<p>I created this solar system model using POV-Ray:</p>

<p><a href="https://i.sstatic.net/fdXpK.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fdXpK.jpg" alt="enter image description here"></a></p>

<p>by following these instructions:</p>

<p><a href="https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf" rel="nofollow noreferrer">https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf</a></p>

<p>The next thing I want to do is orient/rotate each globe correctly according to the time of day, time of year, obliqueness, position in its orbit, etc. but cannot find any instructions on the JPL website. How can I go about completing this task? Thanks.</p>

<p><strong>Part Two</strong></p>

<p>[deleted]</p>

<p><strong>Part Three</strong></p>

<p>So, <em>&alpha;</em> (right ascension), <em>&delta;</em> (declination) and <em>W</em> are Euler rotation angles. But what are the starting conditions before applying these rotations? Should the North Pole of the planet be aligned with the z-axis? Should the plane formed by the prime meridian be perpendicular to the y-axis?</p>

<p>Also, which axes do I rotate around, and in what order? I am guessing <em>&delta;</em> should be rotated first around the y-axis, then <em>&alpha;</em> around the z-axis. But <em>W</em> also looks like it should go around the z-axis. I am confused.</p>

<p><strong>Part Four</strong></p>

<p>I found another PDF document which on page 27 gives an equation for <em>&delta;</em>, <em>&alpha;</em> and <em>W</em>. (Not sure how to reproduce it here.)</p>

<p><a href="https://depositonce.tu-berlin.de/bitstream/11303/6237/4/burmeister_steffi.pdf" rel="nofollow noreferrer">https://depositonce.tu-berlin.de/bitstream/11303/6237/4/burmeister_steffi.pdf</a></p>

<p>I <em>think</em> that according to that PDF file I need to rotate around the z-axis by W, around the x-axis by (90-&delta;), and around the z-axis again by (90+&alpha;), in that order. Lastly, an additional rotation (around the x-axis?) by 23.43928 degrees must be done to get the body out of the ICRF frame and into the ecliptic frame.</p>

<p>But I still don't know the starting conditions. I.e. before applying the transformations, should the globe's North Pole point upward? Should the intersection of the Prime Meridian and Equator lie along the x-axis? Or, am I totally wrong, and should I perform the inverse matrix calculations instead? So far I have not gotten results that match what I see in Celestia for the same Julian Date.</p>

<p><strong>Part Five</strong></p>

<p>In some instances I am able to get "close" results using the above method. In others not. For instance, Mars, Saturn, Uranus and Neptune are "close" to correct. (At least, the poles - the blue arrows - are pointing in the same directions.) The Earth is not.</p>

<p><a href="https://i.sstatic.net/Zk1M6.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Zk1M6.jpg" alt="enter image description here"></a>
<a href="https://i.sstatic.net/4oFkZ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/4oFkZ.png" alt="enter image description here"></a>
<a href="https://i.sstatic.net/oDgzK.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/oDgzK.jpg" alt="enter image description here"></a>
<a href="https://i.sstatic.net/zVepR.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/zVepR.jpg" alt="enter image description here"></a>
<a href="https://i.sstatic.net/TN8xc.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/TN8xc.jpg" alt="enter image description here"></a></p>

<p>The <em>correct</em> results are the ones in the larger Celestia program window. My current POV-Ray results are in the smaller window to the left. The dark arrows indicate the parent (ecliptic) reference frame. The bright arrows indicate the body reference frame. The view in all images is from the top down on to the ecliptic plane.</p>

CC BY-SA 4.0
2018-09-20T18:18:48.200Z
That document has a lot of useful tables, but I am not sure in what order and manner to use them. There are not step-by-step instructions like the orbital elements document I linked to.
posfan12
CC BY-SA 4.0
2018-09-20T20:06:43.460Z
Can you recommend some good keywords to continue my search? I am only getting results that are indirectly related.
posfan12
CC BY-SA 4.0
2018-09-20T23:54:09.167Z
I found that "rotational parameters" (must be in quotes!) got some better results. I'm still confused about how (and when) to change back and forth between ecliptic coordinates (in my first image above), J2000 frame (in my second image above), "body-fixed reference frame", etc
posfan12
CC BY-SA 4.0
2018-09-23T07:28:33.613Z
Use [SPICE](https://naif.jpl.nasa.gov/naif/toolkit.html). It has [planetary constant kernels](https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/individual_docs/19_pck.pdf) that describe the orientation of the planets, several moons, and a few asteroids with respect to the ICRF (or J2000; SPICE ignores the very small sub arc second difference between ICRF and J2000) as functions of time.
David Hammen
CC BY-SA 4.0
2018-09-26T17:52:50.587Z
I would need to rewrite all those (many megabytes) scripts in POV-Ray SDL. A noble effort, but not one I'm willing to make at this time.
posfan12
CC BY-SA 4.0
2018-10-14T22:37:03.187Z
Thanks. The source code is located here: http://lib.povray.org/searchcollection/index2.php?objectName=SolarSystemOrrery&contributorTag=SharkD
posfan12
<orbit><solar-system><rotation>
Modeling planet rotations (time of day, obliqueness, etc.)
posfan12
# Modeling planet rotations (time of day, obliqueness, etc.)

(Asked by: username_0 on 2018-09-19)

I created this solar system model using POV-Ray:

[![enter image description here](https://i.sstatic.net/fdXpK.jpg)](https://i.sstatic.net/fdXpK.jpg)

by following these instructions:

<https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf>

The next thing I want to do is orient/rotate each globe correctly according to the time of day, time of year, obliqueness, position in its orbit, etc. but cannot find any instructions on the JPL website. How can I go about completing this task? Thanks.

**Part Two**

[deleted]

**Part Three**

So, *α* (right ascension), *δ* (declination) and *W* are Euler rotation angles. But what are the starting conditions before applying these rotations? Should the North Pole of the planet be aligned with the z-axis? Should the plane formed by the prime meridian be perpendicular to the y-axis?

Also, which axes do I rotate around, and in what order? I am guessing *δ* should be rotated first around the y-axis, then *α* around the z-axis. But *W* also looks like it should go around the z-axis. I am confused.

**Part Four**

I found another PDF document which on page 27 gives an equation for *δ*, *α* and *W*. (Not sure how to reproduce it here.)

<https://depositonce.tu-berlin.de/bitstream/11303/6237/4/burmeister_steffi.pdf>

I *think* that according to that PDF file I need to rotate around the z-axis by W, around the x-axis by (90-δ), and around the z-axis again by (90+α), in that order. Lastly, an additional rotation (around the x-axis?) by 23.43928 degrees must be done to get the body out of the ICRF frame and into the ecliptic frame.

But I still don't know the starting conditions. I.e. before applying the transformations, should the globe's North Pole point upward? Should the intersection of the Prime Meridian and Equator lie along the x-axis? Or, am I totally wrong, and should I perform the inverse matrix calculations instead? So far I have not gotten results that match what I see in Celestia for the same Julian Date.

**Part Five**

In some instances I am able to get "close" results using the above method. In others not. For instance, Mars, Saturn, Uranus and Neptune are "close" to correct. (At least, the poles - the blue arrows - are pointing in the same directions.) The Earth is not.

[![enter image description here](https://i.sstatic.net/Zk1M6.jpg)](https://i.sstatic.net/Zk1M6.jpg)
[![enter image description here](https://i.sstatic.net/4oFkZ.png)](https://i.sstatic.net/4oFkZ.png)
[![enter image description here](https://i.sstatic.net/oDgzK.jpg)](https://i.sstatic.net/oDgzK.jpg)
[![enter image description here](https://i.sstatic.net/zVepR.jpg)](https://i.sstatic.net/zVepR.jpg)
[![enter image description here](https://i.sstatic.net/TN8xc.jpg)](https://i.sstatic.net/TN8xc.jpg)

The *correct* results are the ones in the larger Celestia program window. My current POV-Ray results are in the smaller window to the left. The dark arrows indicate the parent (ecliptic) reference frame. The bright arrows indicate the body reference frame. The view in all images is from the top down on to the ecliptic plane.

**Tags:** orbit, solar-system, rotation
> **Comments:**
> **username_0**: That document has a lot of useful tables, but I am not sure in what order and manner to use them. There are not step-by-step instructions like the orbital elements document I linked to.  
> **username_0**: Can you recommend some good keywords to continue my search? I am only getting results that are indirectly related.  
> **username_0**: I found that "rotational parameters" (must be in quotes!) got some better results. I'm still confused about how (and when) to change back and forth between ecliptic coordinates (in my first image above), J2000 frame (in my second image above), "body-fixed reference frame", etc  
> **username_1**: Use [SPICE](https://naif.jpl.nasa.gov/naif/toolkit.html). It has [planetary constant kernels](https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/individual_docs/19_pck.pdf) that describe the orientation of the planets, several moons, and a few asteroids with respect to the ICRF (or J2000; SPICE ignores the very small sub arc second difference between ICRF and J2000) as functions of time.  
> **username_0**: I would need to rewrite all those (many megabytes) scripts in POV-Ray SDL. A noble effort, but not one I'm willing to make at this time.  
> **username_0**: Thanks. The source code is located here: http://lib.povray.org/searchcollection/index2.php?objectName=SolarSystemOrrery&contributorTag=SharkD  

---

## 0 answers

