# How to calculate the orientation of planets at current epoch

For an application I am working on I am creating a simulation of the solar system. In this simulation, a user needs to be able to 'move' to any position on any planet, and have the sky be accurately simulated around him.

Using the examples & calculations provided at http://stjarnhimlen.se/comp/ppcomp.html and the data provided at https://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf I am able to compute the POSITIONS of the planets at any date, however, what I am still looking for is the ORIENTATION of these planets at that position (i.e. which way is Long 0 Lat 0 pointing, and which way is Long 0 Lat 90 pointing (with respect to the vernal equinox)). I need this orientation in order to figure out what the rotation (quaternion) of this planet needs to be..

I have been looking around, but have so far not been able to find a source for any kind of information like this. The closest I've found was https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies , but that only gives me an up-vector, not a 'forward' (and is for J2000, not the current Epoch).

Can anyone be of assistance?

• There is no direct answer in this answer but somewhere in there is perhaps at least a start. Somewhere in the JPL spice kernels there are models for the rotations of the planets and their latitude/longitude systems. I don't know exactly where though.
– uhoh
Jun 17 '19 at 14:20
• If I'm not mistaken, because the planets rotate around their polar norths, the 'up'-vector for this planet (Zenith at Long 0 Lat 90) will always be (approximately) the Ra/Dec from en.wikipedia.org/wiki/Poles_of_astronomical_bodies (at any epoch). However, I haven't the faintest idea as to how to calculate the Zenith for Long 0 Lat 0 (the 'forward') Jun 17 '19 at 14:40
• That's certainly the right idea. For short periods of time in the future/past that should work pretty well for major bodies, but I just don't know about Earth's Moon or Mercury. The hard part is the part you mention at the end. There are ephemerides for each of the planets, I think someone may answer with a source. It's pretty amazing for the gas giants to have fixed longitudes but I think they've worked something out even for them. I'm sorry I can't help further though, let's wait and see what other answers appear.
– uhoh
Jun 17 '19 at 16:55
• Jun 18 '19 at 1:50
• – user21
Jun 24 '19 at 2:53

## 1 Answer

The IAU WGCCRE (Working Group on Cartographic Coordinates and Rotational Elements) seem to be the authorities on this. Table 1 in their 2015 report gives the following information for the major planets:

• α0, δ0 are the ICRF right ascension and declination of the planet's north pole. If the planet's axial precession is known, these are expressed in terms of T, the number of Julian centuries since epoch J2000.0.

• W is the rotation angle eastward from reference point Q to the planet's prime meridian at time d, where Q is the intersection of the planet's equator and the ICRF equator at RA α0 + 90°, Dec 0°, and d is the number of days since epoch J2000.0.

They define a planet's north pole as the one pointing north of the solar system's invariable plane. This means that W decreases with time for Venus and Uranus.

Their figure 1 appears to indicate Q's RA as 90° - α0, in conflict with the text. I believe the text is correct.

When you are ready to validate your calculations, the S&T Mars Profiler shows which side of Mars faces Earth at a given time.

• I was able to use these to set all planets, except for the Earth & Moon. For the Earth, the IAU refers to the IERS, but I'm not sure how to use that data (to get the ecliptic position/orientation of the earth) Jun 19 '19 at 15:58
• IERS documents are really hard to read! Jun 19 '19 at 21:18
• Ended up finding the line: 'Previous reports included the rotation and pole position for the ME system using closed formulae in Table 2. We are not continuing to provide those formulae as they are only accurate to approximately 150 m' in the 2015 report.. As 150m is fine for my purposes, I just grabbed the earth & moon-ephemerides from the 2009 report (which can be found at astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/… ) Jun 20 '19 at 14:14