitude) * sin(Ecliptic longitude) + cos(eps) * sin(Ecliptic latitude)]

5- RA (right ascension) = (180/PI) * arctan[(sin(Ecliptic longitude) * cos(eps) - tan(Ecliptic latitude) * sin(eps)) / cos(Ecliptic longitude)]
if arctan result is lower than zero add (PI) to arctan.

6- theta0 (sidereal time (degrees) at Greenwich) = 280.46061837 + 360.98564736629 * (JD - 2451545.0) + 0.000387933 * T * T - T * T * T / 38710000.0

7- theta (local sidereal time at longitude 10° E) = theta0 + longitude (eastern longitudes positive, western negative).

8- tau (local hour angle) = theta - RA

9- altitude = (180/PI) * arcsin[sin(latitude) * sin(delta) + cos(latitude) * cos(delta) * cos(tau)]

10- azimuth = (180/PI) * arctan2[- sin(tau) / (cos(latitude) * tan(delta) - sin(latitude) * cos(tau))]

```

Thanks for reading.

**Tags:** the-moon, mathematics, declination, right-ascension, algorithm

> **Comments:**
> **username_0**: No but it helped me to get the right way to calculate alt & az and  as I mentioned **"and with some help from the questions, I get the same result which they explained in the example."** But this time I have a problem with **declination** and **right ascension** and **ecliptic latitude and longitude**.  
> **username_1**: If you don't need high accuracy, why not just pre-generate the positions of the moon for say, every week for 100 years (using JPL Horizons), and linearly interpolate positions between the two?  High accuracy algorithms are going to have a lot of terms.  
> **username_2**: I don't understand the question. lots of that is constants, like obliquity of the ecliptic. The others are either precalculated or a function of time, which you know. You say they give the right answer.  Do you want to know how the equations are derived?  
> **username_0**: They used in example (that I put it's link) a pre-calculated values for **ecliptic latitude and longitude** to calculate **declination** and **right ascension**, **what I want** in my game is to calculate the position of the moon at specific date and time to do that, I **must** have equation for **ecliptic latitude and longitude** to calculate them at the specific date and time that I want **OR** to calculate**declination** and **right ascension** without **ecliptic latitude and longitude**, because I don't have them equation.  
> **username_3**: I *think* you are looking for simple analytical equations to predict where the Moon is but unfortunately you're going to be out of luck - the motion of the Moon is sufficiently complex that it has defied many attempts to make a simple, accurate theory. There are relatively simple [low precision methods](http://stjarnhimlen.se/comp/tutorial.html#7) or much more complex high precision methods with hundreds of terms; you will need to decide what precision is acceptable for your use. Take a look at the link above which gives ecliptic lat & long and the sec. 8 after it and see if it meets the needs  
> **username_0**: I tried to find out any thing but I failed. is there a formulas for **declination** and **right ascension** without **ecliptic latitude and longitude**? or is it impossible?.  
> **username_4**: Did you look at Paul Schlyter's site, http://stjarnhimlen.se/ that username_3 linked?  

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## 0 answers

