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I created this solar system model using POV-Ray:

enter image description here

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

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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 enter image description here enter image description here enter image description here enter image description here

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.

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    $\begingroup$ astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/… may or may not be helpful $\endgroup$
    – user21
    Commented Sep 19, 2018 at 20:58
  • $\begingroup$ 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. $\endgroup$
    – posfan12
    Commented Sep 20, 2018 at 18:18
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    $\begingroup$ I haven't really looked deeply into that document, but it should tell you how the "0 degree longitude" line is defined for each entity, and a reference time when that 0 degree longitude pointed towards the vernal equinox. That should be enough information to compute the orientation at any time. $\endgroup$
    – user21
    Commented Sep 20, 2018 at 19:07
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    $\begingroup$ "orientation" is the only one I can think of. You might also see how stellarium, celestia, skyfield, and other astronomy programs/libraries handle this issue. I want to say it's a relatively new field, but I could be wrong about that. $\endgroup$
    – user21
    Commented Sep 20, 2018 at 20:30
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    $\begingroup$ Things like skyandtelescope.com/observing/interactive-sky-watching-tools/… may help too. Questions like "which side of x is visible" may help. For our moon, this has been computed to great accuracy, not sure about other planets/moons $\endgroup$
    – user21
    Commented Sep 20, 2018 at 20:39

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